BARYONS 2002
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BARYONS 2002 Proceedings of the 9th International Conference on the Structure of Baryons
Jefferson Lab
Newport News, Virginia, USA March 3 - 8,2002
Editors
Carl E. Carlson College of William & Mary, Williamsburg, Virginia
Bernhard A. Mecking Jefferson Lab, Newport News, Virginia
vp p r l d Scientific
ew Jersey London Singapore Hong Kong
Published by
World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224
USA ofice: Suite 202,1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-PublicationData A catalogue record for this book is available from the British Library
BARYONS 2002 Proceedings of the 9th International Conference on the Structure of Baryons
Copyright 0 2003 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereoJ may not be reproduced in any form or by any means, electronic or mechanical. including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.
ISBN 981-238-409-X
Printed in Singapore by World Scientific Printers (S)Pte Ltd
The Baryons 2002 Conference was dedicated to the memory of Nathan lsgur as a tribute to his contributionsto Nuclear and Particle Physics and especially to the Baryons Community
V
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Preface This volume presents the proceedings of the g t h International Conference on the Structure of Baryons, or more compactly, Baryons 2002, which was held at Jefferson Lab, Newport News, Virginia, from March 3 to 8, 2002. The conference discussed the latest experimental results and theoretical developments in the area of three-quark systems. The last Baryons Conference was held over three years ago, so there was great interest in the field, and much progress was reported. Over 200 participants attended the conference. The stimulating atmosphere that prevailed during the conference was made possible by the enthusiastic involvement of the participants. We particularly want to thank the speakers and the organizers of the parallel sessions for their hard work. We greatly appreciate the advice of the International Advisory Committee, and the work done by the Local Organizing Committee. We would like t o thank Jefferson Lab and the Department of Energy for financial support. Allow us t o give special thanks to the Jefferson Lab Conference Services group and t o the Physics Division secretarial staff. Without their efforts the conference would not have been possible. We would also like to thank Lori Powell for the front cover design. Carl E. Carlson John J. Doming0 Bernhard A. Mecking November 2002
vii
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INTERNATIONAL ADVISORY COMMITTEE University of Massachusetts Los Alamos National Lab University of Illinois University of Maryland NIKHEF TRIUMF Rutherford Lab
Ray Arnold Peter Barnes Doug Beck Betsy Beise J o van den Brand Doug Bryman Frank Close Michael Danilov Enzo DeSanctis Dieter Drechsel Ralph Eichler Brad Filippone Don Geesaman Mauro Giannini Franc0 Iachello Ken’ichi Imai Elizabeth Jenkins Gabriel Karl Jirohta Kasagi Thomas Kirk Robert Klanner Juergen Koerner Sven Kullander Jean-Marc Laget John McClelland Ulf Meissner Volker Metag Chris Michael Richard Milner Piet Mulders Takashi Nakano Dan-Olof Riska Klaus Rith Andrew Sandorfi Carlo Schaerf Berthold Schoch Hans Stroeher
ITEP INFN Frascati Universitat Mainz Paul Scherrer Institute Caltech Argonne National Lab INFN, Genova Yale University Kyoto University University of California San Diego University of Guelph Tohoku University Brookhaven National Lab DESY Universitat Mainz Uppsala University DAPNIA Saclay Los Alamos National Lab Universitat Graz Universitat Giessen University of Liverpool MIT Vrije Universiteit, Amsterdam RCNP, Osaka University of Helsingfors Universitat Erlangen Brookhaven National Lab University of Rome Universitat Bonn FZ Juelich
ix
INTERNATIONAL ADVISORY COMMITTEE (continued) Anthony Thomas Steven Vigdor Thomas Walcher Wolfram Weise
University of Adelaide Indiana University Universitat Mainz Technische Universitat Munchen
LOCAL ORGANIZING COMMITTEE Bernhard Mecking (chair) John Doming0 (co-chair) Keith Baker Volker Burkert Carl Carlson Kees de Jager Latifa Elouadrhiri Rolf Ent Jose Goity Keith Griffioen Sebastian Kuhn Anatoly Radyushkin David Richards Winston Roberts
JLab JLab JLab/Hampton University JLab College of William & Mary JLab JLab/Christopher Newport University JLab JLab/Hampton University College of William & Mary Old Dominion University JLab/Old Dominion University JLab/Old Dominion University JLab/Old Dominion University
X
CONTENTS PLENARY SESSION PRESENTATIONS Successes and Open Issues in Baryon Physics A . Thomas Baryon Spectroscopy in the Quark Model
3
17
S. Capstick Electroexcitation of Nucleon Resonances
29
V. Burkert Baryon Spectroscopy on the Lattice R. Edwards
43
Heavy Quark Physics on the Lattice C. Davies
53
Hadrons in the Nuclear Medium-Role of Light Front Nuclear Theory G. Miller
65
Polarized Structure Functions
78
G. van der Steenhoven Proton Structure Results from the HERA Collider R. Yoshida
90
Baryon Chiral Dynamics T. Becher
102
Electromagnetic Tests of Chiral Symmetry H. Merkel
115
Hadron Structure from Lattice QCD G. Schierhob
126
Xi
xii
Photoexcitation of N * Resonances A. d’Angelo et al.
140
Instantons and Baryon Dynamics D. Diakonov
153
The Strangeness Contribution to the Form Factors of the Nucleon F. Maas
165
Electromagnetic Production of Pions in the Resonance Region - Theoretical Aspects T. Sato
178
Hadronic Production of Baryon Resonances M. Sadler
189
Baryon Resonances and Strong QCD E. Klempt
198
Spin Structure Functions in the Resonance Region R. De Vita
210
Quark-Hadron Duality S. Jeschonnek and J. W. van Orden
222
First Results from SPRING-8 T. Nakano
234
Hybrid Baryons P. Page
243
Nucleon Electromagnetic Form Factors E. Brash
256
Virtual Compton Scattering H. Fonvieille
268
...
Xlll
Generalized Parton Distributions
280
M. Diehl 290
Baryons 2002: Outlook
W. Weise
SESSION ON STRUCTURE FUNCTIONS AND FORM FACTORS The Q2Dependence of Polarized Structure Functions T. A . Forest
303
Measurement of R = ( T L / ( T T in the Nucleon Resonance Region M. E. Christy
307
The Collins Fragmentation Function in Hard Scattering Processes A . Metz, R. Kundu, A . Bacchetta and P. J. Mulders
31 1
Leading and Higher Twists in the Proton Polarized Structure Function gy at Large Bjorken-x S. Simula, M. Osipenko, G. Ricco and M. Taiuti
315
Single-Spin Asymmetries at CLAS H.Avalcian
319
Study of the A(1232) Using Double-Polarization Asymmetries
323
J. Kuhn and A . Biselli CLAS Measurement of
Electroproduction Structure Functions
327
L. C. Smith Kaon Electroproduction at Large Momentum Transfer P. Markowitz
332
xiv
Are Recoil Polarization Measurements of GP,/GP, Consistent with Rosenbluth Separation Data? J. Arrington
338
Effect of Recent R, and R, Measurements on Extended Gari-Kriimpelmann Model Fits to Nucleon Electromagnetic Form Factors E. L. Lomon
342
Measurement of the Electric Form Factor of the Neutron at Q2 = 0.6 - 0.8 (GeV/c)2 M. Seimetz
346
Neutron Electric Form Factor via Recoil Polarimetry R. Madey et al.
350
The Go Experiment: Measurements of the Strange Form Factors of the Proton J. Roche
355
The Nucleon Form Factors in the Canonically Quantized Skyrme Model E. NorvaiSas, A . Acus and D. 0. Riska
359
Soft Contribution to the Nucleon Electromagnetic Form Factors R. J. Fries, V. M. Braun, A . Lenz, N. Mahnke and E. Stein
Electroweak Properties of the Nucleon in a Chiral Constituent Quark Model M. Radici, S. BOB, L. Giozman, W. Plessas, R. F. Wagenbrunn and W. Klink Nucleon Hologram with Exclusive Leptoproduction A. V. Belitsky and D. Muller Deeply Virtual Compton Scattering at Jefferson Lab, Results and Prospects L. Elouadrhiri
363
367
371
384
xv
Twist-3 Effects in Deeply Virtual Compton Scattering Made Simple C. Weiss
388
Measurements of Hard Exclusive Reactions with a Recoil Detector at HERMES R. Kaiser
392
Dispersion Relation Formalism for Virtual Cornpton Scattering off the Proton
396
B. Pasquini, D. Drechsel, M. Gorchtein, A . Metz and M. Vanderhaeghen
SESSION ON BARYON STRUCTURE AND SPECTROSCOPY Meson-Photoproduction with the Crystal-Barrel Detector at ELSA M. Ostrick
403
K-Meson Production Studies with the TOF-Spectrometer at COSY W. Eyrich
409
First Simultaneous Measurements of the T L and TL' Structure Functions in the y*p -+ A Reaction A . Bernstein
413
Photoproduction of Resonances in a Relativistic Quark Pair Creation Model
417
F. Cano, P. Gonzdez, 5'. Noguera and B. Desplanques Relationship of the 3Po Decay Model to Other Strong Decay Models B. Desplanques, A . Nicolet and L. Theussl
42 1
Do We See the Chiral Symmetry Restoration in Baryon Spectrum? L. Ya. Glozman and T. D. Cohen
425
xvi
Virtual Compton Scattering: Results from Jefferson Lab
430
L. Van Hoorebeke Virtual Compton Scattering and Neutral Pion Electro-Production from the Proton in the Nucleon Resonance Region L. Todor
434
The Hypercentral Constituent Quark Model M. M. Giannini, E. Santopinto and A . Vassallo
438
New Search for the Neutron Electric Dipole Moment P. D. Barnes
443
qq Loop Effects on Baryon Masses
448
D. Morel and S. Capstick Learning from Dispersive Effects in the Nucleon Polarisabilities
452
H. W. Grieflhammer Dynamical Baryon Resonances with Chiral Lagrangians
456
C. Bennhold, A . Ramos and E. Oset Pion Electroproduction in the Second Resonance Region Using CLAS H. Egiyan and I. Aznauryan
460
Electron Beam Asymmetry Measurements from Exclusive no Electroproduction in the A( 1232) Resonance Region K. Joo
464
r N N * (1440) and a N N *(1440) Coupling Constants from a Microscopic N N -+ NN*(1440) Potential P. Gonzdez, B. Julici-Diaz, A . Valcarce and F. Fernbndez
468
q Electro-Production At and Above the S11 (1535) Resonance Region with CLAS
H. Denizla
472
xvii r]
Photoproduction from the Proton using CLAS E. A . Pasyuk, M. R. Dugger and B. G. Ritchie
Why is the Wavelet Analysis Useful in Physics of Resonances? Example of p' and w' States V. K . Henner, P. G. Frick and T. S. Belozerova
L = 1 Baryon Masses in the 1/Nc Expansion C. L. Schat Search for Resonance Contributions in Multi Pion Electroproduction with CLAS F. Klein, V. Burkert, H. Funsten and M. Ripani
476
480
485
489
QCD Confinement and Missing Baryons P. Gonzdez, H. Garcilazo, J. Vijande and A . Valcarce
494
Photoproduction of the E Hyperons J. W. Price, J. Ducote and B. M. K. Neflcens
498
Open Strangeness Production in CLAS G. Niculescu
502
K+ Photoproduction at LEPS/SPring-8 R. G. T. Zegers
506
Kaon Photoproduction: Background Contributions and Missing Resonances S. Janssen and J. Ryckebusch
510
Dynamical Description of Nucleon Compton Scattering at Low and Intermediate Energies: From Polarisabilities to Sum Rules S. Kondratyuk and 0. Scholten
514
xviii
SESSION ON HADRONS IN THE NUCLEAR MEDIUM Nuclear Shadowing and In-Medium Properties of the po T. Falter, S. Leupold and U.Mosel Scalar- and Vector-Meson Production in Hadron-Nucleus Reactions W. Cussing Helicity Signatures in Subthreshold p" Production on Nuclei G. M. Huber From Meson- and Photon-Nucleon Scattering to Vector Mesons in Nuclear Matter M. F. M. Lutz, Gy. Wolf and B. Friman
521
525
529
533
Polarization Transfer in the 4He(2,e' $ ) 3 H Reaction S. Strauch
537
s11(1535) Resonance in Nuclei Studied with the C(y,v) Reaction H. Yamazaki et al.
541
Double-Pion Production in y J. G. Messchendorp
+ A Reactions
Quark-Hadron Duality in Inclusive Electron-Nucleus Scattering I. Niculescu, J. Arrington, J. Crowder, R. Ent and C. Keppel Neutron Structure Function and Inclusive DIS From 3H and 3He Targets at Large Bjorken-a: M. M. Sargsian, S. Simula and M. I. Strikman Hadron Formation in Nuclei in Deep-Inelastic Lepton Scattering E. Garutti
545
550
554
558
xix
Nuclear Transparency from Quasielastic A ( e ,e’p) Reactions up to Q2= 8.1 (GeV/c)2 K. Garrow
562
Nucleon Momentum Distributions From a Modified Scaling Analysis of Inclusive Electron-Nucleus Scattering J. Arrington
567
Medium Effects in A(;, e’ ’P’) Reactions at High Q2 D. Debruyne and J. Ryckebusch Study of Nucleon Short Range Correlations in A ( e ,e‘) Reaction at zg > 1 K. Egiyan, H. Bagdasarian and N . Dashyan
571
575
N N Correlations Measured in 3He(e,e‘pp)n R. A. Niyazov and L. B. Weinstein
581
Electroproduction of Strangeness on Light Nuclei F. Dohrmann et al.
585
Hypernuclear Spectroscopy of i 2 B in the ( e le’K’) J. Reinhold
Reaction
589
SESSION ON CHIRAL PHYSICS Goldstone Boson Dynamics: Introduction to the Chiral Physics Session A. M. Bernstein
595
7’Electroproduction Off Nucleons B. Borasoy
599
A Unified Chiral Approach to Meson-Nucleon Interaction E. E. Kolomeitsev and M. F. M. Lutz
603
xx
Measurement of the Weak Pion-Nucleon Coupling Constant, H:, from Backward Pion Photo-Production Near Threshold on the Proton R . Suleiman
yy to NLO in ChPT J. L. Goity
607
xo -+
61 1
The Dependence of the “Experimental” Pion Nucleon Sigma Term on Higher Partial Waves J . Stahov
615
First Beam-Target Double-Polarization Measurements using Polarized HD at LEGS A . Lehmann et al.
619
SESSION ON LATTICE QCD AND HEAVY QUARKS Lattice Calculation of Baryon Masses Using the Clover Fermion Action D. G. Richards, M. Gockeler, P. E. L. Rakow, R. Horsley, C. M. Maynard, D. Pleiter and G. Schierholz Nucleon Magnetic Moments, Their Quark Mass Dependence and Lattice QCD Extrapolations
627
631
T. R. Hemmert and W. Weise Heavy Quark Spectrum from Anisotropic Lattices X . Liao and T. Manke The Doubly Heavy Baryons in the Nonperturbative QCD Approach I. M. Narodetskii and M. A . Trusov
635
639
xxi
Excited Baryons and Chiral Symmetry Breaking of QCD F. X. Lee
643
List of Participants
651
Author Index
669
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Plenary Session Presentations
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SUCCESSES AND OPEN ISSUES IN BARYON PHYSICS A. W. THOMAS Special Research Centre for the Subatomic Structure of Matter and Department of Physics and Mathematical Physics Uniuersity of Adelaide, Adelaide S A 5005, Australia E-mail:
[email protected] We review some of the highlights from recent work concerning the structure of baryons. We concentrate especially on those developments where the interaction with lattice QCD has led to new insights.
1
Introduction
The study of baryon structure, both in vacuum and in a nuclear medium, is currently at a very exciting stage of development. New experimental capabilities at laboratories such as JLab, are extending our knowledge of nucleon form factors, free and bound (as well as transition form factors), into new kinematic domains and with unprecedented precision. We are beginning to see the development of phenomenologically meaningful, covariant models which can be extended to incorporate chiral symmetry. With the development of improved actions, faster computers and better implimentations of chiral symmetry, lattice QCD is beginning to deliver on its promise of new insights into baryon structure. Indeed, in combination with carefully controlled chiral extrapolation, one can expect to calculate properties of the low mass baryons quite accurately within a few years. One can also hope to address some key physics issues in baryon spectroscopy. The issue of possible changes of hadron properties in-medium has generated enormous theoretical and experimental interest. We briefly outline the role of changes of nucleon internal structure within relativistic mean field theory and report on what has the potential to be a very important development in this field, namely the recent determination of GEIGMfor a proton bound in 4He. In the context of understanding nuclear structure in terms of QCD, it is the first firm evidence for a change in the structure of a bound nucleon. After describing recent advances in linking lattice QCD to covariant models of hadron structure, we summarise the crucial issue of chiral extrapolation. The recent progress in this area underpins the prospect of calculating accurate hadron properties, at the physical quark mass, in just a few years. We close the discussion with an overview of the recent progress in hadron spectroscopy. Then we turn to the issue of changes in baryon properties in-medium.
3
4
2
Baryon Structure and Lattice QCD
The non-trivial nature of the QCD vacuum is illustrated by the fact that it For a purely gluonic version contains both quark and gluon condensates is of order -0.5 (GeV/fm)3. This of QCD the vacuum energy density, c,, is an order of magnitude larger than phenomenological estimates such as B in the MIT bag model. Clearly, either the popular idea of the perturbative vaciiiim being fully restored inside a hadron is incorrect or the situation is rather more complicated than commonly assumed. Although covariant models of baryon structure are very much in their infancy, substantial progress has been made in understanding the striicture of the low-lying pseudoscalar and vector mesons within a phenomenological implementation of the Dyson-Schwinger equations '. In addition, there have been some promising developments in the baryon sector based on the Faddeev equations '. Until now the phenomenological input has been chosen to reproduce some limited set of experimental data and then applied to other problems. However, the sophistication of modern lattice gauge theory is such that one can now begin t o check key parts of these covariant calculations against lattice simulations. The natural starting point for comparisons between covariant calculations and lattice simulations are the quark and gluon propagators. For example, there have been some preliminary studies of the quark propagator in Landau gauge. For Euclidean p 2 one can write the quark propagator as Z ( p 2 ) / ( i y , p , + M ( p 2 ) ) . The lattice simulations, so far been carried out with relatively large The current quark masses, show a clear enhancement in the infrared enhancement in the infrared region, leading t o a quark effective mass of order 300 MeV in the chiral limit, is clearly consistent with the general idea of the constituent quark model. This result not only provides a firm theoretical foundation for the concept within QCD, but it also indicates where the concept breaks down. It is clear that in processes involving significant momentum transfer it will be necessary t o go beyond the simple idea of a fixed mass and, indeed, a recent study of the nucleon electromagnetic form factors by Oettel and Alkofer finds considerable sensitivity t o the momentum dependence of the quark mass function '.
'.
516.
2.1
The role of Chiral Symmetry
A central problem in performing calculations a t realistic quark masses is the approximate chiral symmetry of QCD. Goldstone's theorem tells us that chiral symmetry is dynamically broken and that the non-perturbative vacuum is
5
'.
highly non-trivial, with massless Goldstone bosons in the limit m 4 0 For finite quark mass these bosons are the three charge states of the pion with a mass m: cx m . From the point of view of lattice simulations with dynamical quarks (i.e. unquenched) the main difficulty is that the time taken goes as m-3, or worse '. The state-of-the-art for hadron masyes is above 40 MeV. Thus, an increase of computing power t o several hundred tera-flops is needed if one is t o make a direct calculation of realistic hadron properties. A major step forward in last few years has been the realization that that, in terms of tinderstanding baryon strilcture, the lattice data obtained so far represents a wealth of information. Just as the study of QCD as a function of N , has taught 11sa great deal, so the behaviour as a function of f i can give u s great insight into hadronic physics and guide our model building. We begin by summarising the conclusions which emerge from the work of the past three years. 0
0
For quark masses r?~ > 60 MeV or so ( m , greater than 400-500 MeV) hadron properties are smooth, slowly varying functions of something like a constituent quark mass, M M o cm (with c 1). Indeed, M N
-
3 M , Atp+,
-
-
+
N
2 M and magnetic moments behave like l/M.
As m decreases below 60 MeV or so, chiral symmetry leads t o rapid, non-analytic variation, with: b~%fN fi3I2, dpH m y 6 < r2 >chN In m and moments of non-singlet parton distributions m: In m,.
-
-
Chiral quark models, like the cloudy bag model (CBM) ', provide a natural explanation of this transition. The scale is set by the inverse size of the pion source - the inverse of the bag radius in the CBM. When the pion Compton wavelength is smaller than the size of the composite source chiral loops are strongly suppressed. On the other hand, as soon as the pion Compton wavelength is larger than t h e source one begins t o see rapid, non-analytic chiral corrections. The nett result of this discovery is that one has control over the chiral extrapolation of hadron properties provided one can get data a t pion masses of order 200-300 MeV. This seems feasible with the next generation of supercomputers, which should be available within 2-3 years and which will have speeds in excess of 10 tera-flops l o .
6
2.2
Chiral Loops and Non-Analytacity
A s a consequence of spontaneous chiral symmetry breaking there must be contributions t o hadron properties from Goldstone boson loops. These loops have the unique property that they give rise to terms in the functional dependence of most hadronic properties on quark mass, which are not analytic l l . As a simple example, consider the nucleon mass. The most important chiral corrections to M N come from the processes LV + N . i r -+ ,V (u”) and N + An + N ( U N A ) . Independent of the form chosen for the ultraviolet cut-off, one finds that ~ T N Nis a non-analytic function of the quark mass. The non-analytic pi of U N N is independent of the form factor and = - 3 g ~ / ( 3 2 n f ~ ) m ~m3/2. This has a branch point, as a gives ~TNN(LNA) function of m, starting at m = 0. Such terms can only arise from Goldstone boson loops. I t is natural to ask how significant this non-analytic behaviour = -5.6m:, and a t is in practice. If the pion mass is given in GeV, the physical pion mass it is just -17 MeV. However, a t only three times the physical pion mass it is -460MeV - half t h e mass of the nucleon. If one’s aim is t o extract physical nucleon properties from lattice QCD calculations this is extremely important. A s we explained earlier, to connect t o the physical 500MeV t o m, = 140MeV. Clearly world one must extrapolate from m, one must have control of the chiral behaviour. The traditional approach is t o make a fit which naively respects the presence of a LNA term:
-
-
MN
=a
+ am3 + ym,, 3
(1)
with a ,,B and y fitted to the data. While this gives a very good fit t o the data, the chiral coefficient y is only -0.761, compared with the model independent value, -5.60, required by chiral required by chiral symmetry ’. If one insists that y be consistent with QCD, one cannot fit the d a t a with Eq.(l). An alternative suggested recently by Leinweber et QZ. ’, which also involves just three parameters, is t o evaluate U N N and U N A with the same ultra-violet form factor, with mass parameter A, and to fit M N as
MN = a+,Bm~ +UNN(~,,A)+~NA(~,,A), (2) by adjusting a,,B and A. Using a sharp cut-off (u(k) = O(A - k)) these authors were able t o obtain analytic expressions for U N N and U N A which reveal the correct LNA behaviour - and next-to-leading (NLNA) in the An case, ugiNA N m: In mrr. These expressions also reveal a branch point a t m, = M A - M N , which is important if one is extrapolating from large values of m, t o the physical value. This approach does indeed produce an excellent fit t o the lattice data, while preserving the exact LNA and NLNA behaviour of QCD.
The analysis of the lattice data for MN, incorporating the correct nonanalytic behaviour, also yields important new information concerning the sigma commutator of the nucleon, which is a direct measure of chiral SU(2) symmetry breaking in QCD. The widely accepted experimental value is 45 ± 8MeV 12. Using the Feynman-Hellmann theorem one can write &N as mdM^/dm = m^dMnf/dm^, at the physical pion mass. If one has a fit to MAT as a function of m* which is consistent with chiral symmetry, one can use this expression to evaluate
0.6
o o
0.2
cu 0.0
-0.2
0.0
0.2
0.4 2 m
0.6
.(GeV2)
0.8
1.0
Figure 1. Fits to lattice results for the squared electric charge radius of the proton - from Ref. 1 4 . Fits to the contributions from individual quark flavors are also shown (the u-quark results are indicated by open triangles and the
2.3
Electromagnetic Properties of Hadrons
While there is only limited (and indeed quite old) lattice data for hadron charge radii, recent experimental progress in the determination of hyperon charge radii has led us to examine the extrapolation procedure for extracting charge radii from the lattice simulations. Figure 1 shows the extrapolation
8
of the lattice data for the charge radius of the proton, including the In mrr (LNA) term in a generalised Pad4 approximant 1 4 , 1 5 . Clearly the agreement with experiment is much better if, as shown, the logarithm required by chiral symmetry is correctly included rather than simply making a linear extrapolation in the quark mass (or m:). Full details of the results for all the octet baryons may be found in Ref. 1 4 . The situation for baryon magnetic moments is also very interesting. The LNA contribution in this case arises from the diagram where the photon couples to the pion loop. A s this involves two pion propagators the expansion of the proton and neutron moments is: ~
Here p:'") is the value in the chiral limit and the linear term in m, is proportional to m ; , a branch point a t T% = 0. The coefficient of the LNA term is cr = 4 . 4 p ~ G e V - l . At the physical pion mass this LNA contribution is 0 . 6 which is almost a third of the neutron magnetic moment. Just as for M N , the chiral behaviour of p P ( n ) is vital to a correct e x t r a p olation of lattice data. One can obtain a very satisfactory fit to some rather old data, which happens to be the best available, using the simple Pad6 16:
Existing lattice data can only determine two parameters and Eq.(4) hrr9 just two free parameters while guaranteeing the correct LNA behavioiir as m, + 0 and the correct behavioiir of HQE,T at large m:. The extrapolated values of pp and pn at the physical pion mass, 2.85 f 0.22pN and -1.90 zk 0 . 1 5 are currently the best estimates from non-perturbative QCD 16. For the application of similar ideas to other members of the nucleon octet we refer to Ref. 1 7 , and for the strangeness magnetic moment of the nucleon we refer to Ref. The last example is another case where tremendous improvements in the experimental capabilities, specifically the accurate measurement of parity violation in e p scattering 19, is giving us vital information on hadron structure.
2.4
Moments of Structure Functions
The moments of the parton distributions measured in lepton-nucleon deep inelastic scattering are related, through the operator product expansion, to the forward nucleon matrix elements of certain local twist-2 operators which can be accessed in lattice simulations I . The more recent data, used in the
9
present analysis, are taken from the QCDSF 2o and MIT 21 groups and shown in Fig. 2 for the n = 1, 2 and 3 moments of the ti - d difference a t NLO in the MS scheme. To compare the lattice results with the experimentally measured moments, one must extrapolate in quark mass from about 50 MeV to the physical value. Naively this is done by assuming that the moments depend linearly on the quark mass. However, as shown in Fig. 2 (long dashed lines), a linear extrapolation of the world lattice d a t a for the u - d moments typically overestimates the experimental values by 50%. This suggests that important physics is still being omitted from the lattice calciilations and their extrapolations. Here, its for all other hadron properties, a linear extrapolation in m m: must fail as it omits crucial nonanalytic structure associated with chiral symmetry breaking. The leading nonanalytic (LNA) term for the 11 and d distribiitions in the physical nucleon arises from the single pion loop dressing of the bare nucleon and has been shown to behave as m: log m , . Experience with the chiral behaviour of masses and magnetic moments shows that the LNA terms alone are not sufficient t o describe lattice d a t a for m, > 200 MeV. Thus, in order to fit the lattice data a t larger m,, while preserving the correct chiral behaviour of moments as m, t 0, a low order, analytic expansion in m: is also included in the extrapolation and the moments of 11 - d are fitted with the form 24: N
22123
+
where the coefficient 23, CLNA = - ( 3 g i 1 ) / ( 4 ~ f , ) ~The . parameters a,, b, and p are a prioriiindetermined. The mass p determines the scale above which pion loops no longer yield rapid variation and corresponds t o the upper limit of the momentum integration if one applies a sharp cut-off in the pion loop integral. It is taken to be 550 MeV. Multi-meson loops and other contributions cannot give rise to LNA behaviour and thus, near the chiral limit, E,q. (5) is the most general form for moments of the PDFs a t O(m:) which is consistent with chiral symmetry. We stress that p is not yet determined by the lattice d a t a and it is indeed possible t o consistently fit both the lattice d a t a and the experimental values with p ranging from 400 MeV t o 700 MeV. This dependence on p is illustrated in Fig. 2 by the difference between the inner and outer envelopes on the fits. Data a t smaller quark masses, ideally m: 0.05-0.10 GeV2, are therefore crucial t o constrain this parameter in order t o perform an accurate extrapolation based solely on lattice data.
-
10
Figure 2. Moments of the u - d quark distrihution from various lattice simulations. The straight (long-dashed) lines are linear fits t o this data, while the curves have the correct LNA hehaviourin thechiral limit - see the text for details. The small squares are the results of the meson cloud model and the dashed curve through them best fits using Eq. (5). The star represents the phenomenological values taken from NIL) fits in the MS scheme.
2.5 Baryon Spectroscopy The study of the baryon spectrum is a venerable art '. However, the lack of suitable experimental facilities has meant that there h a s been insufficient data t o provide definitive tests for the many theoretical models constriicted over the past 30 years. The availability of high intensity, high duty factor electron accelerators, complemented with multi-particle detectors, means that this situation is changing dramatically. Amongst the open questions t o be
11
addressed initially one might ask: 0
0
What is the Roper resonance (R(1440))? In a naive quark model it would be a 2 )iw excitation of the nucleon, yet it lies below the 1 flu negative parity states. Is it a breathing mode 25 or a channel coupling effect 26? Is the A(1405) a I;” bound state, as suggested originally by Dalitz and Tuan? Is it a result of the coupling of the C?r-I(N channels, taking into account the extremely attractive C n interaction near threshold 27128?
0
0
Do the missing states, predicted by the quark model but not yet seen experimentally, really exist? Are there some states which are not described by the quark model at all, but simply a consequence of very strong rescattering?
We may expect a great deal of experimental insight into these questions in the next few years, from JLab, Mainz and MIT-Bates. At the same time, there are also some exciting developments on the theoretical side. Until now we have had an over-abundance of models, more or less motivated by QCD, with no rigorous way to choose between them. The recent progress in lattice QCD will also have a dramatic impact here. Pioneering work on the 1 f i w and 2 fiw excited states of the nucleon by Leinweber ”, and by Leinweber and Lee 30, is now being developed by at least three groups: at BNL 3 1 , JLab-QCDSF-UKQCD 32 and CSSM 33. The masses of the N’(1/2+), N*(1/2-), A*(3/2-) and even the strange excited states are now being studied with a variety of non-perturbative improvements of the action, as well as with domain wall fermions, to improve the chiral properties of the calculation. Again the computer limitations mean that all calculations so far have been quenched and have also been restricted to relatively large quark mass. Nevertheless some features are already apparent. The data looks very much as one would expect in a constituent quark model. The masses come in the order expected in a simple oscillator picture with 2 )Iw (positive parity) excitations well above the 1 flw states. Consistent with our earlier summary of the large mass region (m above GOMeV), the baryon masses are linear functions of the quark mass. It is clearly vital to extend the calculations to quark masses that are as low as possible and to explore the chiral constraints on the extrapolations of these excited states. It is also important to explore possible connections between results in quenched and full QCD 34. There will be tremendous progress in these areas in the next five years.
12
......
2 2
Udiaa. PWL4
Udlaa. full Udias. full
v
\
+
OMC
.................... .................. ................. ___*--
1.0
_---__---
i
2
> a
v
0.8
t
I
Figure 3. Comparison between the ratio of polarised electron quasi-elastic scattering cross sections on 4He and on the free proton 4 8 . The measured ratio is proportional to the ratio of the proton electric to magnetic form factors of a proton hound in 4 H e to the ratio for a free proton - if the other nuclear effects are correctly handled. The data favour earlier calculations within QMC which include a change in the hound nucleon form factors.
3
Nuclear Systems
The traditional view of nuclei is as a system of unperturbable (point-like) protons and neutrons. In a mean-field treatment they move in a self-consistent binding potential. Within quantum hadrodynamics (QHD) the Lorentz character of the mean-field is taken seriously, with a strong scalar attraction of order 300-400 MeV at nuclear matter density ( P O ) and an almost equally strong vector repulsion 35. On the other hand, if one starts with the aim of understanding nuclear structure in terms of QCD it is fundamental that the protons and neutrons are far from elementary. Indeed, they are quite large composite systems of quarks and gluons. Furthermore, the typical mean scalar field noted earlier is exactly the same size as the energy required to excite a nucleon (300MeV to the A or 500 MeV to the R(1440)). Far from being a surprise that nucleon structure might play a role in nuclear structure, it is difficult to see how it could fail to be significant! One of the central aims of modern nuclear physics must be to investigate this role both theoretically and experimentally. The quest for changes in the structure of hadrons in medium began in the ~ O ’ S ,with considerable attention to the problem being generated by the idea of Brown-Rho scaling 36. At about the same time, Guichon constructed a simple generalization of QHD, in which the point-like nucleon was replaced
13
by an MIT bag and the i~ and w mesons coupled to the confined quarks 37. A self-consistent solution of this problem within mean-field approximation led to a natural saturation mechanism. Rather than the (7 - ‘%1 coupling being a constant it becomes a monotonically decreasing function of the applied scalar field, g,(a). Indeed, because of the low mass of the confined quarks this mechanism is far more effective than the decrease of $ N $ N in QHD, and the mean scalar field a t po is only 50% or so of that in QHD. This model, which is generally known as QMC (the quark-meson coilpling model), has been extensively developed by Guichon , Saito, Tsushima, Exchange contributions Blunden, Miller, Jennings and many others have been considered 42 and eventually one must go to a more sophisticated theoretical treatment than simple mean field theory. Nevertheless, the model gives interesting guidance on the modification of hadron masses 43 and reaction cross sections 44 inside nuclear matter. For instance, it provides an interesting alternative to the naive explanation of J / Q suppression in relativistic heavy ion collisions in terms of a quark-gluon plasma 4 5 . From the point of view of nuclear structure the most interesting development is the application to finite nuclei 38. This leads to a deep conceptual change in our understanding. What occupies the shell model orbits are not nucleons but nucleon-like quasi-particles. These will have different masses, magnetic moments, charge radii and so on from those of free nucleons. From this point of view is less remarkable that bound nucleons shoiild have different properties from free nucleons than that such changes have proven so difficult t o establish. This is why the nuclear EMC effect which is still only partially understood, is so important. In terms of a fundamental theory of nuclear structure there can be few more important challenges than estabIishing the change in the properties of a bound nucleon. In this respect, a recent experimental result from Mainz is potentially extremely important 48. This group measured G E / G Mfor a proton bound in 4He, using the (Z,e’p3 reaction. The change in the ratio of these form factors for the bound nucleon had been studied in detail within QMC and, as shown in Fig. 3, the experimental results support such a modification. Clearly the statistical significance of the effect is not yet great. On the other hand, preliminary indications from JLab are that a similar modification is needed for Q2 u p t o 2.5 GeV2 5 1 . Furthermore, careful theoretical study of the effects of distortion, spin-orbit forces and meson exchange suggests that this particular ratio is extremely insensitive t o such corrections. This measurement is crucial in that it is really the first clear indication of a change in the structure of a bound nucleon. 38,39140,41.
47146,
49350
14
4
Concliision
This is indeed an exciting period in the development of baryon physics. We have seen that developments in lattice QCD, especially more powerfill computers and improved chiral extrapolations, should finally allow the computation of accurate baryon properties within full QCD, at the physical quark masses, within the next five years. Studies of baryon spectroscopy on the lattice will complement important new experimental studies and improved quark models. We have seen that from the point of view of QCD, it is vital to understand the changes in baryon properties that occur as a function of density as well as temperature. I n this sense finite nuclei provide a criicial testing ground for ideas that will eventually be applied at much more extreme conditions. We briefly reviewed a n experiment that gives a tant(a1izing hint of such a change and look forward to further tests of these ideas in t h e next few years.
Acknowledgements This work was supported by the Australian Research Coiincil and the University of Adelaide.
References 1. A. W. Thomas and W . Weise, “The Structure of the Nucleon,” 289 pages.
Hardcover ISBN 3-527-40297-7 Wiley- VCH, Berlin 2001. 2. V. A . Novikov et al., Nucl. Phys. B 191, 301 (1981). 3. P. C. Tandy, Prog. Part. Nucl. Phys. 36, 97 (1996) [nucl-th/9605029]. 4. M . Oettel and R. Alkofer, arXiv:hepph/0204178. 5 . S. Aoki et al. [JLQCD Collaboration], Phys. Rev. Lett. 82 (1999) 4392. 6. J. Skulleriid, D. B. Leinweber and A . G. Williams, heplat/0102013. 7. D. B. Leinweber et al., Phys. Rev. D 61, 074502 (2000). 8. T. Lippert et al., Niicl. Phys. Proc. Suppl. 83 (2000) 182. 9. S. Theberge et al., Phys. Rev. D 22, 2838 (1980) [Erratum-ibid. D 23, 2106 (1980)l; A. W . Thomas, Adv. Nucl. Phys. 13, 1 (1984). 10. Lattice Hadron Physics Collaboration proposal, J.W. Negele and N. Isgur, ftp://www-ctp.mit.edu/pub/negele/LatProp/. 11. S. Weinberg, Physica (Amsterdam) 96 A , 327 (1979); J . Gasser and H. Leutwyler, Ann. Phys. 158, 142 (1984). 12. J. Gasser, H. Leutwyler and M . E. Sainio, Phys. Lett. B 253, 252 (1991). 13. S. V. Wright et a/., Nucl. Phys. A 680, 137 (2000). 14. E. J. Hackett-Jones et al., Phys. Lett. B 4 9 4 , 8 9 (2000) [heplat/0008018].
15
19. 16. 17. 18. 19. 20. 21. 22. 23.
G. V. Dunne et al., Phys. Lett. B531,77 (2002) [hepth/0110199]. D. B. Leinweber et al., Phys. Rev. D 60,034014 (1999). E. J. Hackett-Jones et al., Phys. Lett. B 489,143 (2000). D. B. Leinweber and A . W. Thomas, Phys. Rev. D 62,074905 (2000). K. S. Kumar and P. A. Souder, Prog. Part. Nucl. Phys. 45,S333 (2000). M . Gockeler et al., Nucl. Phys. Proc. Suppl. 53,81 (1997). D. Dolgov et al., Nucl. Phys. Proc. Suppl. 94,303 (2001). A . W. Thomas et al., Phys. Rev. Lett. 85,2892 (2000). D. Arndt and M . J. Savage, nucl-th/0105045; J. Chen and X. Ji, hepph/0105197. 24. W. Detmold et al., Phys. Rev. Lett. 87,172001 (2001). 25. P. A . Guichon, Phys. Lett. B 163,221 (1985). 26. J. Speth et al., Nucl. Phys. A 680,328 (2000). 27. E. A. Veit et al., Phys. Rev. D 31,1033 (1985). 28. N. Kaiser et al., Nucl. Phys. A 594,325 (1995); E. Oset et al., arXiv:nucl-th/0109006. 29. D. B. Leinweber, Phys. Rev. D 51,6383 (1995) [nucl-th/9406001]. 30. F. X. Lee and D. B. Leinweber, Nucl. Phys. Proc. Suppl. 73,258 (1999). 31. S. Sasaki, T . Blum and S. Ohta, heplat/0102010. 32. M. Gockeler et al. [QCDSF Collaboration], heplat/0106022. 33. W. Melnitchouk et al., arXiv:heplat/0202022. 34. R. D. Young et al., arXiv:heplat/0ll1041. 35. R. J. Furnstahl and B. D. Serot, Comm. Nucl. Part. Phys. 2, A23 (2000). 36. G. E. Brown and M. Rho, Phys. Rev. Lett. 66,2720 (1991). 37. P. A. Guichon, Phys. Lett. B 200,235 (1988). 38. P. A . Guichon et al., Nucl. Phys. A 601,349 (1996) [nucl-th/9509034]. 39. K. Saito et al., Phys. Rev. C 55,2637 (1997) [nucl-th/9612001]. 40. P. G. Blunden and G. A. Miller, Phys. Rev. C 54,359 (1996). 41. X. Jin and B. K. Jennings, Phys. Rev. C 54,1427 (1996). 42. G. Krein et al., Nucl. Phys. A 650,313 (1999). 43. K . Tsushima et al., Phys. Lett. B 443,26 (1998). 44. K. Tsushima et al., J. Phys. G G27,349 (2001). 45. A. Sibirtsev et al., Phys. Lett. B 484,23 (2000). 46. D. F. Geesaman et al., Ann. Rev. Nucl. Part. Sci. 45,337 (1995). 47. J . J. Aubert et al., Phys. Lett. B 123,275 (1983). 48. S. Dieterich et al., Phys. Lett. B 500,47 (2001) [nucl-ex/0011008]. 49. D. H. Lu et al., Phys. Rev. C 60,068201 (1999). 50. A. W. Thomas et al., nucl-th/9807027. 51. S. Strauch, contribution to this conference.
16
Danielle Morel and Simon Capstick
Gerrit Schierholz and Christine Davies
BARYON SPECTROSCOPY IN THE QUARK MODEL S. CAPSTICK Department of Physics Florida State University Tallahassee, Florida 32306-4350 E-mail: capstickQcsit.fsu.edu The basis of constituent quark models of the baryon spectrum is reviewed, with a description of the effective degrees of freedom, their confinement, and various models of their short-distance interactions. It is argued that such models should not be compared with the results of analyses of hadron scattering data without considering the effects of quark-antiquark pairs on the spectrum, and a model of such effects is described.
1
Constituent Quark Models of the Baryon Spectrum
1.1 Eflective Degrees of Freedom
In the constituent quark model, baryons are made up of three quasi-particles, with effective masses significantly larger (200-300 MeV) than the currentquark masses in the QCD Lagrangian. They are also not point-like particles, having both electromagnetic1 and strong2 form factors. Although this is a popular approach, and is taken here, other approaches exist and are briefly considered below. Baryons can be described in the soft (low-Q2) regime as being made up of a diquark cluster plus a quark3, with fewer degrees of freedom at low energy and so fewer excited states. Although this can explain the small number of positive-parity excited light-quark ( N and A) baryons seen in analyses of hadron scattering data, it is more likely that such states have weak couplings to the predominant N n formation channel. Additional states, if they exist, will almost certainly be discovered in photo- and electro-production experiments with final states other than N n . A mechanism for strong diquark clustering in baryons is lacking. Algebra-based models4 of the spectrum describe baryons as collective excitations of string-like objects. Such models incorporate radial excitations from rotations and vibrations of these strings, and so have more excited states than models with constituent quarks moving in a potential. The predictions of such models for this richer spectrum are testable in experiments designed to find new baryon states. Baryons can also be described as current quarks moving in a confining bag, with pions coupled to the surface in the cloudy
17
18
bag model5. Although this description has several advantages, it is difficult to describe non-spherical excited states in this framework, and so its application has largely been limited to ground states. 1.2 Constituent Quarks
Constituent quarks have dynamically generated masses, which run with Q’. There is evidence from lattice simulations that at low Q2 this mass is of the order of A,,,, and similar results are found in covariant studies of hadron properties based on the Schwinger-Dyson Bethe-Salpeter field theoretic approach6. In principle, spectral models which use the relativistic kinetic energy operator Ki = (p; m;) could use light-quark masses anywhere from 0 to 250 MeV. However, a study of isospin-symmetry violating mass splittings in mesons7 shows that Kd - K , N 5-10 MeV, comparable to the current-quark mass difference Am = md - mu ‘v 5-10 MeV. However, if Am is much smaller than the quark kinetic energy K , we can expand
+
+
Kd - K , = (p2 [mu
+ Am]’)
+ me) ~li (?)Am,
- (p2
(1)
which together with the above observation that Kd - K , ‘v Am implies that mu ‘v Ku N A Q ~ D‘v 200 MeV. The strange quark is given a mass between 150 and 200 MeV heavier than the light quarks. As effective degrees of freedom, the constituent quarks also should have strong form factors. Such form factors are required to render finite short distance interactions between the quarks. It has also been shown’ that the constituent quarks must be given electromagnetic (EM) form factors in order to fit the nucleon (EM) form factors at moderate Q2 values, in relativistic calculations based on light-cone dynamics. It seems sensible that the strong and EM sizes of quarks should be comparable. Interestingly, the anomalous moments of the quarks are shown in a lattice simulation* to depend on the baryon in which they lie.
1.3 A Model of Confinement In a quenched lattice calculation of the potential between three static (heavy) quarksg, it is found that a good fit to the observed potential energy can be made with the form
19
where Lmin is the length of the minimum-length Y-shaped string connecting the quarks to a junction, and A, u and C are fitted constants. A parallel calculation of the potential between a static quark and antiquark was performed to compare the string tension and Coulomb strength in mesons and baryons. It is shown that U ~ Qand U ~ are Q similar, and that the Coulomb strengths are in the ratio A ~ Q : A,Q = 1 : 2 given by one-gluon exchange. A fit with the part of the potential proportional to u replaced by U A Ci,. Iri - rjl was significantly poorer. This establishes that a confining potentid given by the minimum length of a Y-shaped string between the quarks and a junction is relevant for QQQ baryons. A reasonable starting point is to assume that it is also good for light-quark baryons. Such a potential arises in the flux-tube model", based on strong-coupling lattice QCD. In the strong coupling limit the color fields are confined to narrow tubes with an energy proportional to their length. In baryons a junction is required to maintain global color gauge invariance. When the flux-tube model is combined with the adiabatic approximation, the result is a confining interaction given by V B ( r l , r 2 , r 3 ) = u ( l l + 12 Z3) = aL,i,, where the li are the lengths of the individual strings connecting the quarks to the junction, and u is the meson string tension. Note this confining potential is linear at large quark-junction separations. There is no reason why the string should not be considered dynamical. In the flux-tube model the zero-point energy of this motion should correct the static potential VB, and excited states of the string motion should define new potentials in which the quarks in hybrid baryons movell.
+
1.4
One-Gluon Exchange
The spectrum of ground-state baryons suggests flavor-dependent short-range (contact) interactions between the quarks. One simple assumption is that at short distance, or high Q2,the exchange of a single gluon dominates the interactions between the quarks. This leads to a mass formula for the ground state baryons
where (S3(r12))is a spatial expectation value of a delta function of the separation of a pair of quarks in the (symmetric) ground-state spatial wave function, and S , is the spin of quark i. This gives, for example,
ME-MA 2 = - (1 MA-MN 3
--&) mud
N
2 3(0.4) = 0.27,
(4)
20
which compares favorably with the experimental ratio (1193-1116)/(1232939)=0.26. This model of the short-distance interactions has the advantage that it also explains certain regularities in the meson spectrum, such as the evolution of the vector-pseudoscalar splitting with quark mass. It is unclear why Eq. (3), based on a non-relativistic expansion and the assumption of weak binding, should work for light-quark baryons. This model also includes a tensor interaction with a strength fixed by that of the contact interaction. The best evidence for tensor interactions is the mixings they cause between states with similar spatial wave functions but different total quark spin, which have important consequences for strong and electromagnetic decays of these states.
170 I
unperturbed level
-
160
-: -75 MeV N
150 -
(N*f-)l N*f-
A* f-
Figure 1. Isgur-Karl model predictions for the mass splittings of the negative-parity excited non-strange baryons (lines), shown with the range of central values for the masses from analyses quoted by the Particle Data Group.
The predictions12 of the model of Isgur and Karl for the splittings of the negative-parity excited non-strange baryons (the center-of-mass of the band was fit) are compared with the quoted range of central mass values from the Particle Data Group in Figure 1. The contact interaction splits the states
21
by 612 21 150 MeV, where 6 = M A - M N . The addition of a consistent tensor interaction introduces further splittings, but also causes the mixing which allows the lightest N ’ t - state, associated with the Sll(1535) in N T scattering, to have a substantial decay width to N v . This large decay width is at first surprising, given the small available phase space available, but can be explained by the constructive interference caused by the tensor mixingI2. Associated with these “hyperfine” interactions are spin-orbit interactions, which although they can be arranged to partially cancel with those arising from Thomas precession of the quark spins in the confining potential, are at a level not present in the spectrum found from analyses of data. This is best seen by examining the negative-parity excited strange baryons, where the model without spin-orbit interactions predicts a degenerate lightest A; - and AZ-, in contrast with the splitting of the states A;-(1405) and A$-(1520) seen in analyses. Models based on one-gluon exchange have been applied consistently to all mesons and baryond3 in variational calculations which use large harmonic oscillator bases. The Hamiltonians use the relativistic kinetic energy operator and have relativistic corrections in the potentials. As an example, the contact part of the hyperfine interaction takes the form
+
1
where E, = (p: m:)Z is the kinetic energy of the i-th quark, the strong coupling asis smeared by running with Q2,and ccont is a relativistic parameter fit to the spectrum. The usual delta function is smeared out by the form factors of the interacting constituent quarks. Spin-orbit interactions from both one-gluon exchange and Thomas precession in the confining potential are included with the Coulomb, contact and tensor interactions arising from one-gluon exchange, and spin-orbit interactions in baryons can be arranged to be small. This is due to the use of a smaller value of as(0),partial cancellation of the spin-orbit interactions from the two sources, and the choice of the relativistic parameters. Although reasonable agreement with the spectrum of states from analyses is seen, the problem of the mass of the A;-(1405) is not solved. In addition, the first band of negative-parity excited states is too light by about 50 MeV, and the first positive-parity band too heavy13 by 50 MeV.
22
1.5 One-Boson Exchange Another possibility for the short-distance interactions between quarks in baryons (this model cannot be applied to mesons) is that bosonic hadrons are exchanged between the quarks, and gluons are not. Originally formulated in terms of pion exchangell, this idea was extended to the exchange of an octet of pseudoscalar bosons15, and later scalar and vector bosons16. The flavor dependence of the short-distance interactions is explicit, e.g. in the model of Glozman and Riska15 the contact interaction takes the form
where the A: are flavor SU(3) Gell-Mann matrices. Glozman and Riska fit the radial matrix elements of the pion, kaon and eta-exchange potentials V ( T Q ) to the spectrum, which allows the order of the lightest negative and positiveparity states to be inverted, as illustrated in Figure 2. It is important to
-
-N(1535)-N(1520)
+ -N(1440)
+ N
N
A
A
Figure 2. Masses of low-lying positive and negative-parity excited states of N , A and A baryons in the pseudoscalar exchange model of Glozman and Riska.
note that the masses of the positive-parity excited states of the A and A extracted from analyses are quite uncertain, 155Ck1700 MeV and 1560-1700 MeV, respectively. These exchange potential matrix elements are calculated in a more constrained model using a variational harmonic-oscillator basis, a relativistic kinetic energy operator, and string confinement16. Without the freedom to fit the matrix elements, it is necessary to include the exchange of nonets of vector mesons, and scalars. The spectrum shown in Figure 3 shows that although the Roper resonance is lighter than the lightest non-strange negative
23
parity states, the first excited A:' and A$+ states are now above the lightest negative-parity states of the same flavor. Spin-orbit interactions from Thomas precession in the confining potential are not included, and the problem of the A$-(1405)-A(1520);- splitting is not solved. Y [MeV] 1800 1700 -
Ell- U 7
1600 1500 -
-
1400 -
1300 1200 1100 -
1000 900
N
I
I
1+ 12
2
I
a+ 2
A 1
I
I
I
A
l
l
I
I
I
I
3-
a+
3-
1-
a+
2-
1+ 1- p+ 3-
2
2
2
2
2
2
2
2
2
2
I
s+ 2
I
52
Figure 3. Masses of low-lying positive and negative-parity excited states of N , A and A baryons in the one-boson exchange model of Glozman et aLI6
I . 6 Instanton-Induced Interactions Another explicitly flavor-dependent interaction which has been adopted to explain the spectrum of light baryons is that of instanton-induced interactions. These interactions have the form (q2;S,L,TIWIq2;s , L , T ) = -4gbS,06L,06T,Ow,
(7)
and so act only between two quarks which are in a relative S-wave, and in an isoscalar state with total quark spin zero. The interaction W is a contact interaction. A model based on this interaction has been applied to excited baryon states by Blask, Bohn, Huber, Metsch and Petry17. The model has very few parameters, and shows reasonable agreement with the spectrum of ground states, and P-wave N and A states, although the contact splittings are too small in the P-wave C states, and positive-parity excited states are generally too heavy by about 250 MeV. There are no contact splittings between A states, where all quark pairs have T = 1. A more sophisticated version of this model is described in these proceedings18.
24
1.7 Necessity of a Decay Model It is sometimes overlooked that a model of the spectrum cannot be compared with the results of analyses of scattering data without a calculation of the strong decays of the model states. This is because analyses af hadron scattering data generally find fewer states than are present in models. An obvious explanation, which has been explicitly seen in model calc~lations'~, is that such states do not couple strongly to the T N and K N formation channels comprising most of the data. It is therefore crucial that predictions are made for which of the model states are likely to have been seen in the analyses. A popular phenomenological model of such decays is the 3Po model, which has the advantage that the emitted mesons have structure, and allows correlation of many decays with few parameters. 2
Unquenching the Constituent Quark Model
In QCD, qqq(qq) configurations are possible in baryons, and it may be that many of the outstanding difficulties encountered in model descriptions of the baryon spectrum arise from their neglect. Because of the lack of a unique color configuration, and fall-apart decays into colorless hadrons, it is not possible to solve directly for the masses and properties of baryons in the presence of such states with the usual confining and short-range interactions between the quarks (and antiquarks). Instead, it is natural and consistent with confinement to expand such configurations in a basis of baryon-meson intermediate states. Masses of baryons will be shifted by their couplings to open (and sub-threshold) channels by self energies arising from loops containing baryonmeson intermediate states. Note that calculation of these mass shifts requires a model of baryon-baryon-meson ( B B ' M ) strong vertices and their momentum dependence, and that the high-momentum (short-range) part of the loops contains one-boson exchange between the quarks. Calculation of the vertices, and of mass shifts from intermediate baryons missing from analyses, requires a model of the baryon spectrum and wave functions. The mass shifts are found by solving
self consistently to find the bare mass E at which the sum of the bare mass and self energy is the physical mass M B . Note that the self energy is a sum of self energies arising from all possible baryon-meson intermediate states, including states for which the external baryon mass is below threshold, and those containing excited mesons and baryons. The effect on the spectrum is
25
M _-.-
Figure 4. Contribution to the self energy of a baryon B from a loop containing a baryon B' and a meson M.
examined by evaluating the splittings of the bare masses required to fit the physical masses, and comparing these to model mass splittings.
2.1
Convergence
The self energies of baryons due to individual B ' M loops can be expected to be comparable to their partial widths to these channels, i.e. of the order of tens to hundreds of MeV. Because many such channels are open, due to the density of the spectrum of excited baryon intermediate states, it it not trivial that the sum over intermediate states required to form C s ( E ) converges. The best calculations of this kind20*21have been applied to N , A, A and C ground and light negative parity excited external ( B )states. The intermediate states B'M contain ground state mesons M E {a,K , q , q', p, w , K * } and baryons B' E { N , A, A, C, C*}. Zenczykowski21has shown that without the inclusion of complete sets of intermediate states related by SU(6) flavor-spin symmetry, the self energies of the ground state N and A will not be equal in the SU(6) symmetry limit. This means that any calculation which does not include all of the octet and decuplet ground-state baryons and pseudoscalar and vector ground-state mesons is necessarily incomplete. However, it not enough to include intermediate states made up only of ground state baryons. A calculation22 restricted to B'a intermediate states, but with B' taken from all N and A excited states in the N = 0 , 1 , 2 and 3 oscillator bands, shows that the A - N splitting converges once the N = 3 band states are included, but the splittings between negative-parity states have not. Clearly, the restriction to ground state intermediate baryons is a poor approximation.
26
2.2 Soft vertices In time-ordered perturbation theory, self energies from B'M intermediate states can be found by performing the loop integral
As this samples all momenta, its size depends critically on the poorly constrained size of the strong decay matrix element MB+BtM(k) at large (far off-shell) values of the loop momentum k. The usual 3 P , model gives vertices which are too hard, and the loops get large contributions from high momenta. In a calculation of such effects in mesons, Geiger and I s g ~ give r ~ ~their pair creation operator a (Gaussian) form factor proportional to exp(- fZbq -pq]'), with f = 3.0 GeVW2,which gives the pair-creation vertex a reasonable spatial size of about 0.35 fm, considering that these are constituent quarks. This has the effect of softening the strong decay vertices and making possible the convergence of the sum over intermediate states. A similar form factor is used by Silvestre-Brac and GignouxZ0in their calculation of the splittings of negative-parity excited baryons arising from baryon-meson loop effects. The convergence of the sum over intermediate states in a calculation of meson mass splittings is shown to be more rapid in a covariant, field-theoretic based on the Schwinger-Dyson Bethe-Salpeter approach, partly because the calculated form factors are softer than those found in non-relativistic models. Clearly the off-shell behavior of the strong-decay vertices is of crucial importance to such calculations. 2.3 Non-Strange Baryon Self Energies From the above, it is clear that a calculation of ground state and negativeparity excited-state baryon self energies must include a complete set of SU(6)related intermediate states, and a large set of excited intermediate baryons. Such a calculation has been performed by Danielle Morel, and is reported on elsewhere in these proceedingsz5. The results exhibit convergence of the A - N splitting, with the result that the mass splitting of the physical A and nucleon is only partly due to interactions between the quarks in the bare qqq states, with a significant contribution from these self energies. Convergence of the self energies of the negative-parity excited states in slower, but significant splittings also arise due to the differences in the self energies of these states.
27
3
Conclusions
Given the obvious importance of the effects of qqq(qq) configurations to the mass spectrum of baryons, it may be premature t o draw conclusions about the successes of various approaches to the short-distance interactions between the quarks. It seems likely that such effects may be responsible for the universal lack of agreement between a spectrum calculated with only qqq configurations and certain aspects of the spectrum of states extracted from analyses. With considerable theoretical effort, using a variety of different approaches, it may be possible to resolve these problems and come to a better understanding of the underlying degrees of freedom and their interactions in baryons.
Acknowledgments The work summarized here would not have been possible without my collaborators Nathan Isgur, Danielle Morel, Philip Page, Michael Pichowsky, Winston Roberts, and Sameer Walawalkar. This work is supported by the U.S. Department of Energy under Contract DEFG02-86ER40273.
References 1. P. L. Chung and F. Coester, Phys. Rev. D 44,229 (1991); F. Schlumpf, J. Phys. G 20, 237 (1994); F. Cardarelli, E. Pace, G. Salme and S. Simula, Phys. Lett. B 357, 267 (1995). 2. D. P. Stanley and D. Robson Phys. Rev. D 21, 3180 (1980); J. Carlson, J. B. Kogut and V. R. Pandharipande, Phys. Rev. D 28, 2807 (1983). 3. G. R. Goldstein, TUFTS-TH-G88-5, presented at Workshop on Diquarks, Turin, Italy, Oct 24-26, 1988. 4. R. Bijker, F. Iachello and A. Leviatan, Annals Phys. 236, 69 (1994). 5. S. Theberge, A. W. Thomas and G. A. Miller, Phys. Rev. D 22, 2838 (1980). 6. See, for example, C. D. Roberts and S. M. Schmidt, Prog. Part. Nucl. Phys. 45, S1 (2000). 7. S. Godfrey and N. Isgur, Phys. Rev. D 34, 899 (1986). 8. D. B. Leinweber, R. M. Woloshyn and T. Draper, Phys. Rev. D 43, 1659 (1991). 9. T. T. Takahashi, H. Matsufuru, Y. Nemoto and H. Suganuma, Phys. Rev. Lett. 86, 18 (2001). 10. N. Isgur and J. Paton, Phys. Rev. D 31, 2910 (1985).
28
11. Philip R. Page, these proceedings; see also S. Capstick and P. R. Page, Phys. Rev. D 60,111501 (1999). 12. N. Isgur and G. Karl, Phys. Rev. D 20,768 (1979). 13. S. Godfrey and N. Isgur, Phys. Rev. D 32,189 (1985); S. Capstick and N. Isgur, Phys. Rev. D 34,2809 (1986). 14. D. Robson, Proceedings of the Topical Conference on Nuclear Chromodynamics, Argonne National Laboratory (1988), Eds. J. Qiu and D. Sivers (World Scientific), pg. 174. 15. L. Y. Glozman and D. 0. Riska, Phys. Rept. 268,263 (1996). 16. R. F. Wagenbrunn, L. Y. Glozman, W. Plessas and K. Varga, Nucl. Phys. A 666,29 (2000). 17. W. H. Blask, U. Bohn, M. G. Huber, B. C. Metsch and H. R. Petry, Z. Phys. A 337,327 (1990). 18. Ulrich Loring, these proceedings. 19. R. Koniuk and N. Isgur, Phys. Rev. D 21,1868 (1980); S. Capstick and W. Roberts, Phys. Rev. D 47, 1994 (1993). 20. W. Blask, M. G. Huber and B. Metsch, Z. Phys. A 326 (1987) 413; B. Silvestre- Brac and C. Gignoux, Phys. Rev. D 43,3699 (1991); Y.Fujiwara, Prog. Theor. Phys. 90,105 (1993). 21. P. Zenczykowski, Annals Phys. 169,453 (1986). 22. M. Brack and R. K. Bhaduri, Phys. Rev. D 35,3451 (1987). 23. P. Geiger and N. Isgur, Phys. Rev. Lett. 67,1066 (1991). 24. M. A. Pichowsky, S. Walawalkar and S. Capstick, Phys. Rev. D 60, 054030 (1999). 25. Danielle Morel, Florida State University PhD thesis, and in these proceedings.
ELECTROEXCITATION OF NUCLEON RESONANCES VOLKER D. BURKERT Jefferson Lab, 12000 Jefferson Avenue, Newport News, VA23606 Recent elcctroproductiori results in the domain of schaniiel nucleon rcsoriaricc excitation arc prcsentcd. and preliminary data in the search for missing states will be discussed. I also address a ncw avenue to pursue N * physics using exclusive decply virtual Compton scattering. recently measured for the first time at JLab and DESY.
1
Why N”s are important
Nucleon physics today is focussed on understanding the details of the nucleon spin and flavor structures at varying distances, and on the systematics of the baryon spectrum which reveals properties of the underlying symmetry structure. R.esonance electroproduction has rich applications in nucleon structure studies at intermediate and large distances. Resonances play an important role in understanding the spin structure of the nucleon 2,3. More than 80% of the helicity-dependent integrated total photoabsorption cross section difAt ference (GDH integral) is a result of the excitation of the A(1232) Q2= 1GeV2 about 40% of the first moment rf‘(Q2) =J : gl(s,Q2)dx for the proton is due to contributions of the resonance region at W < 2GeV 5 , 6 . Conclusions regarding the nucleon spin structure for Q2 < 2GeV2 must therefore be regarded with some scepticism if contributions of baryon resonances are not taken into account. The nucleon’s excitation spectrum has been explored mostly with pion beams. Many states, predicted in the standard quark model, have not been seen in these studies, possibly many of them decouple from the N K channel ’. Electromagnetic interaction and measurement of multi-pion final states, may then be the only way to study some of these states. While photoproduction is one way 8, electroproduction, though harder to measure, adds additional sensitivity due to the possibility of varying the photon virtuality. Electroexcitation in the past was not considered a tool of baryon spectroscopy. CLAS is the first full acceptance instrument with sufficient resolution to measure exclusive electroproduction of mesons with the goal of studying the excitation of nucleon resonances in detail. This feature is illustrated in Fig. 1, where the invariant mass W of the hadronic system is plotted versus the missing mass of the e p -+ e p X , where X represents the undetected 412.
29
30 1969-1981: 1995-2000:
I
mm-l
-2oL 0
"I
0.5
CEA 0 DESY 0 NINA 0 ELSA0 JLAB 0 LEGS A MAU
BONN 0
LO
I
I
EATES
1.5
'
2
"
2.5
3
'
3.6
0
1
1
b(GeV/d'
Figure 1. Left panel: Invariant mass M7*,versus missing mass M X for y ' p -+ p X , measured in CLAS. Right panel: REnr and Rskr before the year 2001.
system. The no, 71, and w bands are correlated with enhancements in the invariant mass, and indicate resonances coupling to pro prl, and possibly pw channels. Some of the lower mass states are already well known. However, their photocouplings and the Q2 evolution of the transition form factors may be quite uncertain, or completely unknown. 2
Quadrupole Deformations of the Nucleon and A
An interesting aspects of nucleon structure at low energies is a possible this quadrupole deformation of the nucleon. In the interpretation of ref. would be evident in non-zero values of the quadrupole transition amplitudes El+ and Sl+ from the nucleon to the A(1232). In models with SU(6) spherical symmetry, this transition is due t o a magnetic dipole MI+ mediated by a simple spin flip from the J = f nucleon ground state to the Delta with J = $. Non-zero values for El+ would indicate deformation. Dynamically such deformations may arise through interaction of the photon with the pion cloud or through the one-gluon exchange mechanism '. At asymptotic momentum transfer, a model-independent prediction of helicity conservation requires REhf = El+/M1+ + + l . An interpretation of REhf in terms of a quadrupole deformation can therefore only be valid at low momentum transfer. The data before 2001 ( Fig. 1) show large systematic discrepancies. Taken together no clear trend is visible. At the photon point recent data from MAMI
31 1.22 GeV
W= 1.20 GeV
5,
I
1.24 GeV
I
K O
Y
<
-6
ul -10
-16
-20
)
0.5
I
1.6
2
2.5
3
3.6
4
O'(GeV/c)'
Figure 2. Left panel: Response functions for p r o in the Delta region measured with
CLAS. Right panel: REM and Rshr after 1990, including the latest CLAS results covering the range Q2=0.4 - 1.8GeV2.
l2
and LEGS l 3 are consistent with a value of REhf = -0.0275 f 0.005. The differential cross section for single pion production is given by
(1) where is the azimuthal angle of the pion, and h = f l is the helicity of the incident electron. The response functions ui depend on the hadronic invariant mass W, Q 2 , and polar cms pion angle 0:. CLAS allows measurement of the full angular distribution in azimuthal and in polar angle. The former allows separation of the &dependent and &independent response functions ui at fixed Q2,.W, and C O S ~ ; , while the latter contains information on the multipolarity of the transition. The multipoles can be extracted in some a p proximation through a fit of Legendre polynomials to the angular distribution of the various response functions. Angular distributions of response functions at fixed W values and results of the multipole analysis of the CLAS data are shown in Fig. 2, where data from previous experiments published after 1990 are included as well 12,14. R E h f remains negative and small throughout the Q 2range. There are no indications that leading pQCD contributions are important as they would result in a rise of REhf -+ +1 15. Rshf behaves quite differently. While it also remains negative, its magnitude is strongly ris-
+
"'
32
i
5
4 3'5
a
3
W=l.l
W = 1 . 1 4 GeV
GeV
W = 1 . 1 8 GeV
2.5
...
.
2
~I ~
1.5
1
-0.5 0
0.5
-0.5
0.5
-0.5
- L=2 Legendre Fit
-----
0.5
cosl9;
CLAS Data (a2= 0.65 GeV') MAID2001
-
~
-
Soto-Lee
Figure 3. Preliminary ( T L T ~data from CLAS compared to two predictions of dynam-
ical models. The data indicate strong model sensitivity.
ing with Q2. For Q2 > 0.35GeV2 RSM follows approximately a straight line that may be parametrized as: RSM= -(0.04+0.028 x Q2(GeV2)).The comparison with microscopic models, from relativized quark models l79l8, chiral quark soliton model 16, and dynamical models show that simultaneous description of both REMand RSMis achieved by dynamical models that include the nucleon pion cloud, explicitely. This supports the claim that most of the quadrupole strength is due to meson effects which are not included in other models. Ultimately, we want to come to a QCD description of these important nucleon structure quantities. Currently, there is only one calculation in quenched QCD l9 giving REM= 0.03 f 0.08, which, due to the large uncertainty, has no bearing on our understanding of nucleon structure. This calculation was made nearly a decade ago. Improvements in computer performance and improved QCD actions and lattices should allow a reduction of the error to a level where QCD should provide significant input. The new data establish a new level of accuracy. However, improvements in statistics and the coverage of a larger Q2 range are expected for the near
33
O*, deg Figure 4. Response functions for y*p -+ n d . The data cover the A(1232) and the
2nd resonance regions. Angular distributions are show for each bin in W. The data provide the basis for the analysis with a unitary isobar model (curve).
future, and they must be complemented by a reduction of model dependencies in the analysis. Model dependencies are largely due to our poor knowledge of the non-resonant terms, which become increasingly important at higher Q2. The U L T ~response function, a longitudinal/transverse interferences term is especially sensitive to non-resonant contributions if a strong resonance is present. CLT, can be measured using a polarized electron beam in out-ofplane kinematics for the pion. Preliminary data on C L T ~ from CLAS are shown in Fig. 3 in comparison with dynamical models, clearly showing the model sensitivity t o non-resonant contributions. Both models predict nearly the same unpolarized cross sections, however they differ in their handling of non-resonant contributions.
3
N ” s in the Second Resonance Region
Three states, the elusive ”R.oper” N ; / 2 +(1440), and two strong negative parity states, N;12- (1520), and N;/2- (1535) make up the second enhancement seen in inclusive electron scattering. All of these states are of special interest to obtain a better understanding of nucleon structure and strong QCD.
34
3.1
The Roper resonance - still a mysterg
The Roper resonance has been a focus of attention for the last decade, largely due to the inability of the standard constituent quark model to describe basic features such as the mass, photocouplings, and their Q2 evolution. This has led to alternate approaches where the state is assumed t o have a strong gluonic component ’l, a small quark core with a large meson cloud ”, or a hadronic molecule of a nucleon and a hypothetical sigma meson I N a > 23. Lattice QCD calculations 25 show no sign of a 3-quark state with the quantum numbers of the nucleon in the mass range of the R.oper state. Experimentally, the Roper as a isospin 1/2 state couples more strongly to the n r t channel than to the p r o channel. Lack of data in that channel and lack of polarization data has hampered progress in the past. Fortunately, this sitation is changing significantly with the new data from CLAS. For the first time complete angular distributions have been measured for the nn+ final state. Preliminary separated response functions obtained with CLAS are shown in Fig. 4. These data, together with the p r o response functions, as well as the spin polarized O L T ~response function for both channels have been fitted to a unitary isobar model. The results are shown in Fig. 5 together with the sparse data from previous analyses. None of the models gives a quantitaive description of the data. Much improved data are needed for more definite tests in a large Q2 range. An interesting question is if the Al/2(Q2) amplitude changes sign, or remains negative. The range of model predictions for the Q2 evolution illustrates dramatically the sensitivity of electroproduction to the internal structure of this state.
3.2 The first negative parity state N1;2- (1535) Another state of interest in the 2nd resonance region is the N;12- (1535). This state was found t o have an unusually hard transition formfactor, i.e. the Q2 evolution shows a slow fall-off. This state is often studied in the pq channel which shows a strong s-wave resonance near the 77-threshold with very little non-resonant background. Older data show some discrepancies as t o the total width and photocoupling amplitude. In particular, analyses of pion photoproduction data36 disagree with the analysis of the eta photoproduction data by a wide margin. Data from CLASZ6,together with data from an earlier JLab experiment2’ give now a consistent picture of the Q2 evolution, confirming the hard formfac-
35 tor behavior with much improved data quality, as shown in Fig. 6. Analysis of the nn+ and pro data at Q2= 0.4GeV2 gives a value for A l p consistent with the analysis of the pq data 24. The hard transition formfactor has been difficult t o understand in models. R.ecent work within a constituent quark model using a hypercentral potential 29 has made progress in reproducing the A l p amplitude for the N;,2- (1535), as well as for the N&-(1520). The hard formfactor is also in contrast to models that interpret this state as a ll?C > hadronic molecule 30. Although no calculations exist from such models, the extreme 'ihardness" of the formfactor and the large cross section appear counter intuitive to an interpretation of this state as a bound hadronic system. Lattice QCD calculations also show very clear 3-quark strength for the state ?lz5.
4
Higher Mass States and Missing Resonances
Approximate S U ( 6 ) @ O(3) symmetry of the symmetric constituent quark model leads to relationships between the various states. In the single-quark transition model (SQTM) only one quark participates in the interaction. The model predicts transition amplitudes for a large number of states based on only a few measured amplitudes 31. Comparison with photoproduction results show quite good agreement, while there are insufficient electroproduction data €or a meaningfull comparison. The main reason is that many of the higher mass states decouple largely from the N n channel, but couple dominantly t o the N n n channel. Study of y * p p + n - as well as the other charge channels are therefore important. Moreover, many of the so-called "missing" states are predicted to couple strongly to the Nnn channels 3 3 . ---f
4.1
A new resonances an the p + n - channel?
New CLAS total cross section electroproduction data are shown in Fig. 7 in comparison with photoproduction data from DESY ?. The most striking feature is the strong resonance peak near W=1.72 GeV seen for the first time in electroproduction of the pn n- channel. This peak is absent in the photoproduction data. The CLAS data 32 also contain the complete hadronic angular distributions and p+ and n f n p mass distributions over the full W range. They have been analyzed and the peak near 1.72GeV was found to be best described by a N3f ,+(1720) state. While there exists a state with such quantum numbers in this mass range, its hadronic properties were found previously to be very different from the CLAS state. For example, the PDG gives for the known state a N p coupling of I'Np/l?tot(PDG)M 0.85 while the
+
36
50
0
-50
- 100
0
0.5 1 1.5 (GeV/c)"
2
Q2
Figure 5. Transverse helicity amplitude A112(Q2)for the Roper resonance. The full squared red symbol is a preliminary point from CLAS (see text). Comparisons with varies models are shown
CLAS state has a very small coupling to that channel I'Np/rtot(CLAS)M 0.17. Also, other parameters such as the total width rtot = 88 17MeV, and rArr/rtot = 0.41 f 0.13, and the photocoupling amplitudes, are quite different from what is known or expected from the PDG state. The question arises if the state could be one of the "missing" states. Capstick and Roberts 33 predict a state with these quantum numbers at a mass 1.85GeV. There are also predictions of a hybrid baryon state with these quantum numbers at about the same mass 35, although the rather hard form factor disfavors the hybrid baryon interpretation 21. As mass predictions in these models are uncertain to at least flOOMeV, interpretation of this state as a "missing" N$2+ is a definite possibility. Independent of possible interpretations, the hadronic properties of the state seen in the CLAS data appear incompatible with the properties of the known state with same quantum numbers as listed in Review of Particle Properties 36.
*
37
20
Figure 6.
-
Transverse helicity amplitude A1/*(Q2)for the first negative parity state
N:,2- (1535).
4.2 Hard nucleon spectroscopy The analysis of the p.rr+.rr- data within the Genova/Moscow isobar shows that the cross section ratio R= resonance/background at W = 1.7 GeV is strongly rising with Q2, from R=0.3 at the photon point to R=1.8 at Q2=1.3GeV2. Therefore, electron scattering a t relatively high photon virtuality, Q2, can provide much increased sensitivity in the study of at least some of the higher mass resonances. Qualitatively, this can he understood within a non-relativistic dynamical quark model 37,7. Photocoupling amplitudes for these states usually contain polynomials proportional to powers of the photon 3-momentum vector 14. For virtual photons the 3-momentum 141 for the transition to a given resonances increases with Q2 leading to an enhancement. In the case of the N;/2+ the non-relativistic quark model predicts A l p = C(ld lcj3/3a2)F(14), where a is the harmonic oscillator constant of the model, and F(lq'l) a formfactor which is common t o all states. To the degree that non-relativistic kinematics can he applied, spectroscopy of higher mass states at higher photon virtualities ("hard spectroscopy") has a distinct advantage over the real photon case: as the power n in 14" depends on the specific SU(6) @ O(3) multiplet a state is associated with, it allows enhancing the excitation of certain states over others by selecting specific Q2 ranges.
+
38 CW
25
L
n
g
9 .0
22.5 20
17.5 15 12.5
ir
"I
7.5
20
5
10
2.5
40
' l i ' '1:5
10
'
'lk
'
'1:;
'
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'
'119' '
'
2
'
'
'
0
lur
1.4
1.5
1.6
1.7
1.8
1.9
w GeV
1.4 W GeV
I
2
W GeV
15
1.6
1.7
1.8
1.9
2
I W GeV
Figure 7. Total photoabsorption cross section for y * p + pr+.rr-. Photoproduction data from DESY - top left panel. The other panels shows CLAS electroproduction data at Q2 = 0.65, 0.95, 1.30GeV2 .
4.3 Nucleon states an K A production Strangeness channels have recently been examined in photoproduction as a possible source of information on new baryon states, and candidate states have been discussed 2 8 ~ 8 . New CLAS electroproduction data 38 in the K A channel show clear evidence for resonance excitations at masses of 1.7 and 1.85 GeV as show in Fig. 8. The analysis of the K A channel is somewhat complicated by the large t-channel exchange contribution producing a peak at forward angles. To increase sensitivity to s-channel processes the data
39
0.15
GT + E L OL
:A f 0.1
Bz3
- 1 .- t
, +++++++
*
0.05-
t
tI 1* 16
I I
I
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17
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19
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21
*
.
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*=** 16
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17
18
19
2
21
I
I
W (GeV) CLAS for y'p -+ KfA. The left panel is integrated over the full forward hemisphere in the Kf angular distribution in the KfA cms. The right panel is integrated over the backward hemisphere W (GeV)
Figure 8. Total photoabsorption cross section measured with
have been divided into a set for the forward hemisphere and for the backward hemisphere. Clear structures in the invariant mass emerge for the backward hemisphere (right panel in Fig. 8). While the lower mass peak is probably due to known resonances, the peak near 1.85GeV maybe associated with the bump observed with the SAPHIR. detector 2 8 . A more complete analysis of the angular distribution and the energy-dependence is needed for more definite conclusions.
4.4 Resonances an Vartual Compton Scattering Virtual Compton scattering, i.e. the process y * p + m is yet another tool in the study of excited baryon states. This process has recently been measured by experiment E93-050 in JLab Hall A 39 at backward photon angles. The excitation spectrum exhibits clear resonance excitations in the mass regions of known states, the A(1232), N*(1520), and N*(1650). The main advantage of this purely electromagnetic process is the absence of final state interaction. This interaction complicates the interpretation of hadronic channels. A disadvantage is the low rate that makes it difficult to collect sufficient statistics for a full partial wave analysis.
40
5
Baryon spectroscopy at short distances
Inelastic virtual Compton scattering in the deep inelastic regime (DVSC) can provide a new avenue of resonance studies at the elementary quark level. The process of interest is y * p + yN*(A*) where the virtual photon has a high virtuality ( Q 2 ) . The virtual photons couples to an elementary quark with longitudinal momentum fraction 2 , which is re-absorbed into the baryonic system with momentum fraction z - <, after having emitted a high energy photon. The recoil baryon system may be a ground state proton or an excited state. The elastic DVCS process has recently been measured at JLab 41 and at DESY 40 in polarized electron proton scattering, and the results are consistent with predictions from perturbative QCD and the twist expansion for the process computed at the quark-gluon level. The theory is under control for small momentum transfer to the final state baryon. For the inelastic process, where a N' or A resonance is excited, the process can be used to study resonance transitions at the elementary quark level. Varying parameter E and the momentum transfer to the recoil baryon probes the two-parton correlation functions or generalized parton distributions (GPDs). That this process is indeed present at a measureable level is seen in the preliminary data from CLAS 42 shown in in Fig. 9. The reaction is measured at invariant masses W > 2 GeV. The recoiling baryonic system clearly shows the excitation of resonances, the A(1232), N*(1520), and N*(1680). While these are well known states that are also excited in the usual s-channel processes, the DVCS process has the advantage that it decouples the photon virtuality Q2 from the 4-momentum transfer to the baryon system. Q2 may be chosen sufficiently high such that the virtual photon couples to an elementary quark, while the momentum transfer to the nucleon system can be varied independently from small to large values. In this way, a theoretical framework employing perturbative methods can be used to probe the "soft" N N ' transition, allowing t o map out internal parton correlations for this transition. 6
Conclusions
Electroexcitation of nucleon resonances has evolved to an effective tool in studying nucleon structure in the regime of strong QCD and confinement. The new data from JLab in the A3/2+(1232) and N;,2- (1535) regions give a consistent picture of the Q2 evolution of the transition form factors. Large data sets in different channels including polarization observables will vastly improve the analysis of states such as the "Roper" Nil,+(1440), and many other higher mass states. A strong resonance signal near 1.72 GeV, seen
41
R
14+
JLubKLAS ep -> ey(X+ll) E = 4.3GeV W>2GeV Q2> I GeV2
I
1
12
1.4
16
18
2
22
I,
2.4
I
I
I
I I I
26
I ,
28
,I 3
M(x+n),GeV Figure 9. Inelastic deeply virtual Compton scattering measured in CLAS. The rccoiling (n~') system clearly shows the excitation of several resonances, the A(1232), N*(1520). and "(1680).
with CLAS in the p.lr+.lr- channel, exhibits hadronic properties which are incompatible with any of the known states in this mass region. While schannel resonance excitation will remain the backbone of the N * program for years to come, inelastic deeply virtual Compton scattering is a promising tool in resonance physics at the elementary parton level, which allows the study of parton-parton correlations within a well defined theoretical framework. The Southeastern Universities Research Association (SURA) operates the the Thomas Jefferson National Accelerator Facility for the United States Department of Energy under Contract No. DEAC05-84ER40150.
References
1. N. Isgur, in: Excited Nucleons and Hadron Structure, World Scientific, 2001, eds.: V. Burkert, L. Elouadrhiri, J. Kelly, R. Minehart. 2. V.D. Burkert, and Zh. Li, Phys.Rev.D47:46-50,1993 3. V.D. Burkert and B.L. Ioffe, Phys.Lett.B296:223-226,1992; J .Exp.T heor .Phys. 78:619-622,1994 4. J. Ahrens et al., Phys.Rev.Lett.87:022003,2001 5. R. De Vita, this conferences 6. V.D. Burkert, Nucl.Phys.A699:261-269,2002 7. R. Koniuk and N. Isgur, Phys.Rev.D21:1868,1980 8. A. d'Angelo, this conference
42
9. A. Buchmann and E. Henley, Phys.Rev.D65:073017,2002 10. T. Sat0 and T.S. Lee, T. Sato, this conferences 11. S.S. Kamalov and S.N. Yang, Phys.Rev.Lett.83:4494-4497,1999 12. R. Beck et al., Phys.Rev.C61:035204,2000 13. G. Blanpied et al., Phys.Rev.C64:025203,2001 14. V.V. Frnlov et al., Phys.Rev.Lett.82:45-48,1999 15. G. A. Warren, C.E. Carlson, Phys.Rev.D42:3020-3024,1990 16. A. Silva et al., Nucl.Phys.A675:637-657,2000 17. M. Warns, H. Schroder, W. Pfeil, H. Rollnik, Z.Phys.C45:627,1990 18. I.G. Aznaurian, Z.Phys.A346:297-305,1993 19. D. Leinweber, T. Draper, R.M. Woloshyn, Phys.Rev.D48:2230-2249,1993 20. K. .loo, et al, Phys. Rev. Lett. 88, 122001,2002; L.C. Smith, this conferences 21. Z.P. Li, V. Burkert, Zh. Li; Phys.Rev.D46, 70, 1992 22. F. Can0 and P. Gonzales, Phys.Lett.B431:270-276,1998 23. 0. Krehl, C. Hanhart, S. Krewald, J. Speth, Phys.Rev.C62:025207,2000 24. H. Egiyan, this conference 25. S. Sasaki, T. Blum, S. Ohta Phys.Rev.D65:074503 26. R. Thompson et al., Phys.Rev.Lett.86, 1702 (2001), H. Denizli, this conference 27. C.S. Armstrong et al., Phys.Rev.D60:052004,1999 28. M.Q. Tran et al., Phys.Lett.B445:20-26,1998 29. M.M. Giannini, E. Santopinto, A. Vassallo, Nucl.Phys.A699:308311,2002; E. Santopinto, this conference 30. N. Kaiser, P.B. Siegel, W. Weise, Phys.Lett.B362:23-28,1995 31. W.N. Cottingham and I.H. Dunbar, Z.Phys.C2, 41, 1979 32. M. Ftipani, Nucl.Phys.A699:270-277,2002 33. S. Capstick and W. Roberts, Phys.Rev.D49:4570-4586,1994 34. V.I. Mokeev, et al., Phys.Atom.Nucl.64:1292-1298,2001 35. S. Capstick, P.R. Page, Phys.Rev.D60:111501,1999 36. D.E. Groom et al., EL1r.Phys.J. C15, 1-878, 2000 37. L.A. Copley, G. Karl, E. Obryk, Nucl.Phys.B13:303-319,1969 38. G. Niculescu, this conferences; R. Feuerbach, private communications. 39. H. Fnnvieille, this conferences 40. A. Airapetian et al., Phys.Rev.Lett.87, 182001-l(2001) 4 1. S. Stepanyan et al., P hys.Rev.Lett .87,182002- 1(2001) 42. M. Guidal, private communications (2002)
BARYON SPECTROSCOPY ON THE LATTICE ROBERT G . EDWARDS Jefferson Lab 12000 Jeflerson Avenue Newport News, Virginia 23606, U S A E-mail:
[email protected] Recent lattice QCD calculations of the baryon spectrum are outlined.
1
Introduction
Quantum Chromodynamics (QCD) provides an excellent description of nature; however, the theory suffers from divergences that must be removed to render it finite. Lattice QCD provides an apriori non-perturbative regularization of QCD that makes it amenable to analytic and computational methods. No model assumptions other than QCD itself are needed to formulate the theory. This review surveys the rapidly evolving work in using Lattice QCD for calculations of baryon spectroscopy. Along the way, sources of systematic uncertainties in calculations are described and future directions are outlined. 1.1
Regularization of QCD on a lattice
As the starting point for lattice QCD, the path integral formulation in Euclidean space is used'. The usual continuous space-time of 4-dimensional continuum QCD are approximated with a discrete 4-dimensional lattice, with derivatives approximated by finite differences. Quarks are put on sites, gluons on links. Gluons are represented as 3 x 3 complex unitary matrices U,(z) = exp(igaA,(z)) elements of the group SU(3) with vector potential A,(z), coupling g , and lattice spacing a. The vacuum expectation value of operators involves path integration over gauge and fermion fields
-+
2'
1
dU, 0 (U,M-' ( U ) ) det ( M ( U ) )CSc(').
The Gaussian integration over the anti-commuting fermion fields $ result&l in the det(M(U)) and M - ' ( U ) factors with M ( U ) a lattice form of the Dirac operator. The gauge action & ( U ) approximates the Yang-Mills action of the continuum. The quenched approximation neglects the fermion determinant.
43
44
The choice of working in Euclidean space resulted in no factors of i in the exponent multiplying the gauge and fermion actions. The path integral therefore resembles a 4-dimensional statistical mechanical model making it amenable to analytic as well as Monte Carlo methods for evaluation. Numerical predictions from lattice QCD are in principle exact (to some precision) after systematic errors are controlled. The statistical uncertainties go like 1/mfor N configurations of gauge fields in a Monte Carlo ensemble average. Systematic uncertainties include: (1) Finite volume - the lattice 2fm or more is box must hold a hadron state, typically a lattice size of L needed. Several pion Compton wavelengths are needed m,L 4 . ( 2 ) Chiral extrapolations - calculations with small quark masses are expensive - extrapolate observables to physical quark mass region (delicate!). (3) Discretization effects: inherent O ( a ) or O(a’) lattice uncertainty. One must extrapolate to continuum limit ( a -+ 0) to recover physical quantities. N
2
Confinement and Model Predictions Potentials
-
- Static Quark
A particularly useful r61e of lattice QCD is model testing. There is significant recent activity in the study of 3 quark potentials which provide phenomenological insight into the forces inside a baryon. By gauge invariance, the quarks must be joined by 3 glue strings. These strings meet at a “gluon junction”, which has been conjectured to be a non-perturbative excitation of the QCD vacuum’. What is the area law behavior? One can test two ansatze. The Y-ansatz predicts the potential grows linearly like V,,, 0: o,,Ly where L y is the minimal length of the 3 flux tubes necessary to join the 3 quarks at the Steiner point. It is derived from strong coupling arguments3, and is consistent with the dual superconductivity confinement scenario. At large distances, the A-ansatz predicts instead that the potential grows linearly with the perimeter L a of the quark triangle, e.g. V,,, 0: a,,-La/2. It is derived from a model of confinement by center vortices using a topological argument4. ~ ? ~ Recent work6 claims There is controversy as to which a n ~ a t zholds. that at short distances the potential approaches the A-ansatz but rises like the Y-ansatz at large distances. Departures from the A-ansatz appear above d,, 0.7fm hence the A model is more appropriate inside a hadron. However, recently Simonov7claims there is a field strength depletion near the Y-junction which lowers the potential and could disguise the true behavior. Tests using adjoint sources could help reconcile the various claims. N
45
3 3.1
Hadron Spectrum Chiral Symmetry
As mentioned before, for accurate lattice calculations systematic uncertainties need to be controlled. The discretization of the Dirac operator has been particularly troublesome since lattice QCD’s inception and can significantly affect continuum and chiral extrapolations. The “doubling” problem is easily demonstrated by examining the lattice momentum representation of the free r,a, -+ $ C , 7, sin(up,). The propagator has Dirac operator, namely additional zeros at the momentum corners, e.g. up, = 0 , n so there are 16 species of fermions in general. Originally, Wilson lifted the doublers by adding a Laplacian term that breaks chiral symmetry. In fact, the Nielson-Ninornia no-go theorems state one cannot avoid both doubling and chiral symmetry breaking with a local, hermitian action analytic in the gauge fields. This major theoretical problem has been solved with the recent advent of chiral fermion actions8 (e.g., Domain-Wall or Overlap fermions) and their use is crucial for matrix elements. How important is chiral symmetry for spectroscopy studies? Renormalization theory tells us that breaking a symmetry leads to induced quantum terms in an action. The Wilson fermion action has U ( u ) scaling from the breaking of chiral symmetry. One can add a dimension 5 operator (hyper-fine term) and rigorously improve scaling from U ( u ) to O ( u 2 ) .Scaling violations are dramatically reduced - mostly from improving chiral symmetry. Scaling violations are comparable with chiral fermion formulations. The conclusion is that chiral symmetry is important for accurate spectrum calculationsg at comparatively heavy quark masses. However, the benefits of chiral fermion actions with exact chiral symmetry are now being dramatically demonstrated as near physical quark masses are approached as will be shown below.
c,
3.2
Quenched Pathologies in Hadron Spectrum
Clearly, precisely controlled lattice calculations come with the inclusion of the fermion determinant. However, because of their vastly reduced computational cost quenched calculations are quite prevalent and one can gain important phenomenological insight into QCD, but the potentially large systematic errors induced in this approximation should be carefully ascertained. Suppressing the fermion determinant leads to well known pathologies as studied in chiral perturbation theory”. There are missing vacuum contributions to
46
the disconnected piece of singlet correlators
These effects are manifested in the 7’ propagator missing vacuum contributions with new double pole divergences arising of the form 1
.
How dramatic are these quenched effects and to what extent do they affect the extraction of physical observables? One idea is to incorporate knowledge of quenched divergences in calculations and then attempt to extract useful information.
3.3 Decay in the Quenched Approximation The m; in Eq. (1) is the mass shift needed to recover the pseudoscalar sinthe unique piece of the 7’corglet mass from the non-singlet pion. In relator - the hairpin - was computed directly. The parameter m; was extracted and one sees the lattice data is well described by the xPT prediction. With the shift, the 7’ mass (at non-zero lattice spacing) is determined to be 820(30)MeV with possibly large O(a) scaling uncertaintities. A recent Domain Wall calculation” gives 940(4)MeV. Further dramatic behavior is seen in the isotriplet scalar particle ao. There is an 7’ - 7r intermediate state with missing contributions in the quenched approximation as shown in Fig. (1). In fact, the a0 correlator . xPT, one can goes negative - a clear sign of violations of ~ n i t a r i t y ’ ~From construct the a0 correlator by including couplings between 7’ - 7r states and rescattering states which can be resummed. The lightest a0 correlator is fairly well described by a 1-loop resummed bubble term with 7’ mass insertion fixed. A mass ma”= 1.34(9)GeV was found. The new Domain Wall calculation12 gives mat,= 1.04(7)GeV. The latter results does not exclude the possibility of aO(980) being a qq state.
’’,
3.4
Quenched and Full QCD Hadron Spectrum
The quenched low-lying hadron spectrum has been extensively studied by the CPPACS collaboration using Wilson fermions14. Masses were computed at four lattice spacings and extrapolated to the continuum limit. Lattice sizes
47
ICl
1,ms (lame
unnq
Figure 1. Left: contributions t o the a0 propagator from an q - 7r intermediate state. Right: comparison of scalar a0 propagator with the bubble sum formula fitted t o the interval t=1-6 (Ref. 13).
ranged up to 643 x 112 for a 3.2fm box. At each lattice spacing, the lightest pseudoscalar mass obtained was about 500 to 6OOMeV. Hadron masses were extrapolated in the quark mass via an ansatz motivated by the quenched xPT prediction
+
m $ ~= ,A(m1 ~ ~ m2){1- 6 [In ( 2 A m / A i ) ] m2/ (m2 - ml) ln ( m 2 / w ) }+ B ( m l + m2)2+ 0 (m3) (2) mH (mps) = mo Clpmps + C1m2,~ + C3pm3pS , C l p 0; 6 . The constants A , B , and Ci are fixed in the fits. Quenching effects were more clearly seen in the pseudoscalar channel. The calculation shows the basic hadron spectrum is well determined even in the quenched approximation t o within 10% accuracy. The computational cost was roughly 50 Gigaflop-years. A subsequent two-flavor dynamical calculation was made with four quark masses at 3 lattice spacings15. Box sizes range up to about 2.5fm. In the meson sector, the results are consistent with the original quenched calculations and now agree to within 1%of experiment. Systematic deviations of the quenched calculation from experiment are seen demonstrating that sea quark effects are important. The vector meson masses are increased after unquenching. This increased hyperfine splitting is consistent with the qualitative view that the spin-spin coupling in quenched QCD is suppressed compared to full QCD due to a faster running of the coupling constant. In the baryon sector, two-flavor dynamical sea quark effects are not as apparent. As seen in Fig. (2). The N and A masses are higher than experiment, but other masses are consistent. With only a 2.5fm box, finite-volume effects could well be large. Another concern is that the octet and decuplet chiral extrapolations have many parameters resulting in possibly underestimated er-
+
+
48
1.4
1.1
0.0
0.5 a p?t']
1
1.o
Figure 2. Baryon masses in twc-flavor (filled symbols) and quenched (open symbols) QCD. Both graphs have the same lattice spacing scale. (Ref.15).
rors and will be discussed more next. However, this is a significant calculation involving roughly one Teraflop-year of computations and well demonstrates the efficacy of lattice methods. 3.5 Improved Chiral Extrapolations The Adelaide group has been extensively studying higher order xPT effects on hadronic quantities16. The basic upshot is that the na'ive chiral extrapolations in use are just too na'ive! In particular, they incorporate leading non-analytic behavior from heavy baryon xPT arising from B + B'T B intermediate states with B = N , A ---f
n/r, = ( Y B +
P B ~ :+ C B ( m T , A )
(3)
where C B is a self-energy term. The coefficient of the m; term is actually known analyticl!ly in contrast to Eq. (2). The basic argument is since xPT has a zero radius of convergence (or certainly not a well defined radius), a simple leading order approximation to Eq. (3) is quite a bad approximation at moderate m,. They use a simple regularization of the self-energy term. Fig. (3) shows a comparison of a recent quenched and 2+ 1 dynamical calculation of the low lying hadron spectrum for a variant of staggered fermions at the same (physical) lattice spacing16. The various lines are from fits using Eq. (3). One can see that the self energy term becomes significant for small lattice quark masses. The intriguing result is that the fit parameters ( Y B and PB agree very well between the quenched and dynamical calculations. This
49 0.2 I
I
I
0.1
0.2
I
I
2.0
I
0.8 0.0
I
I
0.1
-203 0
0.0
-0.1 -0.2 -nn
. 1
I
0.0
0.3
m,,’ (CeV’)
0.4
0.5
0.6
‘
I 0.1
0.2
0.3 0.4 m,,’ (GeV’)
0.5
0.6
Figure 3. Left: contributions from various intermediate states to the quenched and unquenched self-energy term C. Right: fit (open squares) to lattice data - quenched (open A) and dynamical (filled A) with adjusted self-energy expressions accounting for finite volume and lattice spacing artifacts. The continuum limit of quenched (dashed lines) and dynamical (solid lines) are shown. The lower curves are for N and upper for A. (Ref. 16.)
result can be used to justify the claim that the dominant effects of quenching is attributed to first order meson loop corrections. While quite intriguing it is fair to say there is some controversy over these results. At issue is the concern that once one uses any model to directly interpret lattice results, one has lost predictably. However, in defense once one used a chiral extrapolation at all one has chosen a model. Ultimately, the Adelaide’s group work has shown that their is interesting structure in the “pion cloud” around a hadron and going to light quark masses is essential. 3.6 Excited Baryons
Understanding the N* spectrum gives vital clues about the dynamics of QCD and hadronic physics. Some open mysteries are what is the nature of the Roper resonance? Why is the ordering of the lowest-lying states - the positive and negative parity states - inverted between the N , A and A channels? The history of lattice studies of excited baryons is quite brief. Recently, new calculations are starting to appear using improved gauge and fermion actions. The nucleon channel is the most studied and work has focussed on two independent local interpolating fields
Ni = Eijk (uTCY.=jdj)U k
,
N2 = E i j k ( U T C d j ) 7 5 U k
.
(4)
Both interpolating fields couple to positive and negative parity states, so in practice parity projection techniques are used. Making the lattice anisotropic with finer discretization in time allows the behavior of the correlators to be
50 3.5
"."
,
I
0.0
I
I
0.8
0.4
0.6
0.8
m, (GeV.)
Figure 4. Left: effective masses for correlators with fields Eq. (4) corresponding to the nucleon (circles), its parity partner (diamonds) and tentatively the lowest positive parity excitation (cross) with an anisotropic clover action (Ref.17). Right: masses in physical units obtained with the isotropic Overlap action (Ref.l8). Solid symbols denote N ( 4 ' ) states: ground lowest
(0)
and 1st-excited (*). Empty symbols denote N ( $ - ) states: lowest (A) and 2nd
(a). The experimental points (*) are taken from PDG.
examined over many more time slices than on isotropic lattices. Additional tuning of the fermion action is needed to recover hypercubic symmetry. The left side of Fig. (4) shows the effective mass for the nucleon and its parity partner on an anisotropic lattice using the clover action" - an action improved to have reduced discretization uncertainties. Long plateaus (clean extraction of a mass) are seen demonstrating the efficacy of the method. For this quark mass, there appears to be the expected ordering of the states Nt1j2+ > N112- > N1/2f. However, there is difficulty in approaching small quark masses, and the mass extracted with the N2 operator appears too large. A recent quenched calculation" using Overlap fermions (a chiral fermion action) going to much smaller quark masses reveals a dramatic decrease in the nucleon masses extracted only with the N1 interpolating field as seen in the right side of Fig. (4). The authors claim the apparent crossing of the first excited N1/2 and lowest N1/2- states is the demonstration of the physically correct ordering of states. However, it is also possible that at such light quark masses a decay threshold has been crossed and the mass observed is affected by missing dynamical effects via the mechanisms described in Sec.3.3. If so, a finite volume check via shrinking the lattice box can reveal this. It is clear lattice calculations are really beginning to probe interesting excited state phenomena. With judicious use of finite volume techniques, physically relevant mass information can be extracted.
51
4
Conclusions
First generation lattice calculations of excited baryon spectroscopy are a p pearing. State of the art calculations require roughly 100 Gigaflop-year in quenched QCD and roughly 1 to 10 Teraflop-years in full QCD. The required resources are not available to the US lattice community. The Dept. of Energy’s SciDAC program is addressing this shortcoming and a large effort is ongoing in the U S . to meet future computational needs. Acknowledgments RGE was supported by DOE contract DEAC05-84ER40150 under which the Southeastern Universities Research Association (SURA) operates the Thomas Jefferson National Accelerator Facility (TJNAF). References 1. I. Montvay and G. Miinster, Quantum Fields on a Lattice, (Cambridge Univ. Press, 1994). 2. D. Kharzeev, Phys. Lett. B 378,238 (1996). 3. N. Isgur and J. Paton, Phys. Rev. D 31,2910 (1985). 4. J. M. Cornwall, Phys. Rev. D 54,6527 (1996). 5. T. T. Takahashi, et.al., Phys. Rev. D 65,114509 (2002). 6. C. Alexandrou, P. De Forcrand and A. Tsapalis, hep-lat/0209062. 7. D.S. Kuzmenko, Yu.A. Simonov, hep-ph/0202277. 8. D.B. Kaplan, Phys. Lett. B288, 342 (1992). R. Narayanan and H. Neuberger, Nucl. Phys. B443,305 (1995). 9. R.G. Edwards, U.M Heller, T.R. Klassen, Phys. Rev. Lett. 80, 3448 (1998). 10. B. Bardeen, et.al., Phys. Rev. D 62,114505 (2000). 11. C. Bernard and M. Golterman, Phys. Rev. D 46,853 (1992). S. Sharpe, Phys. Rev. D 46,3146 (1992). 12. S. Prelovsek and K. Orginos, heplat/0209132. 13. B. Bardeen, et.al., Phys. Rev. D 65,014509 (2002). 14. S. Aoki, et.al., Phys. Rev. Lett. 84, 238 (2000). 15. A. Ali Khan, et.al., Phys. Rev. D 65,054505 (2002). 16. R.D. Young, et.al., hep-lat/0111041. 17. R.G. Edwards, U. Heller, D. Richards, proceedings of Lattice 02. 18. F.X. Lee, et.al., heplat/0208070.
52
______
._
Lucy Collins, Rachel Harris, Linda Ceraul, Mary Fox, and Heather Ashley
Coffee break at CEBAF Center
HEAVY QUARK PHYSICS ON THE LATTICE C. T.H. DAVIES Department of Physics and Astronomy, University of Glasgow, Glasgow, GI2
uf(
SQQ, E-mail:
[email protected]. Irk I describe methods for dealing with b and c quarks within the lattice QCD approach and summarise recent results for phenomenologically important quantities.
1
Introduction
Lattice QCD is a well-established numerical approach to evaluating the Feynman path Integral for QCD, renderred finite by the discretisation of space-time into a Cdmensional lattice. A recent pedagogical review is given in RRf. 1. One of the main aims of this field is to calculate quantities for comparison to, or as predictions for, experiment. There is a long history of such calculations and the methods we use mean that there are systematic and st;b tistical uncertainties associated with the results. These uncertainties have improved steadily over the years, helped particularly by recent approaches to the improvement of systematic errors from discretisation. In many cases the largest remaining source of systematic error is that from the failure so far to include dynamical quarks in the vacuum with realistically low masses. We are now on the threshold of being able to overcome this source of uncertainty with new Teraflops computing power coming onstream in the next three years. This will mean an improvement of lattice systematic errors down to the level of a few percent (depending on the quantity calculated) and then lattice results can have a big impact on experiment. In particular I am concerned with calculations in heavy quark physics and there the determination of the sides of the CKM triangle w i l l be dominated by theoretical uncertainties unless these are improved to a few percent. Below I elaborate on heavy quark results &om current lattice Calculations. Most of these are still &om the quenched approximation, but the methods being developed are directly applicable to configurations which include dynamical quarks once we have them. 2
Heavy quarks on the lattice
Heavy (b or c) quarks present special challenges to lattice QCD because the quark mass in units of the lattice spacing, .mga 2 1. (on typical lattices,
53
54
mba M 2 - 3?m,a w 0.5 - 1. This means that relativistic momenta ji M TTZQ are very distorted by the lattice discretisation and the use of a naive relativistic lattice action (Wilson or clover quarks) will give large errors that depend on mga or ( T T Z Q U ) ~However, . one glance at the spectrum of bound states of b or c quarks shows that they are non-relativistic (the radial and orbital excitation energies are much smaller than the meson masses) and therefore it is possible to control these errors if we take a non-relativistic approach to the physics. Then b and c quarks can be treated accurately on the lattice and indeed heavy quarks physics is one of the most successful areas of lattice phenomenology. There are several ways to proceed, each with its differentproponents: Static quarks. This is the mg = 00 limit. Then the heavy quark is spinless and flavourless and the quark propagator becomes a string of gluon fields in the time direction '. This is a useful limit for comparison to continuum Heavy Quark EffectiveTheory. NRQCD. This is a non-relativistic effective theory with a 2-component heavy quark field 3.
The ci are h e d by matching to full continuum QCD. They represent the effect of states with momenta above the lattice cut-off, n / a , (missingfrom the lattice theory) and so this matching can be done in perturbation theory for large enough d u e s of the lattice cut-off. It may also be done non-perturbatively. The value of the bare mass,~ Q U is, tuned non-perturbatively by requiring one hadron mass to be correct (the standard method for tuning lattice masses). The lattice spacing, a, cannot be taken to zero in this approach to get to the continuum limit; instead we must systematically improve the matching to full continuum QCD by adding higher order terms to remove discretisation errors. We can also improve by adding higher order terms in the non-relativistic expansion and, in general, these two improvements go together. As m ~ -+a 00 we get the static limit. Heavy Wilson @arks (FNAL method). This approach uses the standard relativistic lattice quark action, but interprets the quark propagator in a non, remove a large part of the errors that relativistic way when fixing ~ Q U to this would otherwise give 4.
LQ = &?9
+ mga +
Fop)$
where the first two terms represent the lattice (Wiion) discretisation of the Dirac Lagrangian and the last term is the clover term. A systematic matching to full QCD is possible in this approach with wedependent coefficients. In
55 4.8
4.4
3.2
2.8
Figure 1. The charmonium spectrum from lattice QCD 7. Experimental results are giwn by dotted lines.
the small ~ Q limit U this approach yields standard light quark results. In the large ~ Q limit U it goes over essentially to NRQCD. Wdsson/clouer quarks. This uses the standard clover light quark action (as above), improved to remove the leading discretisation errors. The residual errors are O ( m ~ aand ) ~ may not be large for c quarks. HQET-inspired extrapolations to the b quark can be done provided that care is taken to untangle physical and unphysical (discretisation) dependence on the quark mass 5. These extrapolations tend to give large errors. Improvements to this method may be possible using anisotropiclattice techniques. Then the lattice spacing in the temporal direction is much smaller than that in the spatial direction and m ~ can & be small on manageable lattice volumes even for heavy quarks 7 .
3 The spectrum Extensive calculations of the heavyonium spectrum have been done with the NRQCD and heavy Wilson approaches and, more recently, with anisotropic clover. The static method gives the heavy quark potential which can then be solved within a potential model framework. Several of the radial and orbital excitation energies can be extracted if care is taken to use several different ‘sm&ngs’ to excite dif€erent states from the vacuum. Figure 1shows the charmonium spectrum obtained by the Columbia
56
group using the anisotropic clover action in the quenched approximation. In addition to the standard S, P and D states they find a signal for ‘hybrid’ gluonic excitations, some with exotic quantum numbers. It is important to fix the mass of these more precisely in the presence of dynamical quarks so that they c a be ~ found ~ in the next generation of experiments.
MeV
4
i
-**T
0
-20
t ___ : 0
:
4
:
Fxpaiment.
LatticeQuenchedapprmimatjon. Lattice N f = 2 dyn. quarks at m, from UKQCD.
: : IMrapolate to light d p .
ma6s and
Nf = 3.
Figure 2. Fine structure in the bottomonium spectrum from lattice QCD 8.
Figure 2 focusses on the fine structure in the bottomonium spectrum using NRQCD for the b quarks and comparing results in the quenched a p proximation to those including two flavours of clover dynamid quarks with severd masses dawn to a mass around the strange quark mass *. The hyperh e splitting, between the T and the q b , is obtained quite precisely on the lattice and there is a clear increase on including dynamical quarks and as the dynamical quark mass decreases. If the results are extrapolated linearly in
57
the dynamical quark mass to m,/3 and the number of dynamical flavours is extrapolated linearly to 3, a hypedine splitting of 60 f 15 MeV is obtained. A much more precise result should be possible on configurations with 2+1 flavours of lighter d y n d d quarks with improved detennination of the y codcients in the NRQCD Lagrangan. This will then provide a prediction for the mass of the q b , yet to be seen experimentally. The most complete determination of the spectrum of heavy-light bound states is based on using NRQCD for the b quark and the clover action for the light quark. Propagators for light quarks and heavy quarks are combined to make heavy-light mesons. Since it is not possible to generate light quark propagators with masses close to mU,deven in the quenched approximation, the results must be extrapolated to the chird (light quark) limit to reach the B. Figure 3 shows the spectrum from ref. in the quenched approximation. In common with results for the charmonium spectrum the hyperfine splitting, here between the B and the B' mesons, is underestimated. This is believed to be, at least partially, a result of the quenched approximation. Another source of underestimation is the coefficient, a,which multiplies the coupling of the quark spin to the chromomagnetic field in a non-relativistic treatment of heavy quarks. More precise determinations of this coefficient are underway lo.
B
B'
Figure 3. The spectrum of blight mesons from lattice QCD g .
58 Figure 4 shows results for the heavy-light-light baryon spectrum obtained in a similar way u. T
5.0
Figure 4. The spectrum of blight-light baryons from lattice QCD ”.
3.1 The b mass
Lattice QCD provides a non-perturbative method for fixing the bare quark mass in the lattice QCD Lagrangian. It can be adjusted until a particular hadron mass is correct. This bare m a s can then be converted ta any other mass desired, e.g. the quark mass in the MS scheme. In fact the best current determinationsof the b quark mass use, rather than the bare mass,the binding energy in the static limit. Then
& is the lattice energy ‘offset’ and is known in the quenched approximation, in the static limit, to O(lr:) 12. Z,,,,,t is the continuum renormalisation from h f to ~ mb in ~ the M S scheme and is also known to (?(a:) 13. New non-perturbative methods are also aalso being developed to fix & 14. The ‘world average’ for mb(mb) is currently 4.30(10) GeV in the quenched approximation l5. using the heavy Wilon and light clover methods Recent results on agree on a d u e of 1.26(13) GeV in the quenched approximation 16.
59
4 4.1
Matrix elements fB
The simplest matrix element to calculate is that for the leptonic decay of the B, mediated by the heavy-light axial vector current. The decay rate can be determined experimentally in principle but is difficult in practice so a precise lattice determination is useful.
B
Figure 5. Leptonic B decay.
'888891 '9294
'W97
'98
'99
Figure 6. A time history of lattice rasults for fB in the quenched approximation.
f~ is determined on the lattice from the matrix element of A, between the m u m and a B meson.
< OIApIB >= P p f B We must match A, on the lattice to full continuum QCD. This has been done to O(a,, l/mg, a) for NRQCD and heavy Wilson quarks, and these give
60
currently the most precise results, in agreement with each other 17. For light clover quarks the matching has been done non-perturbatively in the ma 4 0 limit and this cafl be used to obtain a result for fD and extrapolate to fB I*. Results for f~ have improved steadily over the yeass (see Figure 6) as improved techniques have given us more confidence in them. Table 1 gives the typical error budget for a current calculation of fB in the quenched approximation. World averages quoted at the recent Lattice Conferences are: = 173 rt 23 MeV = 203 f 14 MeV fB,/fB= 1-15(5);fD./fD = 1-16(4) 15319
fAQA' fh!A)
Table 1. A typical enor budget for a calculation of j~ in the quenched approximation.
source statistical + interp. disc. O((aA)2) Pert. aQ.2 4/(aM)) NRQCD O ( ( A / M ) 2cr,A/M) , light quark mass a-' (mp) Total
percent 3 4 7 2 +4 4 10
There is evidence that including dynmical quarks gives an increased d u e (by 20%) for fB depending on how the overall scale is determined 19.
The matrix elements for the Cquark operators of the effective weak Hamiltonian appropriate to Bo - B" mixing c i ~ nbe evaluated on the lattice. It is conventional to take the ratio of this to fg and call the answer BB. This is a somewhat harder calculation than f~ but the matching to the continuum has n m been improved to the same level as that for fB and the results from different methods are converging. World averages from recent Lattice Conferences l5>l9 are:
EB&= 1.30(12)(13); fBd&
= 230(40) MeV.
61
Figure 7. l%e box diagram for B0 operator.
mixing becoma the.matrix element of a kquark
1 ' ' ' ' 1 1.6 'T
a"
1.4
sE'dPfPL&kr: I&=& ' 1 ' 'APE extrap to B X Iellouchkln ,'3=6.Z + LeI!ouch&ii~~extrep ta li 0 JLQCD @=5.9 0 Gimenez&Reyes,UKQCD@=6.2+ Gimenez&Reyes,APE,9=6.0 Christensen et al. @=a.O , x m y fit, interp. of 0 ,00 X
m
-
1.2
-r
0.0
0.2
1/M,
0.4 0.6 (GeV)-'
0.8
Figure 8. A summary of results for BB from different methods in lattice QCD 19.
Figure 8 l9 plots a summary of results for BB at different values of the heavy quark mass, indicated by the inverse of the pseudoscalar heavy-light
62
meson mass. It shows clearly the different regions in which different methods work best, and indicates general agreement between the methods in the overlap regions. 4.3 B Semi-leptonic decay
B mesons decay semi-leptonically through the weak decay of the b quark to either a c quark or a u quark, and the decay of the virtual W particle to a lepton pair. The associated dements of the CKM matrix Vcb and Vub can be determined by a compaxison of the theoretical rate (proportional to the square of the unknown CKM element) with the experimental result. They are important inputs to constraints on the self-consistency of the Standard Model through the CKM triangle.
Figure 9. Semi-leptonic decay of a B meson.
B decay to D or D*mesons citn usefully be discussed within a framework in which we consider both the b and the c quarks as heavy and determine corrections to the infinite mass limit in terms of inverse powers of mb and m,. In the infinite mass limit, heavy quarks are spinless and flavorless, as discussed above. Then the form factors for decay B to D and B to D* and elastic B to B scattering all become the same, when plotted against the variable w v', where w is the initial meson and w' the final meson Cvelocity. This form factor is then known as the Isgur-Wise function and calculations on the lattice have been done using a variety of methods m. Of more direct use is a calculation of the form factor at the physical b and c masses in the zemrecoil limit (when V B - V D = 1). There are a number of theoretical simplifications in this limit and the experimental results can be extrapolated to this point for the case of B 4 D*.A direct comparison of the two yields Vcb. At last year's lattice conference there were new results from the FNAL
63
group on the B + D ' form factor at zero recoil using the Heavy Wilson method 21- After perturbative matching to the continuum they obtain a value for the form factor at zero recoil of 0.929(11) in the quenched approximation, X with an error significantly smaller than the experimental errors on V ~ this form factor. Unquenching affects the discrepancy of the theoretical result from unity and so is unlikely to change the result by more than one percent. B semi-leptonic decay to light hadrons is harder to tackle on the lattice because most of the experimental rate occurs where the 7~ or p meson has large momentum. When jh is large, there is the possibility of large discretisation errors. A number of groups have calculated the form factors for B 3 ?r decay but the results are still somewhat uncertain, depending markedly on how the extrapolation to physical light quark masses is done 15. There is also some dispute about how well the soft pion theorem j 0 ( h a z )= fB/ fm is satisfied 19. 5 Conclusions New calculations with much lighter dynamical quarks than before are on the horizon and this will result in significantlyimproved lattice results, to combine with improved experimental results over the next few years. Acknowledgments
I thank my collaborators,particularly S. Collins, J. Hein, G. P. Lepage anf J. Shigemitsu for many useful discussions. This work was supported by PPARC and the EU under HPRN-200@00145 Hadrons/Lattice QCD. References 1. C. T. H. Davies, Proceedings of the 55th Scottish Universities Summer School in Physics, St. Andrews, Scotland, August 2001, hepph/0205181. 2. E. Eichten, Nucl. Phys. B (Proc. Suppl. 4) (1988) 170. 3. B. A. T h d e r and G . P. Lepage, Phys. Rev D43 (1991) 196. 4. A. X. El-Khadra et al, Phys. Rev.D55 (1997) 3933. 5. C. Maynard: LATO1, Nucl. Phys. B (Proc. Suppl. 106) 388, h e p lat/0109026. 6. T. Klassen, Nucl. Phys. B533 (1998) 557. 7. P. Chen et alNucl. Phys. B (Proc. Suppl. 94) (2000) 342. 8. L. Marcantonio et 02 Nucl. Phys. B (Proc. Suppl. 94) (2000) 363. See also N. Eicker et d Phys. Rev.D57 (1998) 4080; T. Manke et al Phys. Rev. D62 (2000) 114508.
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9. J. Hein et 01 Phys. Rev. D62 (2000) 074503. 10. H. Trottier and G. P. Lepage: Nucl. Phys. B (Proc. Suppl. 63 (1998) 865. 11. A. Ali Khan et al Phys. Rev. D62 (2000) 054505. 12. F. Di %nu, and L. Scorzato, JHEP 0102 (2001) 020; G. P. Lepage et a1 Nucl. Phys. B (Proc. Suppl. 83 (2000) 866. 13. K. Melnikov and T. v;tn Ritbergen, Phys. Lett. B482 (2000) 99. 14. J. Heitger and R. Sommer, LATO1, Nucl. Phys. B (Proc. Suppl.l06), 358, heplat/0llOO16. 15. S. Ryan, LATO1, Nucl. Phys. B (Proc. Suppl.l06), 86. 16. D. Becirevic et al hepph/0107124; J . Juge, LATO1, Nucl. Phys. B (Proc. Suppl.106) 847, heplat/O110131. 17. JLQCD, Phys. Rev. Lett. 80 (1998) 5711; Phys. Rev. D61 (2000) 074501; A. Ali Khan et al Phys. Lett. B427 (1998) 132; A. El-Khadra et al Phys. Rev. D58 (1998) 014506. 18. D. Becirevic et 01 Phys. Rev. D60 (1999) 074501; K. Bawler et a1 heplat /0007020. 19. C. Bernard, Nucl. Phys. B (Proc. Suppl. 94)(2000) 159. 20. See, for a m p l e , G. Lacapha, LATO1, Nucl. Phys. B (Proc. Suppl.106) 373, heplat/O109006. 21. J. Simone, LATO1, Nucl. Phys. B (Proc. Suppl.), 394.
HADRONS IN THE NUCLEAR MEDIUM- ROLE OF LIGHT FRONT NUCLEAR THEORY GERALD A. MILLER Department of Physics, University of Washington Seattle, WA 98195-1560 E-mail:
[email protected] The problem of understanding the nuclear effects observed in lepton-nucleus deepinelastic-scattering (the EMC effect) is still with us. Standard nuclear models (those using only hadronic degrees of freedom) are not able to account for the EMC effect. Thus it is necessary to understand how the nuclear medium modifies quark wave functions in the nucleus. Possibilities for such modifications, represented by the quark meson coupling model, and the suppression of point-like-configurations are discussed, and methods to experimentally choose between these are reviewed.
1
Introduction
When the organizers asked me to give a talk entitled “Hadrons in the Nuclear Medium” I thought about what the title might mean. Since the nuclear mass M A M [ N M , Z M p ] ( l - 0.01), and nucleons are hadrons, maybe the title should be “Hadrons are the Nuclear Medium!”. On the other hand, the modern paradigm for the strong interaction is QCD and QCD is a theory of quarks and gluons. Maybe the title should be “Are Hadrons the Nuclear Medium?”. We have known, since the discovery of the EMC effect in 1982, that the structure functions measured in deep inelastic scattering from nuclear targets are not those of free nucleons. So one theme of this talk is to try to understand, interpret and use the EMC effect. Despite the age of this effect, no consensus has been reached regarding its interpretation, importance and implications. The second theme of this talk arises from the kinematic variables used to describe the data. The Bjorken x variable: x = Q 2 / 2 M v is, in the parton model, a ratio of quark to target momenta pz/Pz, where the superscript refers the plus-component of the four-momentum vector. This in turn can be written as: ( p $ / p $ ) (pZ/P;), so that one needs to know how often a nucleon has a given value of plus-momentum, p Z . Conventional nuclear wave functions are not expressed in terms of this variable, so one needs to derive nuclear wave functions which are expressed in terms of plus-momenta. Therefore, I assert that light front nuclear theory is needed.
+
+
65
66
2
Outline
I turn towards a more detailed outline. The first part of the talk is concerned with what I call the “Return of the EMC effect”. This is the statement that conventional nuclear physics does not explain the EMC effect. The physics here is subtle, so I believe that some formal development involving the construction of nuclear wave functions using light front nuclear theory is needed. I try to answer the simple queries: “light front theory- what is it? why use it?”. A partial answer is reviewed in Ref. The saturation of infinite nuclear matter using the mean field approximation is discussed here. The result is that there is no binding effect which explains the EMC e f f e ~ t ~ This ,~. statement is a natural consequence of the light version of the Hugenholtz-Van Hove Theorem4: the pressure of a stable system vanishes. If one goes beyond the mean-field calculations and includes correlations by using a Hamiltonian which involves only nucleon degrees of freedom, there is again no binding effect. Furthermore, I’ll argue that using mesons along with nucleons probably won’t allow a description of all the relevant data. It is therefore reasonable, proper and necessary to examine the subject of how the internal structure of a nucleon is modified by the nucleus to which it is bound. To see how the medium modifies the wave function of nucleon, a particular model of the free proton wave function5 is used. This allows the examination of two different and complementary ideas: the quark meson coupling model6 and the suppression of point-like-configurations7. A quick summary is that the goal is to explain EMC effect and then predict new experimental consequences. This god is not attained but is within reach.
’.
3
Return of the EMC effect
It is necessary to use nuclear wave functions in which one of the variables is the plus-momentum of a nucleon, &. Thus the use of light front quantization, or light-front dynamics, which I now try to explain, is necessary. 3.1 Light R o n t Quantization Lite Light-front dynamics is a relativistic many-body dynamics in which fields are quantized at a time"=^ = zo+z3 z+.The T-development operator is then - P3 G P-.These equations show the notation that a four-vector given by AP is expressed in terms of its f components A* E A’ f A3. One quantizes at z+ = 0 which is a light-front, hence the name “light front dynamics”. The
67
canonical spatial variable must be orthogonal to the time variable, and this is given by x- = xo - x3. The canonical momentum is then P+ = Po P 3 . The other coordinates are as usual XI and PI. The most important consequence of this is that the relation between energy and momentum of a free particle is given by:
+
a relativistic formula for the kinetic energy which does not contain a square root operator. This feature allows the separation of center of mass and relative coordinates, so that the computed wave functions are frame independent. The philosophy, for the beginning of this talk, is to use a Lagrangian density, L: which is converted into an energy-momentum tensor T P ” . The total-four-momentum operator is defined formally as
‘S
PP = -2
d2zldx-T+’,
(2)
with P+ as the “momentum” operator and P- as the ‘Lenergy”operator. We then need to express T+P in terms of independent variables. In particular, the nucleon, usually described as a four-component spinor, is a spin 1/2 particle and therefore there are only two independent degrees of freedom. I’ll start with the well-known Walecka model in which L(4,V P N , ) is expressed in terms of nucleon N , vector meson V p , and scalar meson 4 degrees of freedom. The plan is to first carry out calculations using the mean field approximation, and then include the effects of N N correlations using other Lagrangians. 3.2
Light Front Quantization
The mode equation for nucleons in infinite nuclear matter nuclear matter is given by
( I t - S U Y - ( M + 984))1c,= 0, (3) within the mean field approximation of the Walecka model. The quantity of relevance for understanding deep inelastic scattering is the nuclear plus component of momentum given by3 = (i@ + guV+) $+!A), (4) where $+ = $yay+$, the independent component of the nucleon field. Furthermore
68
In the rest frame we must have P i = MA, P i = MA = E A , a result not obvious from the above equations. However, if we minimize Pi subject to the constraint that the expectation value of ( P i - P i ) vanish, we indeed get the same EA as Walecka and more! The more refers to information about the plus momenta. The result P i = P i means P i = 0, which is a statement that pressure vanishes for a stable system. According to a venerable 1958 theorem by Hugenholtz & Van Hove, a vanishing pressure, plus the definition that the nucleon Fermi energy EF gives EF = = MA A = . Th'1s has important consequences now because we may express the result (4) as
9
P i = MA = A
J
Next we use a dimensionless variable y
d k + f N ( k + ) k+. E
a
(6)
5+ to find that (7)
which means that nucleons carry all of the plus momentum. The relevance of this can be seen by calculating the effects of nucleons in deep inelastic lepton nucleus scattering using a manifestly covariant calculation of the handbag diagram. One finds*
where
The quantity ~ ( kP,) is the nuclear expectation value of the connected part of the nucleon Green's function. This can easily be calculated for our light front nuclear wave functions. The result is
or
69
s
which obeys the baryon d y f N ( y ) = 1 and momentum (7) sum rules, so that nucleons carry all of the plus momentum. This is important because f ~ ( y is) narrowly peaked at y = 1 , so that F Z A ( Z AX) A F ~ N ( Z A )and , there is almost NO Binding Effect. One can see this more directly by expanding FZ(z/y)in Taylor seriesQ about y = 1 to find:
where c = 1 - fil?/MN M 161940. The resulting figure is shown as Fig. 2 of Ref.3, but Eq. ( 1 2 ) shows clearly that F Z N ( Z A ) / F 2 N ( Z ) is too large. Similar calculations can now be done for finite nuclei lo. Although being able to do these calculations is a major technical achievement (according to me), the results also show a huge disagreement with experiment. 3.3
Beyond the Mean Field Approximation
Suppose one assumes nucleons are the only degrees of freedom in the Hamiltonian, so that i
i<j
i<j
Any correct solution gives must be consistent with the Hugenholtz Van Hove Theorem P+ = P- = M A = P,$, so that once more one finds
One may again expand make an expansion about y = 1 to find that
s
dy f ~ ( y ) ( y 1)’. Again there is NO binding effect, and the where y = results are even worse, in comparison with experiment, than before. Using a more elaborate many-body calculation with a Hamiltonian involving only nucleons can not explain the EMC effect. 3.4
Nucleons N and Mesons m
The best version of the conventional approach is to explicitly include the effects of mesons. Then one may compute the nuclear expectation value of
70
so that one would find
J
dY fiv(Y) = 1 - f.
(17)
Many authors can reproduce the EMC binding effect using E M 0.07, but e x 0.07 corresponds to a BIG enhancement of the nuclear sea. Some time ago theorists suggested that the nuclear Drell-Yan process could be used to disentangle the EMC effect’l, but data from E772 at Fermilab12 showed no enhancement, and no nuclear effects. This finding was termed a “Crisis in Nuclear Theory” 13. 3.5 Summary of Return of the EMC Eflect
Conventional nuclear theory is unable to provide an explanation of the EMC effect. Mean field theory gives no EMC effect. Any theory involving using only nucleons as degrees of freedom gives no EMC effect. Including the effects of mesons explicitly (and not buried in the nucleon-nucleon potential) can provide an explanation or description of the EMC effect, but seems to cause a disagreement with the Drell-Yan data. Thus it is entirely legitimate, correct and proper to take very seriously the proposition that the structure of the nucleon is modified by its presence in the nuclear medium. 4
Non-Standard Nuclear Physics
The idea that modification of nucleon properties has important experimental consequences can be termed as non-standard nuclear physics. The main goal I wish to discuss here is that of first finding some model (or models) that reproduce both the EMC effect and the nuclear Drell-Yan data, and then predict other experimental consequences. There are many ideas in the literature. We shall take up only two here. The first involves nucleon wave function modification by the nuclear mean field. This is the quark meson coupling model introduced by Guichon‘ and applied to understanding the EMC effect by Saito and Thomas14. The nucleus is bound by the effects of mesons which are exchanged between quarks in different nucleons, so that the wave function of a quark in a bound nucleon is modified. The second idea involves the suppression of point like configurations (PLC), introduced by Frankfurt and Strikman7 as a consequence of the effects of color neutrality of nucleons. The idea is that the nucleon consists of an
71
infinite number of configurations of different sizes, each having different interactions with the nuclear medium. There are configurations with anti-quarks and gluons which are large and blob-like (BLC).These are influenced by the attractive force provided by other nucleons. There are also rarer configurations consisting of only three quarks which are close to each other. These PLC do not interact because the effects of gluons emitted by such a color-singlet configuration are canceled. The energy differences between the BLC and the rarer PLC are increased by the nuclear medium, so the probability of the PLC are decreased. This is the suppression we speak of. The validity of this idea was checked and confirmed by Frank, Jennings and Miller15. Our attitude is the the quark meson coupling model and the suppression of PLC are different reasonable hypotheses for nuclear modifications of nucleon wave functions which should be taken seriously. 4.1 Light Front Model of Proton
The basic idea is to put a nucleon in the medium and study how it responds to the external forces provided by the other nucleons. We need a relativistic model, and a convenient one is that of Schlumpfj , which was recently exploited by us15716.The model wave function is written in terms of light-cone variables and can be written schematically as
(Pi)
= U b l )U k 2
(P3)$ (Pl 7
p3) 7
(18)
in which pi represent space (cm), spin and isospin variables, and in which the u are conventional Dirac spinors. The function $ depends on spin and isospin and includes a spatially symmetric function @ ( M i ) .The quantity M i is the square of the mass of a non-interacting system of three quarks which plays the role that the square of spatial three momentum would in an ordinary wave function. Thus:
The wave function is now specified. It is expressed in terms of relative variables and is a boost invariant light front wave function. The first application is how the electromagnetic form factors are modified in the medium, so we need to consider the model's version of the form factors of a free nucleon. These are obtained by sandwiching the wave functions around the current operator J+ N y+. The evaluation of this Dirac operator is simplified by making a unitary transformation to represent the wave function Q in terms of light front spinors which have the nice property:
72
c~(p’X’)y+u~(pX) = 2p+6,4,41. This allows us to interpret the results in an analytic fashion. The coefficients of the unitary transformation are known as the Melosh transformation, and one example is given by
The basic idea is that the spin flip term given by ia . (n x p3) is as large as the non-spin Aip term given by rn + (1- 7)Mo. For large momentum transfer, Q , each of these is proportional to Q. The form factor F1 depends on the non-spin-flip term: F1 and F2 depends on the spin-flip term, so QF2 Q . . . , as well. Thus the ratio QF2IF1 is approximately constant for sufficiently large Q. The results are shown in Fig. 1 and are in good agreement with the recent exciting data17,18 . This means we have a reasonable model nucleon to put in the nuclear medium.
-
& . . a ,
N
4.2 Medium modifications of nuclear f o r m factors Let’s start with the quark meson coupling model QMC. We approximate that the nuclear scalar cr and vector potentials are constant over the volume of the nucleon. Then the modification is simply expressed as m + m - a,with the average scalar field experienced by a quark is given by a M 40 MeV. Thus we simply reduce the quark mass used in the previous calculation by 40 MeV. The results are shown in Figs. 2 and 3. These results seem to give huge effects, but one must understand that these are form factors evaluated in the nuclear ground state. The only attempts to observe such effects have involved using the ( e ,e‘p) reaction. Thus only the proton in the initial state is modified in the manner described here. Furthermore, the reaction occurs at the nuclear surface where the a field is falling off towards zero. When such realities are included, the results would be similar to the theory of Ref. 19, and similar to the 4He data of Dieterich et d 2 0 and the l60data Malov et aL21. For 4He, the actual effects are about four times smaller than shown here.
4.3 Suppression ofPLC The idea here is that the interaction of a bound nucleon with a nucleus depends on the distances between the quarks. The relevant operator is
73 1.0
0.8
0.6
0.4
Gf 0.2
0.0
0
2
4
Q2
8
6
10
GeV2
Figure 1. Calculation of Refs. l 5 , I 6 the data are from Ref. from Ref. 3.5 5 Q 2 5 5.5 GeV2
for 2
5 Q2 5 3.5 GeV2 and
so that the nuclear mean field U is given by
which vanishes for PLC. Then, in first-order perturbation theory, the modification of the expectation value of any operator 0 is given by
The resulting form factors are shown in Figs. 10,ll of Ref. 15. The effects of the medium are smaller here than for the QMC. But there are substantial modifications of the valence quark distribution functions, as shown in Fig. 16 of Ref. 15. These are relevant for understanding the EMC effect.
74 1.00
0.98
2
0.94
0
.A
4 (d
0.92
t 0.90
1
~
0
1
2
3
Q2
GeV2
4
5
6
Figure 2. Medium modifications of the ratio G E / G M ,QMC
4.4 Tagged structure functions There are many ideas available to explain EMC effect. More experiments are needed to select the correct ones. Here I only have room to discuss one possibility” in which one studies the reaction: e‘D -+ e N X for the kinematics of deep-inelastic scattering. The ratio
+ +
is extremely sensitive to the different models, in which models giving the same DIS have differences of more than 50%. This is shown in Fig. 6 of Ref. ”.
75 1.00
0.95
0.90
0.85 W
W L h
aw
0.80
\
Bw
0.75
0 0.70
0
1
2
3
Q2
GeV2
4
5
6
Figure 3. Medium modifications of the ratio G E / G I \ . ~QMC ,
5
Summary
The use of the standard, conventional meson-nucleon dynamics of nuclear physics is not able to explain the nuclear deepinelastic and Drell-Yan data. The logic behind this can be understood using the Hugenholtz-van Hove theorem4 which states that the stability (vanishing of pressure) causes the energy of the single particle state at the Fermi surface to be M A / A M 0 . 9 9 M ~ . In light front language, the vanishing pressure is achieved by obtaining P+ = P- = M A . But P+ = J d k + f ~ ( k + ) k + This, . combined with the relatively small value of the Fermi momentum (narrow width of f ~ ( k + ) )means that the probability f ~ ( k + )for a nucleon to have a given value of k+ must be narrowly peaked about k+ = 0 . 9 9 M ~M M N . Thus the effects of nuclear binding and Fermi motion play only a very limited role in the nuclear structure function, and the resulting function must very close to the one of a free nucleon unless some quark-gluon effects are included. This means that some
76
non-standard explanation involving quark-gluon degrees of freedom is necessary. Many contending non-standard ideas available. Testing these models, selecting the right ones, and ultimately determining the dynamical significance depends on having new high accuracy experiments at large momentum transfer and energy. Acknowledgments
This work is partially supported by the U.S. DOE. References 1. G. A. Miller, Prog. Part. Nucl. Phys. 45, 83 (2000) 2. M. C. Birse, Phys. Lett. B 299, 186 (1993). 3. G. A. Miller and J. R. Smith, Phys. Rev. C 65, 015211 (2002) 4. N. M. Hugenholtz and L. van Hove, Physica 24, 363 (1958) 5. F. Schlumpf, hep-ph/9211255. 6. P. A. Guichon, Phys. Lett. B 200, 235 (1988). 7. L. L. Frankfurt and M. I. Strikman, Nucl. Phys. B 250, 143 (1985). 8. H. Jung and G. A. Miller, Phys. Lett. B 200, 351 (1988). 9. L. L. Frankfurt and M. I. Strikman, Phys. Lett. B 183, 254 (1987). 10. J. R. Smith and G. A. Miller, Phys. Rev. C 65, 055206 (2002) 11. R. P. Bickerstaff, M. C. Birse and G. A. Miller, Phys. Rev. Lett. 53, 2532 (1984). M. Ericson and A. W. Thomas, Phys. Lett. B 148, 191 (1984). 12. D. M. Alde et al., Phys. Rev. Lett. 64, 2479 (1990). 13. G.F. Bertsch, L. Frankfurt, and M. Strikman, Science 259 (1993) 773. 14. K. Saito and A. W. Thomas, Nucl. Phys. A 574, 659 (1994). 15. M.R. Frank, B.K. Jennings and G.A. Miller, Phys. Rev. C 54,920 (1996). 16. G. A. Miller and M. R. Frank, nucl-th/0201021 t o appear Phys. Rev. C. 17. M. K. Jones e t al., Phys. Rev. Lett. 84, 1398 (2000) 18. 0. Gayou et al., Phys. Rev. Lett. 88, 092301 (2002). 19. D. H. Lu et al., Phys. Rev. C 60, 068201 (1999). 20. S. Dieterich et al., Nucl. Phys. A 690, 231 (2001). 21. S. Malov et al., Phys. Rev. C 62, 057302 (2000). 22. W. Melnitchouk, M. Sargsian and M. I. Strikman, Z. Phys. A 359, 99 (1997).
LL
POLARIZED STRUCTURE FUNCTIONS G. VAN DER STEENHOVEN Nationaal Instituut voor Kernfysica en Hoge-Energiejysica (NIKHEF) P.O. Box 41882, 1009 DB Amsterdam, The Netherlands E- m ail: yera rdOn ikh ef . nl A review is given of new experimental results that provide information on the spin structure of the nucleon. Inclusive measurements on a longitudinally polarized deuterium target have completed a set of high precision studies of the polarized structure function g1(z) carried out a t HERMES. A high luminosity experiment at SLAC on transversely polarized nucleon targets has produced data on the structure function g2(z). Measurements of the double-spin asymmetry for the photoproduction of pairs of oppositely charged high-pT hadron can be interpreted in terms of evidence for a positive gluon polarization. Exploratory measurements of the beam-spin asymmetry in deeply-virtual Compton scattering (at both HERMES and JLab) were successful, implying that this channel can - in principle- be used t o study the total angular momentum carried by the quarks. Small single-target spin asymmetries observed a t HERMES in semi-inclusive pion production experiments indicate that the only hitherto unmeasured leading order structure function: the transversity spin structure function h l ( z ) :is non-zero.
1
Introduction
According t o the axial anomaly there is a gluonic contribution to the first moment of the polarized structure function g1 (z)of the nucleon. As a result the total (longitudinal) angular momentum of the nucleon is redistributed in a non-trivial way among the constituents of the nucleon: 1 1 - = -A& + A G + L , : 2 2 where AX, represents the contribution of the quark spins! AG the contribution due to gluon polarization! and L , a possible contribution associated with the orbital angular momenta of quarks and gluons. As AX, is known to be relatively small since it was first measured by EMC' ! the other contributions must be significant. Sofar most of the experimental efforts in the field of spin physics have been dedicated to precise measurements of g1(z):from which AX, has been determined. However, in recent years qualitatively new information on the spin content of the nucleon has become available. Both SMC and HERMES have published the results of experiments in which the flavarious contributions These data to AX, were decomposed according to their quark flavour demonstrated that the u and d quarks are oppositely polarized. The question
78
79
that needs to be answered in the nearby future: is whether the sea-quarks contribute with any significance to the total nucleon spin. In section 2 and 3 of this paper new measurements on the spin structure function gl(z):and the flavour decomposition of the nucleon spin are presented, respectively. A value for the gluon polarization can be derived4 from the Q2 evolution of 91 (z). However, as the iincertainties involved are large, it is desirable to also measure AG in a more direct way. It has been argued that a measurement of the target-spin asymmetry of pairs of oppositely charged hadrons with high transverse momentum p l might provide such information5. Using this technique first (low statistics) results have now been obtained using polarized hydrogen and deuterium targets (see section 4). While a direct measurement of L, is not possible, Ji6 has shown that exclusive deeply virtual Compton scattering (DVCS) can be used t o obtain data on the total angular momenta carried by quarks ( J , ) and gluons (Jg). However, as the DVCS process is dominated by the Bethe-Heitler (BH) process up to relatively high incident energies, the process is only accessible through the interference of the DVCS and BH processes. In section 5 , first data on the interference term as obtained by HERMES' and JLab' are presented. All the abovementioned measurements provide information on the longitudinal spin structure of the nucleon. However, the transverse spin structure of the nucleon is expected t o be different as the gluon-splitting contribution is absent. This leads to dramatically different predictions for the distribution ~ . section of angular momentum over the constituents of the n u c l e ~ n ~ : 'In 6 experimental data are shown that seem to imply that the corresponding structure function hl (z) is indeed non-zero. The paper is concluded (in section 7) with a brief outlook on expected measurements that will be carried out in the nearby futures at COMPASS, HERMES, RHIC-Spin and SLAC. It is noted that only very few experimental aspects of the various measurements are described, as the emphasis in this paper is on a coherent description of the physics results that have been extracted from all the new measurements that are now available. 2
Polarized structure functions
The polarized structure functions g1 (z) and 92(2)contain information on the helicity-dependent quark contributions to the deepinelastic scattering cross section. By integrating gl(z) over z the total contribution AX, of the quark spins to the nucleon spin can be determined. The latest result reported by the HERMES collaboration3: which is largely based on measurements on a longitudinally polarized proton target, amounts t o AX, = 0.30 f 0.04 f 0.09
80
(at Q 2 = 2.5 GeV2). clearly showing the need for other soiirces of angular momentum in the nucleon. This conclusion was also obtained by the El55 collaboration" whose analysis yielded AX, = 0.23 f 0.04 f 0.06 at a somewhat higher value of Q' (5.0 GeV'). l 3 14. the emphasis of the With precise data on the proton available" most recent HERMES measurements was on the structure function gf(z).In the left-hand panel of figure 1 the resnlts are shown of an analysis of the data collected in the years 1999 and 2000 on a longitiidinally polarized deuterium target. Instead of the structure function gf(z). the following ratio is displayed:
in which F;" represents one of the unpolarized deuteron structure functions, y and 71are kinematic factors: D is the virtual-photon depolarization factor: Ad /I the measured (raw) asymmetry and A$ the (small) transverse contamination of the asymmetry due to the transverse structure function g$. The ratio g;'/Ff is more directly related to the measured asymmetry '47,; and only involves a choice for the value of A$: for which the recent SLAC results are taken I 4 , l 5 . The results are seen to agree with those obtained at SLAC'1:'4 and CERNI3, but have an improved precision. Since the CERN data have been collected at a considerably higher average Q' value as compared to both the HERMES and SLAC data, the consistency of the various data sets implies that the Q2dependence of g;' is similar to that of FP. Using a parameterization for F P ( z ) :the structure function g f ( z ) has been evaluated. The results are plotted - together with those obtained on polarized proton and 3He targets 1 6 ~ 1 7 ~ 1-8 in the right-hand panel of figure 1. It is concluded that all available data are in good in agreement which each other for each target. Improvements of the data are only needed at very low values of 3: (below 0.004) and very high values of z (above 0.6). As can be seen from Eq. (2) it is important to avail of measurements of the structure function g2(z), from which values for the asymmetry A 2 ( z ) can be derived. It is also of intrinsic interest to measure the structure function g 2 ( 2 ) , since it may provide information on possible non-zero twist-3 contributions. show, however, that the data are The new data obtained at SLAC14~'5~'9 consistent with the Wandzura-Wilczek approximation for g2(z) which only includes the twist-2 part as derived from g1 ( z ) .
81
as
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~ € R ~MR ~~L I~M ~ N A R ~
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('Wdata, no smearing correction)
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Figure 1 . Left: the ratio of the longitudinal spin-dependent structure function g1(z) and the unpolarized structure function F1 (z) as measured by various experiments on a longitudinally polarized deuterium target. In the lower panel the average Q2 value of each measurement for both the NMC data and the HERMES data is shown. Right: the longitudinal spin-dependent structure function g1 (z) (multiplied by z) as measured on longitudinally polarized hydrogen (top panel). deuterium (middle panel) and 3He (lower panel) targets.
3
Flavour decomposition of the nucleon spin
Semi-inclusive deepinelastic scattering experiments that make use of both polarized lepton beams and polarized targets are - in principle - able to determine the polarized quark distributions A q f ( z )for each flavour f . From the experimental data the double spin-asymmetries At (z) are determined for different hadron types h . The asymmetries A: (z) are related to the quark distributions A q j ( z ) through the so-called purity matrix p j . which describes the probability that a hadron h originates from a quark of flavour f . The value of the matrix elements p j is determined from Monte-Carlo simulations based on the Lund string fragmentation model. Using this technique the HERMES collaboration3 has obtained values for Aq,, . Aqd and Aq,,, which are shown in the left panel of figure 2. These data are in agreement with somewhat less precise results that were earlier obtained by SMC'.
82
0.5
0.25
f t
.
*
.
.
.
a
. . . . .
*
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0 4.5
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1
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0.02
--
..~ '
'
'
'
'
'
'
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1 0.7 X
Figure 2 . Left: the longitudinalquark spin distributionfor u-quarks (upperpanel),d-quarks (middle panel) and sea-quarks (bottom panel). The hatched areas represent the systematic uncertainties of the data. The data are the result of an analysis that includes all HERMES data as obtained (on polarized hydrogen: deuterium and 3He targets) between 1995 and spring 1999. Right: simulation of the expected precision of the data that will be obtained if all data collected by HERMES until August ZOO0 are included (closed circles).
Since the results of Ref. 3 were published, the HERMES collaboration collected a large amount of data on a longitudinally polarized deuterium target. As the d-quark purities on deuterium are on average larger than those on hydrogen, these data contain important additional information. Part of the new deuterium data set was included in the results for the quark polarizations (Aq Aq)/(q @)shown in the left panel of figure 2. From these and previous data it is concluded that the u-quarks are strongly polarized in a direction parallel t o that of the proton polarization, while the d quarks are weakly polarized in the opposite direction. The sea quarks are seen to carry little angular momentum: at least when summed over all flavours. If all data collected by the HERMES collaboration in the year 2000 will have been included in this analysis a precise flavour decomposition of the nucleon spin structure functions can be carried out. This is illustrated in the
+
+
83 HERMES PRELIMINAR(
0.2 :
t
o!
p p (GeVlc)
(GeVls)
-0.2 : -0.4 I -0.6
_ - - GSA (4W& - 0.4) . . G S B ( 4 W O - 0.3) : -.-.-, GSC (4W& - -0.1)
.
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Figure 3. Left: the longitudinal double-spin asymmetry for the photoproduction of pairs of oppositely charged high-pT hadrons on a polarized hydrogen target. While placing a p ~ requirement on one of the hadrons, the asymmetry is plotted as a function of the pT-value of the other hadron. Right: the same quantity obtained on a polarized deuterium target. The superscript h+(h-) refers to the charge of the hadron, while the superscript hl(h2) refers t o the leading versus the non-leading hadron. In the lower right panel the asymmetry is shown for identified pion pairs.
right panel of figure 2 which shows the results of a Monte-Carlo simulation that is based on the statistics which have actually been collected on each target by the experiment. As the 2000 data have been obtained using a RICH detector, separate double-spin asymmetries can be evaluated for protons, pions and kaons. Consequently it will be possible to obtain flavour-separated information on the spin structure of the sea quarks. 4
Photoproduction of pairs of high-pT hadrons
Precise measurements of the gluon polarization AG in the nucleon do not exist. A first attempt to determine AG was reported by SMC4. A nexttdeading order QCD analysis of the measured &'-dependence of g1(z: &') yielded an integral value of AG = 0.99+~:~:~~:",',";~~~ i.e. the data do not put large constraints on the gluon polarization. The first direct study of AG/G has been carried out by the HERMES collab~ration'~.By measuring the double-spin asymmetry for photoproduction of oppositely charged high-p.r hadron pairs on a longitudinally polarized
84
hydrogen target, a value of AGlG = 0.41 f 0.18 f 0.03 was obtained at < ZG > = 0.17 and < Q2 > = 0.06 GeV2 (left panel of figure 3). Cnfortunately, this value is model dependent as a Monte-Carlo simulation was needed to determine the relative importance of the photon-gluon fusion and QCD Compton contributions to the yield. In the analysis of these data a pair of oppositely charged hadrons is required. This favours the relevant photon-gluon fusion process, since it leads to oppositely charged hadrons pairs while the competing QCD Compton process will result in more positively charged hadrons (u-quark dominance). This argument'fails if a polarized deuterium target is used. Hence: a smaller asymmetry (if any) is expected on deuterium. The data obtained on a polarized deuterium target are shown in the right panel of figure 3: where the doublespin asymmetry for pairs of high-plr hadrons is observed to be consistent with zero. Detailed Monte-Carlo studies are in progress in order to investigate whether the results obtained on hydrogen and deuterium are consistent. Considerably more precise values of AGIG are expected to come from dedicated measurements at COMPASS, RHIC-spin and SLAC. 5
Deeply virtual Compton scattering
Deeply virtual Compton scattering (DVCS) provides information on the generalized parton distributions (GPDs), which encompass both the well-known parton distribution functions (PDFs) and the niicleon form factors as limiting cases. While the PDFs describe the probability to find a parton with fractional momentum z in the nucleon (forward scattering), the GPDs describe the interference or correlation between two quarks with momentum fractions z and z - [ in the nucleon (off-forward scattering). Hence: the GPD's are sensitive to partonic correlations. In 1997 Ji6 has shown that the first moment of certain GPDs, which can be measured in DVCS: can be related to the total angular momentum of the quarks and the gluons in the nucleon. For that reason the experimental prospects of observing DVCS were being widely discussed. The problem is that it is difficult to observe photons originating from DVCS in an electron scattering environment, because of the dominance of the Bethe-Heitler (BH) process. However, by exploiting the interference between the DVCS and BH processes, one may obtain access to the DVCS amplitude**. As the interference term in the cross section depends on the beam polarization and the azimuthal angle q5 (with respect to direction of the virtual photon), measurements of the &dependence of the beam-spin asymmetry are needed. The beam-spin asymmetry in hard electroproduction of photons has been
+[
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HERMES PRELIMINARY 2wO
-0.6 2
3
1
2
3
4
5
6
7
8
9
1
@ @ad) Figure 4. Left: single beam-spin asymmetry for electroproduction of real photons on an unpolarized hydrogen target as a function of the azimuthal angle 4. The curve represents a sin+fit to the data, of which the amplitude ( p 2 ) and offset ( p l ) are shown. Right: the s i n 4 moment of the beam-spin asymmetry as a function of the squared four-momentum transfer Q2.The hatched area in both panels represents the systematic uncertainty.
measured both by the HERMES experiment at DESY7 and the CLAS experiment at JLab'. In both cases an asymmetry with respect to the helicity state of the incoming lepton beam is observed as a function of the azimuthal angle q5 for data with a missing energy close to the proton mass. The data show a clear sin 4 dependence. an effect caused by the DVCS-BH interference. Since the first results were published. additional DVCS analyses have been carried out by the HERMES collaboration. In the left panel of figure 4 the beam-spin asymmetry is shown as a function of q5 for data collected in the year 2000. The previous observations (which were based on data collected in the year 1997) are confirmed with improved statistics. Moreover. the Q2dependence of the beam-spin analyzing power A$#. which is defined as
where (Pi)
86
P1 I -0.05 t 0.03 (Stat)
A p
l~x<,.,E."=o.ll t0.04(stal)tO.ffl(syo
-01 -0.6
-3
-2
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1
2
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0
1
2
3
4
5
6
o Wad) Figure 5. Left: single beam-chargeasymmetry for the electroproduction of real photons on an unpolarized hydrogen target as a function of the azimuthal angle 9. The curve represents a cos&fit to the data, of which the amplitude ( p 2 ) and offset ( p l ) are shown. Right: the cos+ moment of the single beam-charge asymmetry as a function of the missing mass Mz. The average value of the cos 4 moment of the low M, data is displayed as well.
binning in both x: t and Q 2 : there can be compensating kinematic dependences. If it is assumed that such compensating effects are small: the data possibly provide a first hint that the scaling domain (where the observables should be Q2 independent) has been reached in these measurements. However: the precision of the data has to be improved considerably before more definite conclusions can be drawn. While the beam-spin asymmetries give information on the imaginary part of the DVCS-BH interference amplitudes, the beam-charge asymmetry is sensitive to the real part of these amplitudes. A measurement of the beam-charge asymmetry requires the availability of both electron and positron data at the same experimental set-up. At HERA both types of lepton beams are produced. thus enabling measurements of this kind. In figure 5 the first measurements of the single beam-charge asymmetry for electroproduction of real photons on an unpolarized hydrogen target are shown. The data have low statistics. but do show evidence of the expected cos q5 dependence21. If the cos &moment of the data is evaluated (as displayed in the right panel of figure 5) non-zero values are only seen in the 'exclusive' region around M, %= mproton.The finite resolution7 causes the signal to spread over various bins surrounding the bin at M , % mproton.
87 0.1 HERMES PRELIMINARY
0.04
deuteron
0.2u4.7 0.075
*
0.05
0.02
0.025
0 0
-0.02
0
0.1
0.2
0.3
0
0.1
0.2
0.3
Figure 6. Left: the sin4 moment of the single target-spin asymmetry for electroproduction
of positive and negative pions on a longitudinally polarized deuterium target as a function of zg. Right: the sin 4 moment of the single target-spin asymmetry for positive kaons. The hatched areas in both panels represent the systematic uncertainty.
The new DVCS data demonstrate the feasibility of studying Compton scattering at the partonic level. It is also clear that the statistics of such measurements have to be dramatically improved before DVCS data can be used to extract information on the total angular momentum carried by quarks.
6
Transverse spin
Apart from the structure functions F1.2(2) and g1:2(z): there is a third leadingtwist structure function h l ( z ) that is' known as the transversity distribution. It is of great interest to measure h l ( z ) : for which no data exist: since the transverse spin structure of the nucleon is expected t o be considerably different from the longitudinal spin structure. Both chiral-soliton (instanton) modelsg and lattice gauge calculations" predict that the tensor charge SC, is considerably larger than the longitudinal quark spin contribution AC,. This is caused by the absence of gluon-splitting in the transverse case which results in the predicted relatively weak Q 2 dependence of h 1 ( z ) . Inclusive deepinelastic scattering cannot be used to measure h , ( z ) as it is a chirally-odd quantity. In semi-inclusive DIS information on h l ( z ) can be obtained if combined with a chirally-odd fragmentation function 22.
88
First evidence of a non-zero transversity distribution has been reported by HERMES*3. In this experiment the single target-spin asymmetry for leptoprodiiction of pions was measured on a longitudinally polarized hydrogen target. The data show a small semi-inclusive asymmetry. It can be explained from the small transverse polarization component of the virtnal photon combined with reasonable non-zero values for hl ( x ) and the corresponding chirally-odd fragment at ion fimction. In figure 6 new semi-inclusive single-spin asymmetry data are shown: also measiired by HERMES, but this time using a longitudinally polarized deuterium target. A small positive asymmetry is observed both for pions and kaons. In this case the T- asymmetry is of similar size as the T+ asymmetry, while on hydrogen (not shown) the T- asymmetry is consistent with zero. This is probably related to the reduced importance of u-quark dominance in deuterium. On the basis of the small asymmetries observed on longitiidinally polarized targets, it is expected that sizable asymmetries will be observed if transversely polarized targets are used. Such measiirements are foreseen at HERMES in the near future.
7
Outlook
Experiments studying the angular momentum composition of the nucleon have expanded considerably beyond inclusive deepinelastic scattering experiments with polarized beams and targets. Besides very precise data on gl(+), which became available recently, a whole new class of measiirements has been started. In this context the measurement of the gluon polarization plays a central role. The prospects for such measurements have improved dramatically in the last couple of months. At CERN the COMPASS experiment has been successfully commissioned, and extensive data taking is foreseen in 2002. At BNL it has been demonstrated that it is possible to inject and maintain polarization in proton-proton collisions at RHIC. Moreover. a dedicated gluon polarization experiment (E161) is scheduled at SLAC. It is expected that these experiments (together with the recently started run I1 at HERMES) will not only provide precise measurements of the gluon polarization in the nucleon: but also yield new and complementary data on the flavour decomposed quark spin distributions and the transversity distribution. At the same time new plans have been initiated to further exploit deeply virtual Compton scattering measurements at JLab (CLAS Collaboration) and DESY (HERMES). Hence, there is every reason to believe that o u r understanding of the origin of the nucleon spin will improve significantly in the next couple of years.
89
Acknowledgnient s I would like t o thank all my collegues from the HERMES collaboration for making it possible t o perform an experiment that has produced so many highquality data. I am also grateful to Eva Kabuss (COMPASS). Peter Bosted (SLAC) and Matthias Grosse Perdekamp (BNL) for updating me on the statns of their respective experiments. Wolf-Dieter Kowak and Dirk Ryckbosch are acknowledged for providing me with some helpful suggestions. References J . Ashman et 01 (EMC), Phys. Lett. B 206: 364 (1988). B. Adeva e t a1 (SMC): Phys. Lett. B 420, 180 (1998). K. Ackerstaff et a1 (HERMES)! Phys. Lett. B 464, 123 (1999). B. Adeva et a1 (SMC): Phys. Rev. D 58: 112002 (1998): A. Bravar, D. von Harrach: A. Kotzinian, Phys. Lett. B 421: 349 (1998). X. Ji! Phys. Rev. D 55: 7114 (1997). A. Airapetian et a1 (HERMES), Phys. Rev. Lett. 87:182001 (2001). S. Stepanyan et a1 (CLAS), Phys. Rev. Lett. 87,182002 (2001). H-C. Kim e t a1 Phys. Rev. D 53; R4715 (1996). S. Aoki et 01 Phys. Rev. D 56: 433 (1997). P.L. Anthony et 01 (E155): Phys. Lett. B 463, 339 (1999); and Phys. Lett. B 493, 19 (1999). 12. A. Airapetian et a1 (HERMES): Phys. Lett. B 442: 484 (1998). 13. B. Adeva et a1 (SMC): Phys. Rev. D 58, 112001 (1998); and Phy.9. Rez;. D 60: 072004 (1999). 14. K. Abe et a1 (E143): Phys. Rev. Lett. 76: 587 (1996); and Phys. Reti. D 58: 112003 (1998). 15. P.L. Anthony et 01 (E155): Phys. Lett. B 458: 529 (1999). 16. P.L. Anthony et a1 (E142): Phys. Rev. Lett. 71, 959 (1993); and Phys. Reti. D 54: 6620 (1996). 17. K . Abe et a1 (E154): Phys. Rev. Lett. 79:26 (1997). 18. K . Ackerstaff et a1 (HERMES): Phy.9. Lett. B 404: 383 (1997). 19. P. Bosted et al (E155x): private communication. 20. A. Airapetian et a1 (HERMES), Phys. Reti. Lett. 84: 2584 (2000). 21. M. Diehl et al: Phys. Lett. B 411: 193 (1997). 22. P.J. Mulders and R.D. Tangerman: Nucl. Phys. B 461, 197 (1996). 23. A. Airapetian e t a1 (HERMES): Phys. Rev. Lett. 84: 4047 (2000); and Phys. Rev. D 64: 097101 (2001). 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
PROTON STRUCTURE RESULTS FROM THE HERA COLLIDER R. YOSHIDA Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439 E-mail: rik.yoshidaOanl.gov Recent HERA4data on small-z structure functions as well as DIS dilTraction are presented. The relationship between these processes and possible indications of dynamics beyond the DGLAP formalism are discussed.
1 1.1
Proton Structure Function
F 2
Deep Inelastic Scattering and
F 2
at Small-x
Deep 1nelast)icScattering (DIS) of electrons (or posit,rons) with a prot,on proceeds through the exchange of a virtual boson; in the kinematic range covered in t#histalk, only photon exchange is important,. The reaction can be described completely by two kinematic variables chosen to be the four-momentum transfer squared, Q2 = -q2, and the Bjorken variable] x. In the Quark Parton Model, x is the fraction of the initial proton momentum carried by the struck parton. The DIS cross-section factorizes into a short-distance part which is the partonic cross-section, 6,which can be calculated perturbatively in QCD, and a long-distance non-perturbative part , the parton densities, f . .4t sufficiently high Q2, the parton densities, f , obey the DGLAP equation l , which is written schematically as, d f /dln Q2 f 8 P , where P are the splitting functions that describe the branching of quarks and gluons, and 8 symbolizes a convolution. The DIS differential cross-section can be written in terms of the proton structure function F2 as N
where y = Q2/xs is the inelasticity parameter, and s is the ChlS energy squared of the ep collision. The longitudinal structure function FL and the effects of 2' exchange have been neglected in Equation (1). .4t leading order,
90
91
where q , are the quark and antiquark distributions, respectively. The measurements of F2 a t HERA show that the structure function rises steeply at small x (see Figure 1) 2,3. If F2 a t x < 0.1 is parameterized as 0: x - ~ then , X falls as a function of Q2 from about 0.4 to 0.1 as Q2 falls from 200 GeV2 to 1 GeV2. A4tQ2 of 10 GeV2, X is about. 0.24,5. The naive physical interpretation of the small-x rise of F2 is that it, is caused by more and more gluons (and thus seaquarks) being present at smaller and smaller fractional momenta values, i.e. 2. The scaling violations of Fz (i.e. the Q2 dependence of F2 at, fixed x) at low x are related, in Leading Order (LO) DGLAP, simply t o the gluon density of the proton 6 ,
Figure 1. World’s data on FZ at Q2 = 15 GeV2 as a function of r. The solid line is a DGLAP fit by the CTEQ group.
In Next-to-LO (NLO) DGLAP, the simple relationship of Equation (4) no longer holds. However, the gluon density may be extracted from the NLO DGLAP fits to F2. In keeping with the naive expectation of a gluon-driven F2, these gluons also rise steeply at low x. A4sQ 2 falls, the steepness of the gluon becomes less, as in the case of F2 itself.
1.2 Beyond DGLAP? The interest in small-x physics is that the partons under study are the result of a large number of QCD branching processes. The evolution of the number of partons over a wide kinematic range in x and Q2 should be sensitive t o the applicability of different perturbative approximations of QCD. Figure 2 shows the qualitative expectation of applicability of various pQCD approaches. DGLAP is a resummation of terms proportional to (In Q 2 ) and is expected t o hold in the region of large Q 2 . BFKL is a resummation of terms proportional t o (In l / x ) and, while the stability of the perturbat,ive expansion still under study it is expected t o hold in the region of small x. The CCFM lo equation incorporates both (In l / x ) and (In Q 2 ) terms.
92
At, small enough 2 , the density of partons should become sufficiently UIOO large so that, the interactions between them become important. This lboundary is marked in Figure 2 by 1 u the line labeled “critical line”. The GLR equations “ . l 2 attempt, to take ia these saturation, or shadowing, ef10 D G U W fects into account. I 1 1 I It has been shown that, the 1 U loo WI DGLA4P formalism is able t o de02rGeY*l scribe the currently available F2 data Figure 2. Schematic diagram of the applidown t,o 1 Ge\J2 and 2 of 10-5 in apcability of different pQCD approximations. parent contradiction t,o Figure 2 , at, least with the 1/z scale numbers as drawn. On the other hand, there have also been successful fits t,o a wide range of F2 data using formalisms that incorporate the (In l/z) terms as well as the (lnQ2) terms 1 3 J 4 . In search of clarification, we turn next, t o the phenomenon of DIS diffraction before returning to consider if there are any indications in the F2 data for dynamics beyond DGLAP. ~
I I@
2
a
Diffraction in DIS
One of t,he striking results from HERA is the presence of diffractive events in DIS 15,16 . -4bout 10% of all DIS events have a gap in particle emission between the finalstate proton, or a low mass state, which travels down the beampipe, and the system X , which is measured in the detector (Figure 3). Such a reaction is usually described as an exchange of a colorless object, generically called the Pomeron (IF’). In order t o describe diffractive DIS, two kinematic variables in addition t o x and Q2 are needed. These are t , which is the momenturn transfer at the proton vertex and zp, which is the fractional momentum of
+
P‘
Figure 3. Diffractive DIS scattering.
93
the proton carried by the Pomeron. Another useful variable is = x / x p , which has an interpretfation as the fractional momentum of the Pomeron carried by the struck parton (i.e. the Pomeron analogue of TC for the proton). Any perturbative description of diffractive DIS must, go beyond the simplest. DGLAP picture; t,he lack of color connections between the system X and the proton must mean that, at least t,wo gluons are exchanged. It, is then interest,ing to investigate the connection between the high gluon densities implied by the Fz measurements and the phenomenon of DIS diffraction. 2.1 Diffractiue Factorization and Pomeron Structure The diffractive cross-section, in analogy wit#hthe total cross-section, is written in terms of the diffract,ive structure function FP as
p = 0.01 = 0.04
xF;'3'(p,
Q2, x p ) .
(4)
The cross-section has been integrated over t . It has been proven that F f factorizes into a long and a short, distance cont,ributions, as does the inclusive Fz, i.e. Ff f D @ & where 6 are the usual pQCD hard cross-sections and f are t,he diffractive parton densities, which obey the usual DGLAP equations, and are universal 1 8 . By knowing f D , we can calculate any diffractive DIS final state such as charm or jet production. The diffractive parton densities are functions of four variables: zp, t , b and Q2. However, the DGLAP evolution only concerns the variables z (or R) and Q2. If, for all relevant f D 7 s ,the zp and t dependences decouple from the fi and Q2 dependence, and if the xp and t dependences are the same for all relevant partons, as Regge factorization 19,
p = 0.1
o ' o l w 3! = 0.2
N
1
10
lo2 Q' (GeV')
Figure 4. The diffractive structure function for a bin of x p measured by the HI Collab. See text.
then we arrive at what is known
F ~ D ( x I P , ~ , Q ~=, ~~B( )x I P ,.FF'(iB,Q2). ~)
(5)
94
In this case f ( x p ,t ) can be interpreted as the flux factor of the Pomeron, and FF as the structure function of the Pomeron. In this case DGLAP analysis of FF becomes meaningful. It is a remarkable experimental fact that Regge factorization, which is not required by the diffractive factorization theorem, apparently holds over a large part of the measured phase-space, and that the flux factor, f ( x p , t ) , has approximately the form expected by Regge theory of 1/x2$~-l 16,16 by the H1 collaboration for x p Figure 4 shows the measurements of of 0.005 16,17. The lines are the results of the DGLAP analysis. The resulting gluon distributions in the Pomeron is shown in Figure 5. The analysis finds two stable solutions, one of which (dotted line) favors a rather large amount of gluons at, z p = 1, and t,he second which does not, (solid line). The fractional momentum carried by the parton in the Pomeron is denoted by zp, and the renormalization and factorization scale by p. The recent measurement by H1 of dijet production in diffraction 2o shows that the Pomeron parton distributions extracted from the DGLAP analysis can indeed be used to describe the dijet cross-section in diffractive events (Figure 5). The jet measurement favors the parton distributions labelled “fit, 2” in the figure.
2.2 Diffraction and F2 at Small-x While the analyses based on diffractive factorization have been very successful and powerful, the question of the origin of the phenomenon of DIS diffraction remains unanswered. Furthermore, the relationship between the Pomeron structure and the proton structure is not clear. Figure 6 shows the ratio, for fixed Q 2 , of the DIS diffractive cross section to the total DIS cross-section as measured by the ZEUS collaboration. Although a cut has been made in the mass of the diffractive system, M x , the conclusion is independent of M,u: the ratio is flat as a function of W or, equivalently for fixed Q2, of x 1 5 . The flatness of the ratio implies that the energy depen-
ms. IP (dir.-.f)
n
-
H I 1k2
m5.f only
P
.... ..
200
,....... .,..::. ..............:;,,,.,,.... O% o.<: . .::..... . .,,
...
...... 0 1 : W t
Figure 5. Dijet cross-section for diffractive events compared to predictions based on the gluon momentum distribution of the Pomeron, z g p .
95
dence of DIS diffraction is the same as that of inclusive DIS, i.e. cx W0.4 at Q2 x 10 GeV2. This result is surprising from several points of view. ZEUS 1994 A4naive expectation from the optical theorem would lead to diffractive cross sections that rise twice as fast as the inclusive one. In other words, if ..... ...... .........f............. ............... the rise of the inclusive cross......... section is driven by a gluon 40 60 80 100 120 140 160 180 200 220 density that rises as z-' (or W(GeV) W2'), then for diffractive process that needs to couple to Figure 6. The ratio of diffractive to total DIS crossat least two gluons, the crosssection. The data have been binned in Q2 and a section should rise as x - ~ ' . cut on the mass of the state X , A-l, < 3 GeV has been made. .4t the same time, the energy dependence of the diffractive cross-section also contradicts Regge phenomenology, which expects an energy dependence of W0.25-0.3. The lines in Figure 6 that describe the data qualitatively are from the dipole model of Golec-Biernat and Wiisthoff 21,22, briefly described below.
2.3 Impact Parameter Space (or Dipole) Models The infinite momentum frame of DIS, which is appropriate for the DGLA4P formalism, is obviously not the only possible frame of reference. In the impact parameter, or dipole, formalism, the appropriate frame of reference is that in which the virtual photon dissociates into a quark-anti quark pair (or a more complicated state), which forms a color dipole which collides with the proton. The description of the interaction of this color dipole with the proton distinguishes the various models of this type that have been proposed 2 3 . In this presentation, a particularly simple model due to Golec-Biernat and Wiisthoff (GB&W), which has been shown to describe the HERA diffractive data qualitatatively well, will be described. In the GB&W model, the cross-section of the dipole, 6 d i p o l e , with the proton is modeled simply as a function that smoothly interpolates between two limits; at small dipole radius, T , 6 d , p o l e increases as r2 in keeping with the behavior of perturbative QCD. At large T , 6 d i p o l e becomes constant to preserve unitarity. The saturation of the dipole cross-section can be qualitatively shown
96
to correspond to the saturation of partons in the proton 24. In the model, the point, at which the r 2 dependence of the cross-sect,ion changes to the const,ant behavior depends on the density of the partons in the proton. Specifically, a parameter, & l/xg(x) x x , which can be interpreted as the separation of partons in the proton, is introduced. When T < < &, 6dZpole is in the “p&CD” region, while when T >> &, it is in the saturation region (Figure 7a and 7b, respectively). The dipole radius, T , enters through the wave function of the virtual photon, \E, , and the diffractive cross-section is written, up to a t dependence, as,
-
OD
c€
J d2r J dzl*,
-
( z ,T ) 1 2 ~ ~ , p o l eT () ~ ,
(6)
where z is the fractional momentum of one of the quarks in the dipole. The diffractive cross-section is explicitly related to the total cross-section, which is, Otot 0: ~ d ~ r J d z l l , ~ z , T ~ l ~ r i ~ , . 1 . ~ x , T ~ .
(9)
The fact that nD/vtot is constant as a function of W (or z), as shown in Figure 6 , can be shown to occur only if the dipole cross-section is being probed in these processes beyond the small T region into the sat,uration region. The implication of this for the total cross-section will be discussed below. 3
F2 at Small-x Revisited
(b)
/fq
Figure 7. Schematic representation of the GB&W model. The characteristic radius of the dipole is proportional to the Q2 of the virtual photon, y’. The parameter & corresponds to the separation of the partons within the proton. The relative size of T and &, determines the behavior of the dipole cross-section.
In the first part of this presentation, it was stated that the proton F2 measured so far at HERA and else where is well described by fits using DGLAP equations above Q2 of 1 Ge\J2. The dipole model description of the total DIS cross-section (or F2) is given in Equation (9). Currently the
97
formal connection between the DGLAP interpretation and the dipole models is far from clear 24,23,26. However many dipole models, in particular the GB&W model, describe the dynamics of cross-section saturation which goes beyond the physics of the DGLAP picture. Thus, it is appropriate to revisit the inclusive DIS data and ask if there are any indications of behavior beyond DGLAP, even though t,he DGLAP fits are successful. The DGLAP evolution equations, a t low x and at LO, imply that, the partial derivative of F2 with 0 ZEUS95-97 1-7 -1 respect to (lnQ2) 5 is proportional 9 t o x g ( x , Q 2 ) , the 4 gluon momentum density of the proton (Equation 3 (3)). On the other hand, a t sufficiently low Q 2 , 2 F2 must vanish as Q2 from current, 1 a conservation, behavior built into t,he GB&W 0 model but not in the DGLAP formulation of DIS: Figure 8. FZ measurements in bins of I as a function of Q2. The solid lines are the results of the fits described in the text.
aF2 slog Q2
Q2co.
(10) Since W at low x is related t o x and Q2 by W 2 Q 2 / x , the plot of dF2/dlogQ2a t a constant W ,over the Q2 range covered by the data, should show a transition from the behavior according to Equation (3) to that of Equation (lo), provided xg(x,Q 2 ) has a weak Q2 dependence and (TO, which corresponds t o the photoproduction cross-section, has a weak x (or equivalently energy) dependence. Since there is no quantitative prediction for the kinematic region in which the DGLAP formalism is applicable, the determi-
98
nation of the Q2 and x at which this transition occurs is of great interest and may help in clarifying the nature of the transition 27. Figure 8 shows recent -01.2 measurements Y of F2 from the g’ ZEUS collabora0 0.6 tion along with 0.4 the fixed target measurements 28 0.2 from the NhlC 0 and the E665 lo-‘ 1 10 12 12 10’ collaborations. F2 is shown as a function of Q 2 for bins of fixed x . Where necessary, the measurements have been interpolated to the appropriate values of x using the X ALLM parameFigure 9. The logarithmic slope of F2 at a constant Mi as a functerization 29. The tion of Q2 and z. See text. F2 in each bin of fixed x is offset by an additive factor of (- log,, x ) to ensure that the vertical separation between the bins is monotonic in x . The parameterization A ( x ) B ( x ) log,, Q 2 C ( x ) ( l o g l oQ2)’ has been used to fit the F2 measurements at each value of x . The quality of the fit, is good, and the result is shown in Figure 8 as solid lines. The constant W points on the parameterizations have been found according to the formula W 2= Q 2 ( 1 / x - l), and are indicated on the plot with dashed lines. It is interesting to note the distortion in the fixed-W lines that occurs at x =lop4 at relatively high Q2 M 5 GeV2 and at W above 85 GeV. In Figure 9, the derivatives of F2, evaluated from the fit B 2Cl0glOQ 2 , are shown. The errors of the derivatives are evaluated using the errors on, and correlations between, the parameters B and C obtained from the polynomial fits. Figure 9a shows the derivatives at constant W as a function of Q 2 , whereas Figure 9b shows the same as a function of x . h
P
+
+
+
99
Figure 9a shows that a t lower Q 2 ,corresponding to lower x in Figure 9b, the derivatives fall as Q2 decreases and tend t o become independent of W' at, Q2 of about 0.4 GeV2. This is in line with the expectation of Equation (10). Figure 9b shows t,hat at, higher 2, corresponding t o higher Q 2 in Figure 9a, the derivatives fall with increasing x and tend to become independent of W at, a: > 0.003, in line with the expectation of Equat,ion (3), if xg(s, Q 2 )has the form x P x and only a slow dependence on Q 2 . The value of Q 2 ,or x, where the slope of the derivatives changes sign can be read off from Figures 9a and 9b. This transition, for values of W above 85 GeV, happens a t a relatively high Q2 of 2-6 GeV2 a t the corresponding z of 5.10-4 to $loP3. The dashed lines in Figure 9 are the predict,ion of t,he GB&W model, which explicitly incorporates the transition between the behaviors described in Equations (10) and (3) as a transition between the pQCD region and the saturation region of the dipole cross-section. The lines are drawn only at x < 0.01 where the model is applicable. The solid line is the result of a DGLA4P fit by the ZEUS collaboration. The line is drawn only above Q2 > 2.7 GeV2, where data have been fit,. In case of the DGLAP fit, the peaking behavior of Figure 9 is related t o the rapid decrease of the gluon density at low x bet,ween Q2 of 10 GeV2 and 1 GeV2 15930.
4
Discussion and Outlook
The measurements of the proton structure a t small z at HERA are now very precise. However, in spite of the expectation that these measurements should show some manifestation of dynamics beyond that incorporated in the (In Q 2 ) expansion of the DGLAP formalism, the DGLAP fits t o the data give a good description above Q2 of about 1 GeV2. The question of whether the success of DGLAP fits merely indicates the flexibility of the parton parameterizations and the still-limited (In Q 2 ) range of the measurement a t small-z is not likely to be answered by looking a t F 2 alone, at least in the currently available kinematic range. While the qualitative features of F2 at small-a: (and necessarily small Q 2 ) ,show some characteristics expected by a saturation model, the DGLAP fits can reproduce those same features without any parton saturation. One of the most promising ways of investigating the small-z proton structure is t o look at the inclusive DIS measurements together with t,he diffractive DIS reactions. While the theoretical understanding of the relation of small-x and diffraction is not yet very rigorous, the data sets from HERA provide many interesting indications of the underlying dynamics.
100
References
1. L. N. Lipat,ov, Sou. J . Nucl. Phys. 20, 94 (1975); V. N. Gribov and L. N. Lipatov, Sou. ,I. Nucl. Phys. 15, 438 (1972); G. -4ltarelli and G. Parisi, Nucl. Phys. B 126, 298 (1977); Y. L. Dokshitzer, Sou. Phys. JETP46, 641 (1977). 2. C. Adloff et al. [Hl Collaboration], Eur. Phys. C 21, 33 (2001). 3. ZEUS Collaboration, paper 412, XXXt,h International Conference on High Energy Physics, July 27-August 2, 2000, Osaka, .Japan. 4. C. Adloff et al. [Hl Collaboration], Nucl. Phys. B 497, 3 (1997). 5. J . Breitweg et al. [ZEUS Collaboration], Eur. Phys. J. C 7, 609 (1999). 6. K. Prytz, Phys. Lett. B 311, 286 (1993). 7. V. S. Fadin, E. A . Kuraev and L. N. Lipatov, Phys. Lett. B 60, 50 (1975); E. -4.Kuraev, L. N. Lipatov and V. S. Fadin, Sou. Phys. J E T P 4 4 (1976) 443; E. A . Kuraev, L. N. Lipatov and V. S. Fadin, Sou. Phys. JETP45 (1977) 199; I. I. Balitsky and L. N. Lipatov, Sou. J. Nucl. Phys. 28, 822 (1978). 8. V. S. Fadin and L. N. Lipatov, Phys. Lett. B B429, 127 (1998); M. Ciafaloni and G. Camici, Phys. Lett. B 430, 349 (1998). 9. J. Blumlein and A . Vogt, Phys. Rev. D 57, 1 (1998). J. Blumlein, V. Ravindran, W.L. van Neerven and PI. \logt, hep-phf9806368. 10. M. Ciafaloni, Nucl. Phys. B 296, 49 (1988); S. Catani, F. Fiorani and G. hlarchesini, Nucl. Phys. B B336, 18 (1990); S. Catani, F. Fiorani and G. Marchesini, Phys. Lett. B 234, 339 (1990). 11. L. V. Gribov, E. hl. Levin and hl. G. Ryskin, Phys. Rep. 100, 1 (1983). 12. J . Bartels, G. -4.Schuler and J. Blumlein, Z. Phys. C 50 (1991) 91. 13. R. S. Thorne, Nucl. Phys. B512, 323 (1998). 14. H. Jung, Nucl. Phys. Proc. Suppl. 79, 429 (1999). 15. J. Breitweg et al. [ZEUS Collaboration], Eur. Phys. J. C6, 43 (1999). 16. C. A4dloffet al. [Hl Collaboration], 2. Phys. C 76,613 (1997). 17. H1 Collaboration, paper 571, XXIXth International Conference on High Energy Physics, July 23-29, 1998, Tampere, Finland. 18. J. C. Collins, Phys. Rev. D 57, 3051 (1998). 19. G. Ingelman and P. E. Schlein, Phys. Lett. B 152, 256 (1985). 20. C. Adloff e t al. [Hl Collaboration], hep-ex/0012051. 21. K. Golec-Biernat and M. Wusthoff, Phys. Rev. D 59, 014017 (1999). 22. K . Golec-Biernat and M. Wusthoff, Phys. Rev. D 60, 114023 (1999). 23. E. Gotsman, E. Levin and U. Maor, Nucl. Phys. B 493, 354 (1997);
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E. Gotsman, E. Levin and U. Maor, Phys. Lett. B 425, 369 (1998); E. Got,sman, E. Levin, U. Maor and E. Naftali, Nucl. Phys. B 539, 535 (1999); N. Nikolaev and B. G. Zakharov, 2.Phys. C 49, 607 (1992); N. Nikolaev and B. G. Zakharov, 2.Phys. C 53, 331 (1992); V. Barone, PI.Genovese, N. N. Nikolaev, E. Predazzi and B. G. Zakharov, Phys. Lett. B 326, 161 (1994); J. R. Forshaw, G. Kerley and G. Shaw, Phys. Rev. D 60,074012 (1999); \%’. Buchmuller, T. Gehrmann and A. Hebecker, Nucl. Phys. B 537, 477 (1999); -4. H. Mueller and B. Patel, Nucl. Phys. B 425, 471 (1994); -4. H. hlueller, NU^. Phys. B 415, 373 (1994); \V. Buchmuller and A. Hebecker, N7lcE. Phys. B B476, 203 (1996); \%’.Buchmuller, M. F. McDermot,t and -4. Hebecker, Nucl. Phys. B 487, 283 (1997). -4. H. Mueller, hep-ph/9911289. J . Bartels, J. Phys. G 26, 481 (2000). M. F. McDermott,, hep-ph/0008260. ZEUS Collaborat,ion, paper 416, XXXt,h Int,ernational Conference on High Energy Physics, July 27-August 2, 2000, Osaka, Japan. &I. R. Adams et al. [E665 Collaboration], Phys. Rev. D 54, 3006 (1996); M. Arneodo et al. [New Muon Collaboration], Nucl. Phys. B 483, 3 (1997). H. Abramowicz, E. &I. Levin, A . Levy and U. hlaor, Phys. Lett. B 269, 465 (1991). H. Abramowicz and A. Levy, hep-ph/9712415. -4. D. Martin, R. G. Roberts, \%’. J. Stirling and R. S. Thorne, Eur. Phys. J. C 4, 463 (1998).
BARYON CHIRAL DYNAMICS THOMAS BECHER Stanford Linear Accelerator Center Stanford University, Stanford, CA 94309, U S A E-mail:
[email protected] After contrasting the low energy effective theory for the baryon sector with one for the Goldstone sector, I use the example of pion nucleon scattering to discuss some of the progress and open issues in baryon chiral perturbation theory.
1
Higher, faster, swifter?
Many of the constraints of chiral symmetry on the interaction of pions and nucleons at low energies were worked out long before the advent of QCD (Current algebra, PCAC). Later it was realized that the corrections to these symmetry relations can be obtained by implementing the chiral symmetry and its breaking by the quark masses into an effective Lagrangian describing the interaction of mesons and baryons. This method is called chiral perturbation theory (CHPT).l It allows one to compute the expansion of QCD amplitudes and transition currents in powers of the external momenta and quark masses; it has become one of the standard tools to analyze the strong interactions at low energy. Over the last few years, the progress in this field in the baryon sector has been twofold: on one hand, we have reached a new level of precision in many of the classical applications: by now, the full one loop result for the nucleon form factors and the pion-nucleon scattering amplitude in the isospin limit is k n ~ w n Even . ~ ~ the ~ first two-loop result has been obtained: the chirai expansion of the nucleon mass has been worked out to fifth order.4 On the other hand, the framework has been extended and applied to a whole range of new processes: the effective Lagrangian has been extended to include electromagnetism, making it possible to disentangle strong and electromagnetic isospin ~ i o l a t i o nThis . ~ effective theory of QCD+QED has been used to calculate next-to-leading order isospin violating effects in the pion-nucleon scattering amplitude6 and to study the properties of the r - p bound state.7 Another extension of the framework incorporates the A-resonance as an explicit degree of freedom into the effective Lagrangian, thereby summing up the potentially large higher-order terms in the chiral expansion associated with this resonance.a Despite all of this impressive progress, we are still short of having the answers to some very old questions, like, for example, what is the value of the
102
103
a-term, and the agreement with data in many cases is not quite as satisfactory as in the Goldstone sector. In my talk, I will contrast the baryon with the meson sector and illustrate some of the peculiarities that arise, once the baryon field is included into the effective Lagrangian. I will illustrate my discussion with the example of 7rN-scattering and conclude that the low energy theorems for this amplitude hold to high accuracy. Chiral symmetry governs the amplitude in a small region around the Cheng-Dashen point. However, the momentum dependence of the chiral representation for the amplitude is not accurate enough t o make direct contact with experimental data. After discussing some of the difficulties associated with the extrapolation of the experimental results to the low energy region, I show how the simple structure of the result in the low energy theory can be implemented into a dispersive analysis of the data. As I focus the discussion mostly on 7rN-scattering, I will fail t o report on many important developments over the past few years. Fortunately, my sense of guilt for omitting electromagnetic probes of the nucleon was relieved by the plenary talks of Ed Brash, Helene Fonvieille, Frank Maas and Harald Merkel as well as a number of interesting talks on these matters in the parallel sessions. Unfortunately, there were no talks covering the few nucleon sectorg, nor about the recent work on quenchedlO and partially quenched" baryon CHPT. 2
Baryons versus mesons
While this is not the place t o give an introduction to CHPT12, it is instructive t o point out some of the differences between CHPT in the baryon and the Goldstone sector. All in all, the inclusion of the baryon field leads to three complications: i) in general, one has t o deal with a larger number of low energy constants than in the vacuum sector, ii) from the viewpoint of the low energy theory, the physical region is a t higher energies, iii) the singularity structure of the amplitudes is more complicated. On the upside, there are much more and more precise data available than in the meson sector. 2.1
Effective Lagrangian
For vanishing up- and down-quark masses, the pions are the Goldstone bosons associated with the spontaneous breaking of chiral symmetry. The interactions between Goldstone bosons tend t o zero at low energies and they decouple from matter fields. Accordingly, the effective Lagrangian is organized in pow-
104
ers of derivatives on the Golstone fields. At low energies, the terms with higher powers of derivatives on the meson field are suppressed by powers of the meson momenta. Because of decoupling, the interactions of the baryon and the meson involve at least one derivative on the meson field. The lowest-order, effective Lagrangian for the pion-nucleon interaction reads
The ellipsis stands for terms which involve higher powers of the pion field. Their coefficients are fixed by chiral symmetry. At second order, the effective Lagrangian also contains terms proportional to the quark masses. The fact that the lowest-order Lagrangian is fully determined by the nucleon mass and the matrix element of the axial charge shows how chiral symmetry constrains the interactions of mesons and baryons. However, the rapid increase in the number of parameters at higher orders makes it evident that it is not nearly as restrictive as in the meson sector. The number of parameters entering at each order is shown in brackets:
The larger number of low energy constants arises from the spin-; nature of the nucleon and because it stays massive in the chiral limit, so that the effective Lagrangian involves odd as well as even powers in the chiral expansion. In a given process only a handful of the outrageous number of terms in the fourth-order Lagrangian will contribute. The fact that the effective Lagrangian contains 118 terms a t fourth order,13 however, means that the chances that the same combination enters two different observables are rather dim: there will hardly be any symmetry relations valid to fourth order in the chiral expansion. 2.2
The low energy region and the role of resonances
The strongest constraints from chiral symmetry on the 7rN-scattering amplitude are obtained a t unphysically small values of Mandelstam variables, a t the Cheng-Dashen point s = u = m:, t = 2M:. In figure 1 the Mandelstam triangles for m r - and 7rN-scattering are compared. The figure makes it evident that the physical threshold for 7rN-scattering is a t higher energies: the
105
increase in s from the Cheng-Dashen point to the threshold is of O ( M T )for rN-scattering, while it is O(M:) for mr scattering. At threshold, higher-order
Figure 1. Comparison of the Mandelstam triangles for mr-and rrN-scattering.
terms in the chiral expansion will therefore be more important in n N - than in mr-scattering. This observation is confirmed by looking at the position of the first resonance. The increase in s from the Cheng-Dashen point to the first resonance is roughly the same in both cases: mz - m$ M m:. The relevant expansion parameter for the resonance contributions at threshold is, however, much larger for 7rN-scattering: 2mNM,/(m: x 0.4 >> 4M,/mE x 0.1. While the effective theory for the mcson sector will still yield meaningful results well above threshold, the A-resonance must be included into the Lagrangian if one wants to arrive at an accurate description of the meson nucleon amplitude above threshold. This can be done in a systematic way by counting the mass difference S = m, - mN as a small quantity of the same order as M,. This procedure is referred to as “small scale expansion” and allows one to resum the potentially large corrections associated with the resonance.8 While it is certainly important to get a handle on the resonance contributions, a few words of caution are appropriate: we are still performing a low energy expansion and there are higher-order terms not associated with the resonance. In particular, the inclusion of the A has so far only be performed in the non-relativistic
mt)
106
framework for baryon CHPT (to be discussed in the next subsection) and the higher-order kinematic corrections are important already in the threshold region. Furthermore, the effective theory which includes the A is not unique: recently it has been claimed that the effective Lagrangian is compatible with different counting schemes; it seems in general not possible to decide from first principles at which order a given operator enters. l4 The 7rN-scattering amplitude has been calculated to third order in this combined expansion in 6 and the meson momenta.15 The calculation confirms that the bulk of the A contribution stems from the resonance pole term. According to the authors, the energy range in which their results reproduces the existing data is only slightly larger than for the fourth-order calculation in pure CHPT. 2.3 Formulation of the eflective t h e o y In the low energy expansion, the baryon four momentum Pp has to be counted as a large quantity, since P 2 = rn; is of the size of the typical QCD scale squared. If we choose a frame, where the baryon is initially at rest and let it interact with low energy pions, the nucleon will remain nearly static, its three momentum being of the order of the meson mass. The chiral expansion of the corresponding amplitudes in the momenta and masses of the mesons therefore leads to an expansion of the nucleon kinematics around the static limit. This expansion is implemented a b initio in the framework called heavy baryon chiral perturbation theory (HBCHPT).l' However, the expansion of the kinematics fails t o converge in part of the low energy region. The breakdown is related t o the fact that the expansion of the nucleon propagator in some cases ruins the singularity structure of the amplitudes. This makes it desirable to perform the calculations in a relativistic framework. In doing so, the correct analytic properties of the amplitudes are guaranteed, and one can address the question of their chiral expansion in a controlled way. In the relativistic formulation of the effective theory a technical complication arises from the fact that in a standard regularization prescription, like dimensional regularization, the low energy expansion of the loop graphs starts in general at the same order as the corresponding tree diagrams.17 Since the contributions that upset the organization of the perturbation expansion stem from the region of large loop momentum of the order of the nucleon mass, they are free of infrared singularities. In d-dimensions, the infrared singular part of the loop integrals can be unambiguously separated from the remainder, whose low energy expansion to any finite order is a polynomial in the momenta and quark masses. Moreover, the infrared singular and regular parts of the amplitudes separately obey the Ward identities of chiral sym-
107
metry. This ensures that a suitable renormalization of the effective coupling constants removes the infrared regular part altogether, so that we may drop the regular part of the loop integrals and redefine them as the infrared singular part of the integrals in dimensional regularization, a procedure referred to as infrared regularization. l8 The representation of the various quantities of interest obtained in this way combines the virtues of HBCHPT and the relativistic formulation: both the chiral counting rules and Lorentz invariance are manifest at every stage of the calculation. In the meantime, this relativistic framework has been used to calculate the scalarls, axiallg and electro-magnetic form factors20 as well as the elastic pion-nucleon amplitude3 to fourth order in the chiral expansion. Recently, the Gerasimov-Drell-Hearn sum rule has been reanalyzed and it was found that the recoil corrections, which are summed up in the relativistic approach, are rather large.21 3 3.1
Pion-nucleon scattering
Low energy theorems
Chiral symmetry constrains the strength of the 7rN-interaction as well as the value of the scattering amplitudes at the Cheng-Dashen point. The fourthorder result for the scattering amplitude allows us to analyze the corrections to the low energy theorems that arise at leading order in the expansion and we find that the symmetry breaking corrections are rather small. As a first example, let us consider the Goldberger-Treiman relation
If the masses of the up- and down-quarks are tuned to zero, the strength of the .rrN interaction is fully determined by gA and F,: ACT = 0. Up to and including terms of third order in M,, the correction has the form
ACT = cM:
+ O(M:).
It is remarkable that the correction neither involves a term of the form M: In(%) (a “chiral logarithm”) nor a correction of order M,. Such inm N frared singular terms are present in the chiral expansion of g,N, QA, F, and m,, but they cancel out in the above relation. To this order, the correction is thus analytic in the quark masses. If the low energy constant c is of typical size, c M 1/GeV2, the correction to the Goldberger-Treiman relation is 2%. If one evaluates the above relation with value for the coupling constant given in Hohler’s comprehensive review of .rrN-scattering22,one finds ACT = 4%. The
108
data accumulated since then seems t o favor a smaller value of g,N reducing the correction t o 2-3%. Another well known low-energy theorem relates the value of the isosymmetric amplitude D f at the Cheng-Dashen pointa C = F,D 2 -+ ( s = m t , t = 2M:) to the scalar form factor
(N‘I mu Uu
+ m d dd IN) = a ( t )U’U .
The relation may be written in the form C = a(2M:)
+ A,,
.
The theorem states that the term A,, vanishes up t o and including contributions of order M,”. The explicit expression obtained for C when evaluating the scattering amplitude t o order q4 again contains infrared singularities proportional to M: and M: lnM,”/m;. Precisely the same singularities, however, also show up in the scalar form factor at t = 2M;, so that the result for AGO is free of such singularities:
A,,
= d M,“
+ O(M,).
A crude estimate like the one used in the case of the Goldberger-Treiman relation indicates that the term A,, must be very small, of order 1 MeV. Unfortunately, the experimental situation concerning the magnitude of the amplitude at the Cheng-Dashen point leaves much t o be desired. The inconsistencies between the results of the various partial wave analyses need to be clarified in order t o arrive at a reliable value for g , N . Only then it will be possible t o extract a small quantity like the C-term from data.’ 3.2
M o m e n t u m dependence: analyticity and unitarity
To obtain the amplitudes in the region around the Cheng-Dashen point, the experimental results need to be extrapolated to the subthreshold region. The extrapolation can only be performed reliably, if the correct structure of the singularities of the amplitude is implemented into the data analysis. Having to deal with functions of two variables, this is not a simple task and while all aThe bar indicates that the pseudwvector Born term has been subtracted. *Jugoslav Stahov has reported a t the conference that discrepancies in the higher partial waves of different partial wave analyses can explain the inconsistencies between different determinations of the C-term.23
109
modern partial wave analyses incorporate some of these constraints, subsequent analyses have not kept up with the high level of sophistication reached by the Karlsruhe-Helsinki collaboration in the eighties. Because of the complexity of a dispersive analysis, it is tempting to use the representation obtained in chiral perturbation theory to perform the extrapolation to the unphysical region, since the use of a relativistic effective Lagrangian guarantees the correct analytic properties in the low energy region. The problem with this approach is that unitarity is not exact in the chiral representation, but only fulfilled to the order considered. At one loop level, the imaginary part will be given by the current algebra amplitudes squared. Since the corrections to the current algebra result become sizeable above threshold, the violation of unitarity will prevent an accurate extrapolation to the subthreshold region in this framework. This is illustrated in figure 2, where we compare the result obtained in CHPT with the KA84 solution.24 The parameters in the chiral representation have been adjusted t o the KA84 solution a t the threshold and we want to check the energy range in which we reproduce the KA84 solution. For the amplitude D+, the deviation in the region around the Cheng-Dashen point would translate into a 10 MeV uncertainty in the C-term. The accuracy is better in the case of the amplitude D - , but also in this case the chiral representation starts to deviate soon after threshold. There are various prescription^^^ t o fix the problem by hand: one can, e. g. ,use the K-matrix formalism to unitarize the amplitudes found in CHPT. Once some resonances are added in, these unitarized amplitudes usually fit the data very nicely, however, this “solution” has its price: the unitarizations usually ruin crossing symmetry and analyticity, by introducing unphysical singularities into the results, making their use for an extrapolation to lower energies doubtful. We have set up a framework that combines the analytic structure found in CHPT with the constraints from ~ n i t a r i t y one : ~ starts by writing a dispersive representation for the result found in the low energy effective theory. This representation splits the amplitude into a polynomial part and nine functions of a single variable, which are given by integrals over the imaginary parts of the amplitude. In the elastic region, unitarity then leads a set of coupled integral equations for these functions, similar to the Roy equations in m-scattering. Replacing the imaginary parts found in CHPT by the experimental imaginary parts in the inelastic region and solving the equations iteratively one arrives at a representation of the amplitude that fulfills both the constraints from unitarity and analyticity. In addition to the imaginary parts, this system of equations also needs four subtraction constants as an input. One of them can
110
- CHPT O(g4) I
1-80 1
02
04
06
v
I
OX
%l?!D0.7 1 I
70 60
0.2
0.1
0.6
0.8 Y
1
1.:
1.4
Figure 2. Real part of the pion-nucleon amplitude at zero momentum transfer. The variable v denotes the lab. energy of the incoming pion. The reaction threshold is at v = M,. The red line is the result obtained at the fourth order in the chiral expansion. The black curve corresponds to the KA84 solution.
be expressed as an integral over the total cross section, while the other three need to be pinned down from the experimental information at low energies. The results from the study of pionic hydrogen, to be discussed below, should subject these constants to stringent bounds. 3.3 Isospin violation, pionic hydrogen
To study strong isospin breaking, one needs to disentangle it from electromagnetic isospin violation. Since both are of similar magnitude, they need to be treated simultaneously, making it necessary to incorporate the photon field as an additional degree of freedom into the low energy effective Lagrangian. In
111
-
the baryon sector, the corresponding Lagrangian has been worked out to third order5 in a simultaneous expansion in m, q2 e2 and the result for the pion-nucleon scattering amplitude has been worked out to the same order.6 An important application of the low energy effective theory of QCD+QED is the extraction of the hadronic scattering length from the measurements of the strong interaction width and level shifts of hadronic atoms. The goal of the experiments with pionic hydrogen (the bound state of a T- with a proton) at PSI 26 is to measure these quantities at the level of one per cent. In order to extract the pure QCD scattering lengths from the measurements, one needs to remove isospin breaking effects with high precision. The framework for the calculation has been set up and by now, the calculation of the strong energy shift has been carried out to next-to-leading order in isospin breaking.7 The results differ significantly from earlier potential model calculations which fail to consistently incorporate all of the interactions present even at the leading order. At present, the main uncertainty in the result of the effective theory is the value of the low energy constant fi , whose value is as yet unknown. 4
Conclusions
We have a good understanding of how chiral symmetry manifests itself in the baryon sector. Chiral symmetry breaking effects, on the other hand, are small and their determination from measurements is nontrivial. The reason being that, in many cases, we cannot directly confront the low energy theorems of the symmetry with the experimental data taken at higher energies. In this situation, the precise extrapolation of the data to lower energies becomes a central issue. While the representations obtained in CHPT are not suitable for this purpose, their analytic structure can be implemented into a dispersive analysis.
Acknowledgments I would like to thank the organizers for this stimulating and pleasant conference. This work has been sponsored by the Department of Energy under grant DE-AC03-76SF00515. References 1. J. Gasser and H. Leutwyler, Annals Phys. 158,142 (1984), J. Gasser and H. Leutwyler, Nucl. Phys. B 250, 465 (1985)
112
2. N. Fettes and U. G. Meianer, Nucl. Phys. A 676, 311 (2000) [hepph/0002162]. 3. T. Becher and H. Leutwyler, JHEP 0106, 017 (2001) [hep-ph/0103263]. 4. J. A. McGovern and M. C. Birse, Phys. Lett. B 446, 300 (1999) [ h e p ph/9807384]. 5. G. Muller and U. G. Meianer, Nucl. Phys. B 556, 265 (1999) [hepph/9903375]. 6. U. G. MeiBner and S. Steininger, Phys. Lett. B 419, 403 (1998) [hepph/9709453], N. Fettes and U. G. Meifher, Phys. Rev. C 63, 045201 (2001) [hepph/0008181], N. Fettes and U. G. MeiOner, Nucl. Phys. A 693, 693 (2001) [hepph/0101030]. 7. J. Gasser, M. A. Ivanov, E. Lipartia, M. MojiiS and A. Rusetsky, Groundstate energy of pionic hydrogen to one loop, hep-ph/0206068. 8. T. R. Hemmert, B. R. Holstein and J. Kambor, J. Phys. G 24, 1831 (1998) [hep-ph/9712496]. 9. For a recent review, see H. W. Griesshammer, An Introduction to Few Nucleon Systems in Effective Field Theory, nucl-th/0108060. 10. J. N. Labrenz and S. R. Sharpe, Phys. Rev. D 54, 4595 (1996) [heplat/9605034]. 11. J. W. Chen and M. J . Savage, Phys. Rev. D 65, 094001 (2002) [heplat/0111050]. 12. Two recent reviews are H. Leutwyler, Chiral dynamics, in Shifman, M. (ed.): At the frontier of particle physics, vol. 1, 271-316 [hep-ph/0008124], U. G. Meifher, Chiral QCD: B a y o n dynamics, ibid. , 417-505 [hepph/0007092]. 13. N. Fettes, U. G. Meifher, M. MojiiS and S. Steininger, Annals Phys. 283, 273 (2000); Erratum-ibid. 288, 249 (2001), [hep-ph/0001308]. 14. T. R. Hemmert and W. Weise, hep-lat/0204005. 15. N. Fettes and U. G. Meifher, Nucl. Phys. A 679, 629 (2001) [hepph/0006299]. 16. E. Jenkins and A. V. Manohar, Phys. Lett. B 255, 558 (1991). V. Bernard, N. Kaiser, J. Kambor and U.-G. MeiBner, Nucl. Phys. B 388, 315 (1992). 17. J . Gasser, M. E. Sainio and A. Svarc, Nucl. Phys. B 307, 779 (1988). 18. T. Becher and H. Leutwyler, Eur. Phys. J . C 9, 643 (1999) [hepph/9901384].
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19. J. Schweizer, Low energy representation for the axial f o r m factor of the nucleon, diploma thesis, Bern 2000. 20. B. Kubis and U. G. MeiBner, Eur. Phys. J. C 18, 747 (2001) [hepph/0010283]. B. Kubis and U. G. Meiher, Nucl. Phys. A 679, 698 (2001) [hepph/0007056]. 21. V. Bernard, T. R. Hemmert and U. G. Meifher, hep-ph/0203167. 22. G. Hohler, in Landolt-Bornstein, 9b2, ed. H. Schopper (Springer, Berlin, 1983). 23. J. Stahov, The dependence of the experimental pion-nucleon sigma term o n higher partial waves, hep-ph f0206041. 24. R. Koch, Z. Phys. C 29 (1985) 597. 25. For recent work along those lines, see e. g. U. G. MeiOner and J. A. Oller, Nucl. Phys. A 673, 311 (2000) [nuclth/9912026], M. F. Lutz and E. E. Kolomeitsev, Nucl. Phys. A 700, 193 (2002) [nuclth/0105042], S. Kondratyuk, Pion nucleon amplitude near threshold: The sigma-term and scattering lengths beyond few loops, nucl-th/0204050. 26. G.C. Oades et al. , Measurement of the strong interaction width and shijl of the ground state ofpionic hydrogen, PSI Proposal R-98-01, H. C. Schroder et al. , Eur. Phys. J. C 21, 473 (2001).
114
Harald Griesshammer and Harald Merkel
Leonid Gloman and Yuri Simonov
ELECTROMAGNETIC TESTS OF CHIRAL SYMMETRY HARALD MERKEL for the A1 COLLABORATION Institut f i r Kernphysik, Johannes Gutenberg-Universitat, 55099 Mainz, Germany E-mail:
[email protected] An overview of recent results in threshold pion production is given. While the photoproduction data are in impressive agreement with calculations in the framework of Chiral Perturbation Theory, electroproductiondata at low four-momentum transfer shows severe deviations from these calculations.
1
Introduction
Chiral Perturbation Theory is a consistent scheme to utilize the symmetries of QCD to predict observables at the confinement scale. An overview of the theoretical status of this field is given by the contribution of Th. Becher in these proceedings. In this talk, the current status of the neutral pion photo- and electroproduction experiments near threshold is discussed. Since the pion is the Goldstone Boson of the chiral symmetry breaking, these experiments are well suited to test the predictions of Heavy Baryon Chiral Perturbation Theory (HBChPT)l. 2
Neutral Pion Photoproduction
First experiment^^>^ on threshold pion photoproduction were aimed to test the predictions of Low Energy Theorems4 for the threshold value of the s wave multipole amplitude Eo+. The severe disagreement between these theorems and the experiments was resolved in the following years by refined calculations in HBChPT5, which also gave predictions for the p wave multipole combinations
Pi P2 P3
Mi+ - M i = 3&+ - Mi+ + M i = 2M1+ + Mi-. = 3E1+ -j-
(1)
(2)
(3) The calculations showed, that the s wave amplitude is only slow converging in the chiral expansion, while the p wave combinations Pi and P2 are strong predictions in this framework. P3 is given by a low energy constant of HBChPT and has to be determined by the experiment.
115
116
4.5
.
A. Schmidtetal.
4.0 . 0 M.Fuchsetal. 0 J.C. Bergstrom et al. 3.5 .n
am
3.0
a 2.5
\
2.0 1.5 1.o
0.5 0.0 144
147
150
153
156
159
162
165
168
E, I MeV Figure 1. The total cross section for neutral pion photoproduction a t threshold. Data from SAL6 and MAMI
2.1
Differential Cross Section
The first experimental access to the multipoles is the measurement of the differential cross section. With the assumption, that only s and p waves contribute at threshold, the angular structure of the cross section is given by c(O) = -9( A + B . c o s O + C . c o s 2 0 )
k with the phase space factor f and three angular coefficients A = Ei+
+ 51 (Pz2+ P32)
(4)
B = 2 . Re (EO+Pl') c = P12- -21 (P22+ P32) Fig. 1 summerizes the quality of the existing data sets by the total cross section versus the incoming photon energy. The SAL data6 and the new MAMI data7 agree, while the old MAMI data set8 seems to have some systematic errors at higher energies.
117
0.4
0.3 0.2 0.1
W 0.0 -0.1
I
1
1
.....,..... HBChF'T
--- DR
-0.2
-0.3
' 0
- fit to the data
H A. Schmidt et al.
20
40
60
80
100 120 140 160 180
Figure 2. Polarized photon asymmetry measured a t MAM17 in comparison with calculations in ChPT5 and in Dispersion Relations formalismg.
2.2 Polarized Photon Asymmetry From unpolarized cross section experiments, the s wave multipole IEo+l and the p wave combinations PI and P23 = i(P2' P3') can be extracted. To further decompose all multipoles, a further observable has to be measured. A convenient choice is the polarized photon asymmetry C with the multipole decomposition
+
Such an experiment was performed at MAM17 at the tagged photon beam of the A2 collaboration with the TAPS detector for the detection of the 7ro decay photons. The polarized photon beam was produced by coherent Bremsstrahlung from a diamond crystal. Fig. 2 shows the asymmetry C, averaged over the energy range of the experiment. With this experiment, for the first time a complete separation of the p waves is possible. The results are given in table 1, in comparison with the predictions of Chiral Perturbation Theory (CHPT)5 and Dispersion Relati~ns(DR)~. Within the error bars, the two existing high resolution ex-
118 Table 1. Experimental multipole amplitudes for photoproduction from MAMI' and SAL6 in comparison with Chiral Perturbation Theory (CHPT))5 and Dispersion Relations (DR).
(10-~/""
MAMI SAL ChPT
-1.31f0.08 -1.321t0.05 -1.16 -1.22
(qlc. 1 0 - ~ / ~ : ) (qlc. 1 0 - ~ / ~ : ) ( q k .1 0 - ~ / ~ 9 )
10.02f0.2 10.26f0.1 10.33k0.6 10.54
-10.5f0.2
13.1f0.1
-11.Of0.6 -11.4
11.7f0.6 10.2
periments and the quoted calculations agree. The deviation for p% of ChPT can be removed by re-fitting the low energy constants to the new data set.
3
Electroproduction at low Q2
Additional information on the pion production mechanism can be extracted from electroproduction experiments. While e.g. the multipole combination flj is basically a fit parameter in the description of the photoproduction data, the extention of this quantity to virtual photons is given in ChPT without further degrees of freedom. In addition, the longitudinal s wave amplitude LO+and two further p wave combinations can be extracted. First experiments at a photon virtuality of Q2 = 0.1 (GeV/c)2 aimed to extract the s wave amplitudes at threshold'0:''.12. These experiments were in reasonable agreement with calculations'3, but the value of Q2 = 0.1 (GeV/c)2 is somewhat to high for the convergence of ChPT. Therefore, a further experiment at an intermediate value of Q2 = 0.05 (GeV/c)2, half way between photoproduction and the existing data was performed at MAMI14. The results were surprising, as can be seen in fig. 3, which shows the differential cross section for the virtual photon polarization E = 0.72. In this figure, the cross section at four different values of the center of mass energy W is compared with CHPT and the phenomenological model MAID15. To show the consistency of the data, a fit with the assumption of only s and p waves contributing to the cross section is also included. As can be seen, the magnitude of the cross section is nearly half the prediction of ChPT and MAID. To illustrate the discrepancy further, figure 4 shows the total cross section as function of Q2. In this observable, the statistical error of all data points is very small and only systematic errors play a role. Thus, the clear discrepancy between data and calculations, but also the increasing discrepancy between ChPT and MAID is visible.
119
-
AW = 1.5 MeV
30
L
cn
\
a
d 20 *n
& = 10 13 0 0"
45"
90" 135" 180" 0"
45"
90" 135" 1E 3"
Figure 3. Differential cross sections for the first 4MeV above threshold for the virtual photon polarization 6 = 0.72. The solid line represents a fit with the assumption of only s and p waves contributing, the dashed and dash-dotted lines represent the predictions of ChPT13 and MAIDIS.
Table 2 tries to compare all existing data of pion production from the proton by using the same kind of fit for all experiments. The extracted multipoles deviate from the quoted values in the corresponding publications, since most of them were extracted in the past with further model assumptions to reduce the error bars. As can be seen, the deviation seems to be burried in the multipole combination P23, which is already fixed by photoproduction and can not be adjusted in the calculation to describe the data. Since the discrepancy is large and surprising, this subject urgently needs further investigation. An experiment at MAMI is planned to cover a continuous range in Q2, while an independent experiment is planned at JLab16 with extended kinematical coverage using a large acceptance spectrometer.
120
2.0-
1.o
-
-
--
AW = 0.5 MeV
*
L
v)
\
a
A0.5 -
1.5:
AW = 1.5 MeV
--
1.0-
c
d
0.00
0.05
0.10
0.00
0.05
0.1
Figure 4. The total cross section utot versus Qz, at a value of E = 0.8. The solid (dashed) line is the prediction of ChPT13 (MAID"), data points a t Q2 = 0 and 0.1 GeV2/c2 from 7,12.
4
Electroproduction from the Deuteron
The low energy constants of ChPT were adjusted, as shown above, to describe the existing pion photo- and electroproduction data from the proton. By this, one looses some of the predictive power of CHPT, since in threshold experiments the complete amplitude is already given by only few parameters. On the other hand, from the description of the proton amplitudes one can extract predictions for the pion production from the neutron without introducing further degrees of freedom.
121 Table 2. Extracted multipole amplitudes in comparison with the threshold values of ChPT13 and MAID". The AmPSll value for JLo+l was extracted from their value for a0 x e ~ l L o + I ~For . the AmPS lo fit LO+ was fixed, since no Rosenbluth separation was performed
MAM17 ChPT MAID
MAMI12 AmPSlO ChPT MAID
-1.33 -1.14 -1.16
-1.70 -1.29
0.58 f0.18 1.99 f0.3 1.42 2.2
Q2 = 0.1 GeV2/c2 573 -1.38 fll fO.O1 526 -1.33 fixed f 7 -1.33 571 -1.12 315
111 105 95
9.5 9.3 9.3
15.1 50.8 16.4 f0.6 20.1 17.1
-0.6 -3.0
-2.3 f0.2 -1.0 f0.4 -0.6 -1.1
-0.2 2.2
.
0.1 f0.3 -1.0 f0.4 -0.1 1.4
Despite this theoretical advantage, the experimental access to the free neutron amplitude is, as usual, quite difficult. The most promising access seems to be the coherent pion production from a deuteron target. In impulse approximation, the production amplitude is basically given by the coherent isescalar sum of the free proton and free neutron amplitude, corrected by form factors as parameterization of the deuteron structure. In this formalism, special care has to be taken for the rescattering contribution by charged pions in the intermediate state. Current calculations for photo17 and electroprod~ction~~ are restricted to predictions of the threshold s wave amplitudes, since the mixing of the free p wave amplitudes in the re-
122
gion of the breakup of the deuteron to the coherent p wave amplitude from the deuteron requires a substantial extension of the formalism. A first measurement of the photoproduction amplitude was performed at SAL20. The IGLOO detector was used to detect the decay photons of the T O decay in coincidence. By this technique, the missing mass resolution is not sufficient to separate the coherent channel from the deuteron breakup. By calculating this contribution in a simple model the authors were able to extract the threshold value of the s wave amplitude to Ed = (-1.45f0.09) x lO-"/m,. This value falls about 20% below the prediction of ChPT17 of Ed = (-1.8 f0.6) x 10-'/m, but the agreement seems reasonable within the error bars. The extension of this experiments to finite Q2introduces further experimental difficulties. Due to the background conditions for electroproduction the detection of the pion decay photons has to be replaced by the detection of the recoil deuteron, which suffers at the low energies at threshold from energy loss and multiple scattering. On the other hand, by this technique the coherent channel is clearly separated from the deuteron break up reaction and can be extracted without model assumptions. A first threshold measurement of d(e, e'd).rrO was performed at MAMI18. The detection of the deuteron limited this experiment to a four momentum transfer of Q2 = 0.1 (GeV/c)2. As for the similar experiments from the proton, the full center of mass angle was covered up to 4 MeV above threshold and a Rosenbluth separation was performed. While the complete angular structure was measured, only for the s wave threshold multipoles existed a prediction from ChPT. To extract these amplitudes, a fit with the assumption of only s and p wave contributions was performed (fig. 5). Since the electric s wave contribution to the cross section is very small, only an upper limit could be extracted for Ed:
5 0.42. w 3 / m , lLdl = (0.50 f 0.11) ' 10-'//m,. Fig. 6 shows this result in comparison with the calculations of ChPTlg. The dash-dotted curve shows the calculation without rescattering contributions while the solid curve shows the full calculation. The dashed lines are the full calculation with the contribution of the free neutron amplitude varied by f10-3/m, to picturize the sensitivity to this amplitude. As can be seen from this comparison, the electric multipole E d is in agreement within the error bars with the calculations, while the longitudinal multipole Ld is clearly overestimated by theory. In terms of the s wave cross section 00 = €LILd12 the discrepancy is an order of magnitude.
+
123
CMS Energy AW [MeV] Figure 5. The total cross section for three different values of the photon polarization E. The lines show the result of a least squares fit with the assumption of only p and s waves contributing t o the cross section near threshold.
An attempt to explain this huge discrepancy was made by Rekalo and Tomasi-Gustafsson21. They argued, that the contribution of the rescattering terms with an intermediate pion should be suppressed by the Pauli principle and parity conservation. Omitting these graphs would lead to an agreement between the ChPT calculations and the MAMI data.
Acknowledgments This work was supported by the Deutsche Forschungsgemeinschaft(SFB 441) and the Federal State of Rhineland-Palatinate.
124
Ewald et al. Bergstrom et al.
I 0
I
0.05 2 2 -q2 [GeV / c ]
0.
2.01
Figure 6. The extracted 3 wave multipoles from MAMI's(circles) in comparison with the prediction of ChPTXg.The photon point of SAL2' is plotted as a square. For the explanation of the curves see text.
125
References 1. 2. 3. 4.
5.
6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
V. Bernard et al., Nucl. Phys. B 383 (1992) 442 E. Mazzucato et al., Phys. Rev. Lett. 57, 3144 (1986). R. Beck et al., Phys. Rev. Lett. 65, 1841 (1990). P. de Baenst, Nucl. Phys. B24, 633 (1970); I. A. Vainshtein and V. I. Zakharov, Nucl. Phys. B36, 589 (1972). V. Bernard, N. Kaiser, J. Gasser, and U.-G. MeiBner, Phys. Lett.B268, 291 (1991); V. Bernard, N. Kaiser, and U.-G. MeiBner, Z. Phys. C 70,483 (1996). J. C. Bergstrom et al., Phys. Rev. C 53, R1052 (1996). A. Schmidt et al., Phys. Rev. Lett. 87, 232501 (2001). M. Fuchs et al., Phys. Lett. B 368, 20 (1996); A. M. Bernstein et al., Phys. Rev. C 55, 1509 (1997). 0. Hanstein et al., Phys. Lett. B 399 (1997) 13 H. B. van den Brink et al., Phys. Rev. Lett. 74, 3561 (1995). T. P. Welch et al., Phys. Rev. Lett. 69, 2761 (1992). M. 0. Distler et al., Phys. Rev. Lett. 80, 2294 (1998). V. Bernard, N. Kaiser, and U.-G. MeiBner, Nucl. Phys. A607, 379 (1996); A633, 695(E) (1998). H. Merkel et al., Phys. Rev. Lett. 88, 012301 (2002) D. Drechsel et al., Nucl. Phys. A645, 145 (1999); S. S. Kamalov et al., Phys. Lett. B 522, 27-36 (2001). R. Lindgren et al., Experiment E01-014, JLab, 2001. S.R. Beane et al., Nucl. Phys. A 618, 381 (1997) I. Ewald et al., Phys. Lett. B 499, 238-244 (2001) V. Bernard, H. Krebs, U.-G. MeiBner, Phys. Rev. C 61, 58201 (2000) J. C. Bergstrom et al., Phys. Rev. C 57 6, 3203 (1998) M. Rekalo and E. Tomasi-Gustafsson, nucl-th/Ol12063
HADRON STRUCTURE FROM LATTICE QCD* G. SCHIERHOLZ John won Neumann-Institut fur Computing NIC, Deutsches Elektronen-Synchrotron DESY, 0-15738 Zeuthen, Germany and Deutsches Elektronen-Synchrotron DESY, D-22609 Hamburg, Germany E-mail:
[email protected] I present an overview of both the technical issues involved and the progress made so far in the study of hadron structure using lattice QCD.
Introduction
1
Understanding the structure of hadrons in terms of quark and gluon constituents, in particular how quarks and gluons provide the binding and spin of the nucleon, is one of the outstanding problems in particle physics. While perturbative QCD has been crucial in extracting quark, gluon and helicity distributions of the nucleon from experiment, it is inadequate for the more fundamental challenge of calculating them from first principles. The lattice formulation of QCD, combined with numerical simulations, is the only known way of addressing the non-perturbative properties of the theory without any model assumptions. Lattice calculations of hadron matrix elements are rather complex and progress has been slow. However, continuing advances in computing power, and recent theoretical developments, such as - O(a) improvement of the action and the operators, to reduce finite cut-off
effects and to facilitate the extrapolation to the continuum limit, - (non)-perturbative renormalization and matching of the (bare) lattice
operators, -
chiral perturbation theory, to extrapolate reliably from the masses where the lattice calculations are performed to the physical pion mass,
have now brought lattice QCD to the point that definitive quantitative calculations of a host of hadron observables are becoming possible. *This talk is largely based on work done by the QCDSF Collaboration: S. Capitani, M. Gockeler, R. Horsley, B. Klaus, W. Kiirzinger, H. Perk, D. Petters, D. Pleiter, P. W o w , S. Schaefer, A. Schafer, G. Schierholz and A. Schiller.
126
127
In this talk I will highlight recent developments in lattice calculations of hadron structure functions. Special attention will be devoted to higher twist contributions. Due to lack of space I will not be able to cover recent results on nucleon form factors, and I refer the interested reader to the 1iterature.l 2
Theoretical developments
Before I present any results, let me briefly comment on the theoretical developments. There are various choices of discretizing the QCD action, and here the fermion action is of particular interest. The original, unimproved Wilson action S F has discretization errors of O ( a ) , which can be as large as 20% at typical lattice spacings of a M 0.1 fm.2 On top of that it breaks all chiral symmetries. The most promising action is Neuberger's a ~ t i o nwhich , ~ has discretization errors of O ( a 2 )only and possesses an exact chiral ~ y m r n e t r y But .~ numerical simulations of this action take a factor of O(100) more computer time, which limits it to exploratory studies at the moment. A fair compromise is the non-perturbatively improved Wilson action
which, likewise, reduces discretization errors to O ( a 2 )in on-shell quantities, such as masses and matrix elements, if the operators are improved as well:
+
0 + (1 co a m p
+a
c
ci Oi.
i2l
The condition is that the coefficients CSW, cot c1, . . . are computed to nonperturbative precision. The improvement program can be extended to off-shell quantities ~ o o . Furthermore, ~ , ~ the axial Ward identities can be satisfied to so that a systematic restoration of chiral symmetry is possible. The coefficient csw is known non-perturbatively,' while the improvement coefficients of the operators are largely known in one-loop perturbation theory,6910 and to a lesser extent non-perturbatively.ll But the list of non-perturbatively known coefficients is steadily increasing. l2 Another important theoretical issue is renormalization. The lattice operators are, in general, divergent (in the limit a -+ 0) and need to be normalized, O S ( p )= Z@(a),
S : scheme,
(3)
where S must match the normalization condition of the corresponding, perturbatively calculated Wilson coefficient. Usually this is the scheme. As
m
128
5.0 4.0
~
t
1.o
1
#
10
100
(r,d Figure 1. The non-perturbative renormalization constants Z R G r (solid symbols) for quenched Wilson fermions at ,B = 6.0 as a function of ( r ~ p(where ) ~ TO = 0.5 fm), compared with the perturbative results (dashed lines).
long as there are at most logarithmic divergences present, a perturbative calculation of the renormalization constants is possible, and many results have been reported in recent years, both for unimproved l 3 and improved Wilson fermiom6 Because the coupling constant is large, perturbative results are not always reliable, and non-perturbative techniques have been developed. 14,15716 In Fig. 1 I show a comparison of perturbative and non-perturbative renormdization constants for the operators that give the first three moments of the unpolarized structure function of the nucleon, (z), (z2) and (z3).The renormalization constants have been converted to the renormalization group invariant ( R G I ) form ZRG' = AZsZs, using tadpole improved, renormalization group improved, boosted perturbation theory.I7 For the lower two moments the agreement is surprisingly good. The lattice data show distinct discretization errors at larger p2 values though, which grow with the size of the operators (in lattice units) involved. We have made the observation that most of the discretization errors are perturbatively calculable,'8 which should help to remove this source of error and find more convincing plateau values from our simulations. The lattice calculations are currently limited to quark masses that are equivalent to pion masses of m, 2 400 MeV in the quenched case, and to m, 2
129
500 MeV in full QCD. As a result, the lattice data have to be extrapolated to the chiral limit before they can be compared with experiment. Such an extrapolation is far from trivial and must respect the constraints imposed by chiral symmetry, in particular as the existence of Goldstone bosons leads, in general, to a behavior which is non-analytic in the quark mass. At small pion masses hadronic observables can be systematically expanded in a series in m, using chiral perturbation theory. Recently, one-loop formulae became available for the moments of the unpolarized and polarized structure functions of the nucleon, as well as for the tensor charge:”
analytic terms, analytic terms, analytic terms, where NS stands for the non-singlet or valence quark contribution, g A is the axial vector coupling of the nucleon, and A is a phenomenological parameter which determines the scale above which pion loops no longer yield rapid variation. Similar formulae are available for singlet contributions 2o and nucleon form factors.21 The message is that the pion loop (cloud) results in a large deviation from linearity at small m,. This suggests that important physics is omitted by a naive (linear) extrapolation, and even though one need not calculate at the physical pion (quark) mass, the pion mass must be small enough that the parameters of the chiral expansion are well determined by the lattice calculations. 3
Structure functions
Basics
The nucleon has four structure functions, zF1, F2, g1 and g2. The operator product expansion (OPE) relates moments of them to nucleon matrix elements. For the unpolarized structure functions this reads
130
where the Wilson coefficients c are independent of the target, and vi2)are the leading, twist-two reduced matrix elements of the nucleon defined by
and being renormalized at the scale p. I will return to higher-twist contributions in the next section. In parton model language @ =: ( p - l
(8)
where qT (z, p ) (qI (z, p ) ) , the parton distribution function, measures the probability of finding a quark q (= u, d, . . . ) with fractional momentum 2 and helicity + (-) inside the nucleon. Similarly, for the polarized structure functions we have
In parton model language 1
-2 an
=: An4 =
1'
dsz"
(dZ,p ) - a(",P ) )
where Au - Ad = QA
7
131
o'6 h
0
II
s PI
t
1
0.4
A
x v
0.2
0
Figure 2. The lowest non-singlet moment (z)against (m.rro)2 (where TO = 0.5 fm) for improved quenched Wilson fermions, together with the phenomenological value (*). 0.a
0.6
h
0
0.2
0
Figure 3. The same as Fig. 2, but for improved N f = 2 dynamical Wilson fermions.
132
(A := A'), while d,, has twist three and no parton model interpretation. The structure of the nucleon is not completely described by the parton distributions (8) and (10). In addition we have22
where q l ( x , p ) (qT(Z,p)) measures the probability of finding a quark in an eigenstate $Iy5 = +1/2 (-1/2) in a transversely polarized nucleon, and g T ( p ) = 6u - 6d
(13)
is the tensor charge of the nucleon. The moments (12) are obtained from H H . . . Dp,,$, and reduced matrix elements of operators of the form i&,,ysDpl q L ( z ,p ) and q ~ ( ~ ,can p )be measured in Drell-Yan processes. The expressions given above refer to the continuum and chiral limit. The moments must not depend on the scale parameter p. In principle one could compute the Wilson coefficients in lattice perturbation theory ( p = l / u ) . This would save us from having to renormalize the operators (and the Wilson coefficients). But lattice perturbation theory converges badly, and it is extremely hard to do calculations beyond one (fermion) loop. At first sight it seems that all one has to do now is compute the reduced matrix elements on the lattice and renormalize the operators within the class of operators stated. However, the matter is complicated by the fact that current lattice fermions break chiral symmetry, which gives rise to mixing with lower dimensional operators of opposite chirality not showing up in the (continuum) OPE. I will restrict myself to a few highlights now. Among them are the chiral extrapolation of (sn), which is a hot subject right now, the axial vector coupling and the tensor charge, the former being a benchmark calculation of QCD, and the twist-three contribution d2 to the lowest moment of g2, which is of considerable phenomenological interest and a theoretical challenge as well.
Moments of unpolarized structure function In Figs. 2 and 3 I show the lowest non-trivial moment of the unpolarized parton distribution function for improved quenched 23 and improved N f = 2 dynamical Wilson fermions. (For a very recent calculation with unimproved Wilson fermions see Ref. 25.) Both quenched and dynamical results have been extrapolated to the continuum limit. (In the dynamical case the lever arm is very short though.) The quenched and dynamical results hardly differ. The lines are linear extrapolations to the chiral limit. They overestimate the phenomenological result 26 by approximately 40%. I estimate that 17324
133 0.6
0.4
om
ZZ
x
v
0.2
fl
X 0 Chiral MRS extrapol. 0
Chiral extrapol.
i1 0
Figure 4. The non-singlet moment (2)for quenched Wilson fermions at 0 = 6.0. The two leftmost points with larger error bars are obtained on 323 48 lattices, the other points on 243 32 and 163 32 lattices.
the renormalization constants have a systematic uncertainty of a few per cent only and, hence, cannot account for this discrepancy. The higher moments, which I cannot show here, show a similar effect. The arrows on the right-hand side of the figures point to the non-relativistic result. It is important to understand the origin of this deviation. It has been argued l9 that the light pion cloud is not adequately represented by a linear extrapolation in the quark mass. To test that, we are currently doing simulations at pion masses of 300 MeV and smaller on large lattices (m,L > 4, L being the linear extent of the lattice) for quenched Wilson fermions. (In the quenched approximation one encounters a pion cloud as well with slightly reduced coupling^.^^) In Fig. 4 I show some very preliminary results, which indicate that the data indeed bend down towards the phenomenological value, though it is too early to jump to conclusions. The curve shows an (unconditioned) fit of (4) to the lattice data, which reproduces the phenomenological number and gives A M 350MeV. If true, this means that one will have to do simulations at pion masses of m, 5 300 MeV in order to determine the parameters of the non-linear expansion reasonably well.
134
Axial vector coupling and tensor charge Before one can make contact with chiral perturbation theory, one has to extrapolate the lattice data not only to the continuum limit, but also to the infinite volume. In the unpolarized case we did not see significant finite volume effects in quenched and full QCD. For gA this is different. In the dynamical case g~ increases by x 10% if the lattice size is increased from L = 1.5 fm to L = 2.2 fm. In Fig. 5 I show Q A extrapolated to the infinite volume for improved dynamical f e r m i o n ~ The . ~ ~ data points lie on a straight line, as before. However, this time a linear extrapolation gives good agreement with experiment, while a non-linear extrapolation of the form (5), with A = O(400 MeV), would undershoot the experimental value by 30-40%. It should be noted that the amount of curvature depends crucially on the value of A, which is a phenomenological parameter and can vary from process to process. A different finds a rather flat dependence of gA on mT,combining chiral perturbation theory with Pad6 techniques. The arrow on the righ-hand side of the figure shows again the non-relativistic result. ~' In Fig. 6 I show our prediction for the tensor charge gT = ( 6 ~ - 6 d ) ~for improved dynamical fermions. It appears that it saturates Soffer's inequality 29
2gT 5 1 + g A .
(14)
Twist-three matrix element In our first paper3' on g2 we computed operator
d2
from the matrix element of the
and the corresponding renormalization constant Z 5( u p ) was computed perturbatively. The operator (15) has dimension five. This calculation has been copied by other authors25. It misses the point though that for Wilson-type fermions the operator (15) mixes with the operator
which has dimension four and opposite chirality to (15). Thus, the correct renormalization condition reads
The renormalization constant Z 5 ( a p ) and the mixing coefficient Z " ( a p ) have been computed recently.31 At p2 = 5GeV2 we find Z"/Z5 M -0.2, which
135
Figure 5 . The axial vector charge gA against ( r n , r ~ for ) ~ improved Nf = 2 dynamical Wilson fermions, together with the experimental value (*). 2
1.5
0.5
0
Figure 6 . The tensor charge ( b ~ - b d ) ~against ~' ( r n , r ~for ) ~improved Nf = 2 dynamical Wilson fermions.
136
0.00
.
-0.01.
zigure 7. The reduced matrix element dz a t p2 = 5GeV2 against the lattice spacing a for )roton (open symbols) and neutron (solid symbols), together with the experimental values at a = 0).
ias a big effect on the result of d 2 . In Fig. 7 I show d2 for quenched Wilson ermions and three /? values. The numbers have been extrapolated linearly o the chiral limit. Now, with mixing effects taken properly into account, we ind good agreement with experiment.
L
Higher twist contributions
'ower corrections to structure functions provide insight into the mechanism hat binds quarks and gluons to hadrons. Phenomenological determinations Nf quark and gluon distribution functions msume that power corrections are .egligible down to Q2 5 1 GeV'. But that has never been testified. The evaluation of power corrections is a very difficult task.32. Let us reonsider the lowest moment of F2, now including the twist-four contribution:
general, the twist-four matrix element v P ' ( p ) has an UV renormalon amiguity in any soft renormalzation scheme, which must be cancelled by a xresponding IR renormalon ambiguity in the Wilson coefficient c p )(Q 2 ,p ) . I
137 0.12,
,
I
I
I
,
I
O . 0O 4 5L - - - - - J
10
,
I
Q2
I
I
,
I
[G e15V ]
I
I
I
,
I
I
I
,
20
Figure 8. The non-singlet moment M 2 ( Q 2 )against Q2 in the quenched approximation at /3 = 6.0, compared with the phenomenological (parton model) result. T h e nucleon matrix elements have been extrapolated linearly t o the chiral limit.
To achieve this, one will have to compute the Wilson coefficient to very high orders in perturbation theory. The problem is unambiguously defined and amenable to calculation if operators and Wilson coefficients are regularized on the lattice:
Due to the hard cut-off (- l/a) "?)(a) has no renormalon ambiguity. Kowever, it will develop a quadratic divergence, which has to be cancelled by exactly the same singularity in the Wilson coefficient. This is only possible if c?)(Q2,p ) is computed non-perturbatively, i.e. on the lattice, as well. The moments (7) and (9) are obtained from the OPE
bIJp(dJv(-dlP)
+ '.= '
c
c ~ " p l . . . p , ,a( )~bl"E...pn l lP)
(20)
m,n
after Nachtmann i n t e g r a t i ~ n where ~ ~ , q is the euclidean photon momentum (q2 = Q2). On the lattice the left-hand side will receive contributions from seagull terms, which are denoted by dots. We truncate the series at spin > 4, which amounts to neglecting power corrections cx l/Q4. To determine the Wilson coefficients, we compute (plJ,(q)J,(-q)lp) . . and ( p I c 3 ~ . , , p , z Ifor p) a large set of quark states lp) of different momenta. This then defines a linear set of equations, which we can solve for ~ ~ ~ ~ ~ . by . ,a singular ~ ~ ( qvalue , ~ ) d e c o m p o ~ i t i o nTo .~~ obtain the moments of the nucleon structure function, we
+.
138
finally have to combine this calculation with a calculation of the appropriate nucleon matrix elements. A bonus of the calculation is that we do not have to renormalize the operatots. We encounter strong mixing effects between the twist-four matrix element "?)(a) and the Wilson coefficient c?)(Q2,a ) , as was to be expected. The net power corrections turn out to be small though. In Fig. 8 I show our results for the moment M2(q2)of proton minus neutron structure functions. The errors originate almost entirely from the nucleon matrix elements (which are independent of Q 2 ) , and so are highly correlated. We thus may conclude that power corrections are small down to Q2 values of a few GeV2. A recent experimental analysis comes to the same c o n c l u ~ i o n . ~ ~ 5
Conclusions
The precision of numerical results is steadily improving, due to increasing computer power, the use of improved actions and improved operators, and non-perturbative renormalization. The price is high though. For a modest calculation one needs to determine O(20) parameters to non-perturbative precision. First results on nucleon structure functions (and form factors) including the effects of dynamical quarks are available now. We do not see big differences between quenched and dynamical results in non-singlet quantities. By and large we find good agreement with experiment, except for (xn). Whether (z) will eventually approach the phenomenological value at small m,, as suggested by chiral perturbation theory, is currently being investigated. To estimate the range of applicability of chiral perturbation theory, and in particular to understand why it fails in the case of g A , a two-loop calculation would be very helpful. We were able to compute higher-twist contributions to nucleon structure functions in a completely non-perturbative setting. The resulting power corrections to the lowest moment of F2 turn out to be small, which I consider an important prediction.
References 1. M. Gockeler et al. [QCDSFCollaboration], Nucleon electromagnetic form factors from lattice QCD, to be published shortly. 2. M. Gockeler et al., Phys. Rev. D57 (1998) 5562. 3. H. Neuberger, Phys. Lett. B417 (1998) 141. 4. M. Luscher, Phys. Lett. B428 (1998) 342.
139
5. B. Sheikholeslarni and R. Wohlert, Nucl. Phys. B259 (1985) 572. 6. S. Capitani et al., Nucl. Phys. B593 (2001) 183. 7. G. Martinelli et al., Nucl. Phys. B611 (2001) 311. 8. S. Capitani et al., Nucl. Phys. (Proc. Suppl.) 63 (1998) 871. 9. K. Jansen and R. Sommer, Nucl. Phys. B530 (1998) 185; pvl. Guagnelli et al., Phys. Lett. B459 (1999) 594. 10. S. Sint and P. Weisz, Nucl. Phys. B502 (1997) 251. 11. For a summary of results see: T. Bhattacharya et al., Phys. Rev. D63 (2001) 074505. 12. R. Horsley, Nucl. Phys. (Proc. Suppl.) 94 (2001) 307. 13. G. Martinelli and Y.-C. Zhang, Phys. Lett. B123 (1983) 433; S. Capitani and G. Rossi, Nucl. Phys. B433 (1995) 351; G. Beccarini et al., Nucl. Phys. B456 (1995) 271; M. Gockeler et al., Nucl. Phys. B472 (1996) 309; S. Capitani et al., Nucl. Phys. B570 (2000) 393. 14. K. Jansen et al., Phys. Lett. B372 (1996) 275. 15. G. Martinelli et al., Nucl. Phys. B445 (1995) 81. 16. M. Gockeler et al., Nucl. Phys. B544 (1999) 699. 17. S. Capitani et al., Nucl. Phys. (Proc. Suppl.) 106 (2002) 299. 18. M. Gockeler et al. [QCDSF Collaboration], in progress. 19. W. Detmold et al., Phys. Rev. Lett. 87 (2001) 172001; D. Arndt and M. Savage, Nucl. Phys. A697 (2002) 429; J.-W. Chen and X. Ji, Phys. Lett. B523 (2001) 107. 20. D. Arndt and M. Savage, Ref. 19. 21. B. Kubis et al., Phys. Lett. B456 (1999) 240. 22. R.L. Jaffe and X. Ji, Phys. Rev. Lett. 67 (1991) 552. 23. M. Gockeler et al. [QCDSF Collaboration], in preparation. 24. M. Gockeler et al. [QCDSF-UKQCD Collaboration], in preparation. 25. D. Dolgov et al., hep-lat/0201021. 26. A.D. Martin et al., Phys. Lett. B354 (1995) 155. 27. J.W. Chen and M. Savage, nucl-th/0108042. 28. T.R. Hemmert, private communication. 29. J . Soffer, Phys. Rev. Lett. 74 (1995) 1292. 30. M. Gockeler et al., Phys. Rev. D53 (1996) 2317. 31. M. Gockeler et al., Phys. Rev. D63 (2001) 074506. 32. G. Martinelli and C.T. Sachrajda, Nucl. Phys. B478 (1996) 660. 33. 0. Nachtmann, Nucl. Phys. B63 (1973) 237. 34. S. Capitani et al., Nucl. Phys. (Proc. Suppl.) 73 (1999) 288; M. Gockeler et al. [QCDSF Collaboration], in preparation. 35. C.S. Armstrong et al., Phys. Rev. D63 (2001) 094008.
PHOTOEXCITATION OF N* FtESONANCES ANNALISA D'ANGEL0'i2i* FOR THE GRAAL COLLABORATION 0. BARTALIN13p4,V. BELLIN15, J.P. BOCQUET', M. CASTOLD17, ANNALISA D'ANGELO',', ANNELISA D'ANGELO'>', J.P. DIDELEZ', R. DI SALVO'>', A. FANTINI'>', G. GERVINOg, F. GHIO", B. GIROLAMI", A. GIUSA5, M. GUIDAL', E. HOURANY8, V. KOUZNETSOV'~", R. KUNNE', A. LAPIK", P. LEV1 SANDR14, A. LLERES', D. MORICCIANI', V. NEDOREZOV", L. NICOLETT15i6, C. RANDIER15, D. REBREYEND', F. RENARD', N.V. RUDNEV", C. SCHAERF'?', M. L. SPERDUT05, C. M. SUTERA5, A. TURINGE'3, A. ZABRODIN1', A. ZUCCHIATT17 Universitci degli Studi d i Roma "Tor Vergata", Via della Ricerca Scaentifica,l I-00133 Rome, Italy
' INFN, Sezione d i Roma 11, Italy Universita d i T k n t o , Italy INFN, Laboratori Nmionali d i fiascati, Italy Universitci d i Catania and INFN, Sezione LNS, Italy
' INZP3, Institut des Sciences Nuclbaire, Grenoble, fiance INFN, Sezione Genova, Italy IN2P3, Institut de Physique Nucl6aaire, Orsay, Fmnce INFN, Sezione d i Torino, Italy lo
Istituto Superiore d i Sanitci and INFN Sezione d i Roma I, Italy
'' Institute for
'' Institute for l3
Nuclear Research, Moscow, Russia
Theoretical and Experimental Physics, Moscow, Russia
L. Kurchatov Institute of Atomic Energy, Moscow, Russia * E-mail: annalisa.dangeloQmma2.infn.it
We present an overview of most recent experimental results of photonuclear reactions in the resonance energy region. High precision and polarization obsenables are the key issues in the study of N ' resonance properties.
140
141
1
Introduction
The excited states of the nucleon were observed for the first time in n-- N scattering experiments, as clear peaks in the cross-section. Partial-wave analysis of n- - N elastic scattering data and charge exchange reactions have provided quantum numbers, masses and widths of most of the baryonic (N and A) resonances . Smaller sets of data are available for pion induced reactions with Nq, A K , AE or N m produced in the final state. They have provided information on the branching fraction for the N' decaying into different baryon-meson channels. Meson photoproduction reactions have been used to extract the electromagnetic transitions amplitudes (the A1i2 and the A3/2 helicity amplitudes), providing complementary dynamical information on the composite structure of the baryons. It is very difficult to eliminate the model dependence in the extraction of baryonic parameters from experimental results. For example a model independent multipole analysis of meson photoproduction would require precise measurements of cross section and polarization observables for a complete set of results. These must include a minimum of eight single and double polarization observables, in the case of pseudoscalar meson photoproduction. The minimum number of independent observables increases to 23 in the case of vector meson photoproduction. In lack of such complete information, the extraction of resonance parameters relays on both the choice of a theoretical model and on the quality of data. At energies above the &3(1232) the task is complicated by the overlapping of several broad resonances. Having these resonances fixed quantum numbers, their contribution to a scattering process appears only in specific multipoles. However the values of resonance parameters extracted in a multipole analysis depend on the procedure used to discriminate the resonant from the background contribution. Recently a new generation of precise data on meson photoproduction, including single and double polarization measurements, has become available. This is due to the advent of high quality, polarized and tagged electron and photon beams (MAMI-B, ELSA, LEGS, GRAAL, LEPS, JLAB, BATES), coupled with large solid angle detectors and, in some cases, also with polarized targets. At the same time these results have stimulated the theoretical community to refine the models and t o increase their efforts to understand and quantify the theoretical uncertainties of resonance parameters, by comparing results obtained by different procedures on the same data set. This is the case of the Baryon Resonance Analysis Group (BRAG) that is promoting the collaboration among theoretical and experimental physicists to work towards a commonly accepted review of the resonance parameters, extracted from modern electromagnetic and hadronic facilities.
'
142
2
The First Resonance Region and the A(1232) EMR
In the energy region corresponding to masses up to 1400 MeV, the excitation of the A(1232) resonance dominates the reaction mechanisms. It is therefore possible to extract its parameters with high precision, not yet achieved at higher energies. The yN + A transition proceeds mainly through magnetic dipole (M1 or M:?), due to a quark spin flip. The presence of a d-wave admixture in the nucleon wave-function allows for a small contribution from the electric quadrupole (E2 or E:c) transition amplitude. The origin of the d-wave component, that breaks the spherical symmetry of the nucleon, differs in various models of the nucleon. In constituent quark models (CQM), inspired to Quantum Cromo-Dynamics (QCD), the d-wave component arises from the introduction of an effective color-magnetic tensor interaction, while in chiral bag models the nucleon deformation is ascribed to the asymmetric coupling of the meson cloud to the nucleon spin. The ratio of resonant E2 to M1 transition strengths (EMR) is the experimental quantity of interest. Its value has been extracted from a large amount of available data, using different analysis procedures. The decomposition of amplitudes into a resonant and a background term is model dependent and not unique. Most analysis do not explicitly calculate the influence of non-resonant mechanisms on the resonance properties, such as interference contributions from Born terms and meson rescattering. It is not the bare value of the EMR to be extracted in such analysis, but the value the EMR dressed by the meson cloud. Precise measurements, including polarization observables, on 7 p -+ 7ro p , 7 p -+ 7r+ n and Compton scattering have been provided by the Mainz and Legs laboratories. Because the A decays into TRN final states with 99.4% branch and back to the yN state with 0.6% branch, the analysis of simul-
Table 1. Values of the dressed A(1232) resonance EMR and helicity amplitudes extracted by the most recent multipole analysis by Legs and Mainz groups. Results are compared with the latest edition of the Review of Particle Physics.
Mainz analysis Legs analysis PDG
REM (%)
AlI2 ( 1 0 - ~ / a
All2 ( 1 O r 3 / m
-2.5 f 0.1 f 0.2 -3.07 f 0.26 f 0.24 -2.5 f 0.5
-( 131 f 1) -(135.7 f 1.3 f 3.7) -(135 f 6)
-(251 f 1) -(266.9 f 1.6 f 7.8) -(255 f 8)
143
220 240 260 280 300 320 340
220 240 260 280 Mo 320 340 360
Figure 1. Differential cross sections and beam polarization asymmetries for the reactions T p + y p , T p -+ xop and q p -+ x+n, measured by the mainz (open circles) [2,4] and the Legs (full circles)[3,5] laboratories.
taneous measurements of previous channels has the potential to extract A properties with high accuracy. Figure 1 shows results obtained for the dif-
144
Table 2. Results for M1, E2 and EMR from the analysis of various groups belonging to BRAG [6,7].Values for M1 and E2 are expressed in units those for EMR are given in %.
REM
Effective Lagrangian RPI Partial wave anal. GWU SAID Multipole anal. fixed-t disp. relations H A Multipole anal. unitary isobar mod. MAID Dynamical mod. by Yang & Kamalov KY Fixed-t disp. relations by Aznauryan AZ Multipole anal. by Omeiaenko O M Average
-
281
-6.6
278
-5.3 -6.2 -6.3
281.3 & 4.5
-6.6 f 0.8
-2.55 -2.57 -2.35 -1.93 -2.24 -2.28 -2.77 -2.38 f0.27
&
ferential cross section and the beam polarization asymmetries for Compton scattering and no photoproduction, at polar angle equal to 90" in the center of mass. Also data at 85" in the center of mass for the n+n reaction channel are plotted. Full circles are Legs measurements, empty circles are those from Mainz. Very high precision results and good agreement among data are obtained for the beam polarization asymmetries C. While Compton scattering differential cross section data nicely agree, a 10% overall scaling factor is necessary t o reconcile the differential cross section results of pion photoproduction reactions. Table 1 shows results obtained for A resonance parameters extracted by multipole analysis performed by the two laboratories on their own measurements. Results are compared with the latest Review of Particle Physics' evaluation. The differance between the two laboratories results may be ascribed to the disagreement among measured differential cross sections. The Baryon Resonance Analysis Group (BRAG) 6,7 has performed the analysis of a "bench-mark" data set of 1287 points on photoreactions and pion induced reactions, not including the latest results from Mainz and Legs, using several theoretical approaches to study the model dependence in the extraction of the dressed values of the M1 and E2 strengths. Results were published in and are reported in Table 2. The average result should not be taken as a final value, because it is based on the chosen data set, which does not include all recent experiments. However the results fluctuation is very small and the extraction of a 2% effect may be obtained with a 0.3% percent model dependence.
145
t
I 0
200
:140
101)
500
6(w)
70(1
,yno
E, (MeV) Figure 2. Measured values of the total absorption cross section difference between the two relative helicity states of the proton and the longitudinally polarized photon. Results are from Mainz (open and full circles). Data are compared with predictions by Hanstein et al. (dot-dashed curve), rnultipole analysis by SAID (solid curve) and the Unitary Isobar Model (MAID) (dotted curve).
3
Double polarization measurements and the GDH sum-rule
The first measurements obtained with a polarized photon beam on a polarized target represent an important break through in the study of photonuclear reactions. First data on photoabsorbtion cross sections on the proton have been obtained at Mainz using a longitudinally polarized beam on a frozen spin butanol target in the energy range 200 < E, < 800 MeV. The difference between the total cross section measured in the two relative spin configurations of photons and protons in the initial state, namely 0312 is plotted in Figure 2. Open and full circles are experimental results, compared with predictions by Hanstein et al.” (dot-dashed curve), multipole analysis by SAID12 (solid curve) and the Mainz Unitary Isobar Model (MAID)I3 (dotted curve). Only the last calculation includes multi-pion and 9 photoproduction 879910
146
contributions and predictions fail to reproduce the full strength of the cross section difference in the second resonance region. These first measurements may be used to experimentally verify the GDH14 sum-rule, defined as follows: (0312
- 0112)-
du u
2x2a =-IC~
M2
= 204pb
where u is the photon energy, uo is the pion photoproduction threshold, a is the fine-structure constant, M is the proton mass and IC is the anomalous magnetic moment of the proton. The experimental contribution to the integral appearing on the left side of the sum-rule, in the measured energy range, is 226 f 5 f 12pb. The combination of this result with estimations of the contributions in the missing energy ranges, provides a total result which is consistent with the GDH sum-rule within the experimental errors. The extension of this measurement to higher energies is underway at the Bonn laboratory15. First results using a polarized Compton backscattered ?-ray beam on a frozen spin HD target, have been obtained at Legs16. Very promising measurements have been obtained in three days of data taking, only. The beam polarization was changed regularly among six states: circular polarization parallel or antiparallel to the proton polarization, linear polarization with the polarization vector oriented vertically, horizontally or at an angle of f45". For the first time it was possible to extract all double polarization asymmetries involving beam and target. More data taking is expected in the near future. 4
Single and double pion photoproduction
New precise results on the differential cross section and C have been obtained at GRAAL for the 7 p -+ xo p reaction, in the energy range from 600 to 1100 MeV17, and for the beam asymmetry C for the T p -+ x+n reaction at energies from 600 to 1500 Comparison with existing well established results provided excellent confidence on the quality of the data. The inclusion of these results in the latest GWU-SAID data base12 has produced significant modifications in some of the partial cross section of the SAID Partial Wave Analysis. The new solution (FAO1) requires a stronger contribution of the Pl3(1720) resonance and a suppression of the &,(1620), with respect to previous analysis, to reproduce the complex structure of the experimental results. Important new data have been obtained also on the two-pion photoproduction channels ( y p + x+xon and -yp -+ xo.rrop) by the Mainz group20921.
+
+
147
The resonant excitation mechanisms have been understood to be dominated by the &(1520) excitation”, subsequently decaying into Ao7r+ or Ao7ro. The model however could not reproduce the full strength of the 7r+7ro channel. The measurement of the invariant mass spectra of the x7r systemsz1 was the key to reveal for the first time the direct decay D13(1520) -+ pN in the 7r+7ro channel.
5
q photo-production
Most of the CQM models predict more states than those experimentally observed. It is possible that the “missing” states have not been observed because they are weekly coupled to 7rN channels. Evidence of their existence may be observed in other channels, such as q N , p N , Kh and wN. The study of the q meson photeproduction offers the advantage of a reduced complexity for the resonances involved in the reaction. Since 7) carries isospin I = 0, only I = 1/2 N* resonances may be excited and only those having significant qN branching ratio may contribute. Measurements of the C polarization observable add the ability to pin down small contributions from higher multipole resonances through their interference with the main terms. Extraction of the qN partial widths and photocoupling amplitudes of the corresponding resonances are then possible, even if the qN branching ratios are very smallz7. Very precise results for the differential cross section have been obtained by the GRAAL collaboration from the reaction threshold up to E, = 1.1 GeV. They cover the full angular range, for a total of 233 data points.24. The data are in good agreement with existing Maimz6 data and confirm the near isotropic behavior of the angular distribution up to E, = 0.9 GeV, arising from the dominance of the Sll(1535) excitation. A multipole expansion up to second order shows that deviations from isotropy at higher energies are mainly due to quadrupole terms, associated with the 013(1520) resonance. However, the onset of the P-wave is clear at energies above E, = 1.0 GeV, confirming similar results from q electro-prod~ction~~.
Table 3. Values of the Sll(1535) resonance parameters extracted from 9 photwproduction.
0.3 - 0.55
148
0.8
0.6
Ey=0.7458GeV
1
Ey=0.7965GeV
Ey=0.8596GeV
t
0.4
0.2 0 Ey=0~9308GeV
Ey=0.9909GeV
t
0.6
+
-
0
-
0
-
0
0 -
-
'
'
1
'
'
'
'
-
0
0 O & I
0
Q
0
0.4 -
0.2
t
I
I
I
4
-
0 L
Q
I
I
,
,
L
Figure 3. Preliminary results for the beam polarization asymmetry for the reaction: ? + p -+ q + p from the GRAAL collaboration. Open squares are results obtained with the UV Laser line and a maximum y-ray energy of 1487 MeV. They are compared with the previous results obtained with a maximum y-ray energy of 1.1 GeV, shown with open circles. Dashed lines show the latest Partial Wave Analysis of the SAID group[l2], including GRAAL data. Bold and dotted lines show the analysis based on the Li and Saghai quark mode1[25]. Solid lines show a global fit [27] of the GRAAL beam asymmetries (231, the Mainz differential cross sections [26] and the Bonn target asymmetries[28].
Results for the total cross section are available up to E7 = 1.1 GeV. These measures cover the full energy range of the Sll(1535) resonance for the first time. Fig. 3 shows published C beam asymmetry resultsz3 together with a sample of preliminary data up t o E7 = 1.48 GeV. The observable is dominated by the interference of the D13(1520) with the main S-wave.
149
Deviations from the sin% distribution are due to contributions from other multipoles. Data are compared with the multipole analysis performed by the GWU groupl2 including all GRAAL data (B012 solution), plotted as a dashed line. Curves from a new analysis based on a chiral constituent quark modelz5, that includes all known resonances up to 2 GeV and does not incorporate tchannel exchange terms, are also reported. This model requires the inclusion of a third &1(1730) K A quasi-bound state to reproduce the forward peak in the cross section. Bold and dotted curves in Fig. 3 show the results with and without the third 4 1 “missing” resonance. A global fitz7, combining Mainz differential cross section data26, published GRAAL asymmetry dataz3 and Bonn target asymmetry resultsz8, is plotted as a solid line. Results have been also included in the MAID 2000 analysis using an isobar modelz9 and in a coupled-channel analysis using an Effective Lagrangian model and BetheSalpeter equation in K-matrix appro~irnation~~. The values for the SII(1535) resonance parameters, extracted using these different approaches, are summarized in Table 1 and are compared with the values quoted by the Particle Data Group. Clear discrepancies still remain among the values of the resonance width and of the photocoupling amplitude. 6
K+ A and w photo-production
New data are available on the KX channel from the SAPHIR c o l l a b o r a t i ~ n ~ ~ . They show a structure in the differential cross section that has been reproduced33 using an isobar model which includes a missing D13(1960) resonance. The same model predicts for C trends of opposite sign if the missing resonance is included or not. Very preliminary data for the C beam asymmetry in the K + A reaction channel have been produced by the GRAAL collaboration. They have clearly positive values in the energy range from E, = 1050 MeV to E7 = 1400 MeV and confirm the presence of the 013(1960) resonance. More data are expected from the SAPHIR and LEPS collaborations. Very promising results are expected for the y p + w p reaction channel. Total and differential cross sections are dominated by the diffractive terms, described by Pomeron and meson (KO, 77) exchange mechanisms in the t-channel, while resonance contributions have some importance at low energies and backward angles. Polarization observables on the contrary are p r e d i ~ t e d ~ to *’~~ be very sensitive to resonance excitation. Diffractive terms are expected to give very small contribution t o the beam polarization asymmetry C and large asymmetry values are a direct evidence of resonance excitation contributions. First very preliminary measurements on the C asymmetry have been pro-
150
r/
-c.3 -c.4
-0.6 -E.8
F
Figure 4. Very preliminary results from the GRAAL collaboration for the beam asymmetry C integrated over the w decay solid angle, for the reaction G p + wp. Results are compared with prediction from [35]. Dashed curve is the contribution from Pomeron and meson exchange terms alone. Solid curve is the full calculation, including all resonances with masses up t o 2 GeV.
duced by the GRAAL collaboration in the energy region from threshold to 1500 MeV. A sample of these data is reported in Figure 4, together with predictions from Q. Z h a ~ Dashed ~ ~ . curve is the calculation including t-exchange terms only, solid curve is the full calculation including all N* resonances contributions with masses up to 2 GeV. General agreement between data and theoretical predictions is observed and the sizable strength of the C observable is expected to be very sensitive to the inclusion of specific resonances, such as the PI3(1720).
Acknowledgments We are grateful to C. Bennhold, A. Waluyo, Wen-Tai Chiang, B. Saghai and I. Strakovsky for useful discussions and communication of their work prior to publication. We would like to thank J. Ahrens for very useful information and we are very obliged to A. Sandorfi, A. Lehmann and all the Legs-Spin Collaboration for communication of their results prior to publication.
151
References
1. Rev. of Part. Phys. 2000, Eur. Phys. J. C 15, 1-878 (2000). 2. R. Beck et al, Phys. Rev. Lett. 78, 606 (1997). 3. R. Blampied et al, Phys. Rev. Lett. 79, 4337 (1997) 4. R. Beck et al, Phys. Rev. C 61, 035204 (2000). 5. G. Blampied et al, Phys. Rev. C 64, 025203 (2001). 6. R. M. Davidson, NSTAR 2001, Proceedings of the Workshop on the Physics of Excited Nucleons Mainz, Germany 7 -10 March 2001, Ed. D. Drechsel and L. Tiator, World Scientific, 203-206, (2001). 7. R.A. Arndt et al., nucl-th/0106059, 2001. 8. J. Ahrens et al., Phys. Rev. Lett. 84, 5950 (2000). 9. J. Ahrens et al., Phys. Rev. Lett. 87, 022003 (2001). 10. A. Braghieri these proccedings. 11. 0. Hanstein et al. Nucl. Phys. A 632, 561, (1998). 12. Partial Wave Analysis by SAID at GWU. R.A. Arndt, 1.1. Strakovsky and R.L. Workman, Phys. Rev C 53 430, (1996). Said solutions and data base are available at
[email protected]. 13. D. Drechsel, 0. Hanstein, S. Kamalov and L. Tiator, Nucl. Phys. A 645, 145 (1999). Predictions are available at URL http://www.kph.unimainz.de/MAID2000. 14. S.B. Gerasimov, Siv. J. Nucl. Phys. 2, 430 (1966); S.D. Drell and A.C. Hearn, Phys. Rev. Lett. 16, 430 (1966). 15. Michael these proceedings. 16. A. Lehman these proceedings. 17. F. Renard Thesis, Univ. J. Fourier, Grenoble, (1999). 18. J. Ajaka et al., Phys. Lett. B 475, 372, (2000). 19. 0. Bartalini et al. accepted for pubblication by Phys. Lett. 20. M. Wolf et al. Eur. Phys. J. A 9, 5 (2000). 21. W. Langgaerten et al., Phys. Rev. Lett. 87, 052001 (2001). 22. J.A. Gomez Tejdor and E. Oset, Nucl. Phys. A 600, 413, (1996). 23. J. Ajaka et al, Phys. Rev. Lett. 81, 1797 (1998). 24. F. Renard et al., Phys. Lett. B 528, 215 (2002). 25. B. Saghai and Z. Li, Eur. Phys. J. A 11, 217 (2001). 26. B. Krusche et al, Phys. Rev. Lett. 74, 3736 (1995). 27. L. Tiator, D. Drechsel and G . Knochlein Phys. Rev. C 60,035210 (1999). 28. A. Bock et al, Phys. Rev. Lett. 81, 534 (1995). 29. Wen-Tai Chiang et al. Proceedings of the Workshop on the Physics of Excited Nucleons Mainz, Germany 7 -10 March 2001, Ed. D. Drechsel and L. Tiator, World Scientific, 171 (2001).
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30. C. Bennhold et a1 nucl-th/9901066, nucl-th/0008024; T. Feuster and U. Mosel, Phys. Rev. C 59, 460 (1999). 31. R. Thompson et al, Phys. Rev. Lett. 86, 1702 (2001); C. S. Armstrong et al, Phys. Rev. D 60,052004 (1999). 32. M.Q. "ran et all Phys. Lett. B 445, 20 (1998). 33. C. Bennhold et al. nucl-th/0008024. 34. Y . Oh et al. Phys. Rev. C 63,025201 (2001). 35. Q. Zhao, Phys. Rev. C 63, 025203 (2001). Curves are from private communication.
INSTANTONS AND BARYON DYNAMICS DMITRI DIAKONOV NORDITA, Blegdamsuej 17,DK-2100 Copenhagen, Denmark E-mail: diakonovOnordita.dk PNPI, Gatchina, St. Petersburg 188 300, Russia I explain how instantons break chiral symmetry and how do they bind quarks in baryons. The confining potential is possibly irrelevant for that task.
1
Introduction
According to common wisdom, moving a quark away from a diquark system in a baryon generates a string, also called a flux tube, whose energy rises linearly with the separation. The string energy, however, exceeds the pion mass m, = 140MeV at a modest separation of about 0.26fm, see Fig. 1. At larger separations the would-be linear potential is screened since it is energetically favorable to tear the string and produce a pion. Virtually, the linear potential can stretch to as much as 0.4fm where its energy exceeds 2m, but that can happen only for a short time of l/m,. Meanwhile, the ground-state baryons are stable, and their sizes are about 1fm. The pion-nucleon coupling is huge, and there seems to be no suppression of the string breaking by pions. The paradox is that the linear potential of the pure glue world, important as it might be to explain why quarks are not observed as a matter of principle, can hardly have a direct impact on the properties of lightest hadrons. What, then, determines their structure? We know that, were the chiral symmetry of QCD unbroken, the lightest hadrons would appear in parity doublets. The large actual splitting 940) implies that chiral symmetry between, say, N ( !j-, 1535) and N ( is spontaneously broken as characterized by the nonzero quark condensate < ijq >= -(250MeV)3. Equivalently, it means that nearly massless (‘current’) quarks obtain a sizable non-slash term in the propagator, called the dynamical or constituent mass MCp), with M ( 0 ) -N 350MeV. The pmeson has roughly twice and nucleon thrice this mass, ie. are relatively loosely bound. The pion is a (pseudo) Goldstone boson and is very light. The sizes of these hadrons are typically l/M(O) whereas the size of constituent quarks is given by the slope of M ( p ) and is much less. It explains, at least on the qualitative level, why constituent quark models are so phenomenologically successful.
if,
-
153
154
r/fm
2.50
-
2.00
-
1.50
-
1.00
-
0.50
-
0.00
1
2
3
4
5
Figure 1. The lattice-simulated potential between static quarks exceeds mrrat the separation of 0.26 fm (left). The screening of the linear potential is clearly seen in simulations at high temperatures but below the phase transition (right). As one lowers the pion mass the string breaking happens at smaller distances; the scale is fi N 425 MeV N (0.47 frn)?'.
We see thus that the spontaneous chiral symmetry breaking (SCSB) rather than the expected linear confining potential of the pure glue world is key to the understanding the origin of the ground-state hadrons. It may be that for highly excited hadrons the importance of confinement forces 'usSCSB is reversed: I discuss it at the end of the paper. In the main part I briefly review the instanton mechanism of the SCSB suggested and worked out by Victor Petrov and myself in the middle of the 80's. Much analytical and numerical work calculating hadron observables has supported this mechanism, for reviews. There is also growing support from direct lattice see Refs. simulations, see below. Instantons induce strong interaction between quarks, leading to bound-state baryons with calculable and reasonable properties. 334
576
2
What are instantons?
Being a quantum field theory, QCD deals with the fluctuating gluon and quark fields. A fundamental fact is that the potential energy of the gluon field is a periodic function in one particular direction in the infinite-dimensions functional space; in all other directions the potential energy is oscillator-like. This is illustrated in Fig. 2. Instanton is a large fluctuation of the gluon field in imaginary (or Euclidean) time corresponding to quantum tunneling from one minimum of the potential energy to the neighbor one. Mathematically, it was discovered by Belavin, Polyakov, Schwarz and Tiupkin; the tunneling interpretation was given by V. Gribov. The name 'instanton' has been introduced by 't Hooft lo
155
Figure 2. Potential energy of the gluon field is periodic in one direction and oscillator-like in all other directions in functional space.
Figure 3. Smoothing out the normal zero-point oscillations reveals large fluctuations of the gluon field, which are nothing but instantons and anti-instantons with random positions and sizes. The left column shows the action density and the right column shows the topological charge density for the same snapshot. l 1
who studied many of the key properties of those fluctuations. Anti-instantons are similar fluctuations but tunneling in the opposite direction in Fig. 2. Instanton fluctuations are characterized by their position in space-time z p, the spatial size p and orientation in color space 0, all in all by 12 collective coordinates. The probability for the instanton fluctuation is, roughly, given
156
by the WKB tunneling amplitude,
( 4i2F;")
exp(-Action) = exp --
Jd4z
= exp
(-F).
(I)
It is non-analytic in the gauge coupling constant and hence instantons are missed in all orders of the perturbation theory. However, it is not a reason to ignore tunneling. For example, tunneling of electrons from one atom to another in a metal is also a nonperturbative effect but we would get nowhere in understanding metals had we ignored it. Indeed, instantons are clearly seen in nonperturbative lattice simulations of the gluon vacuum. In the upper part of Fig. 3 (taken from the paper by J. Negele et al. 11) a typical snapshot of gluon fluctuations in the vacuum is shown. Naturally, it is heavily dominated by normal perturbative UV-divergent zero-point oscillations of the field. However, after smearing out these oscillations (there are now several techniques developed how to do it) one reveals a smooth background field which has proven to be nothing but an ensemble of instantons and anti-instantons with random positions and sizes. The lower part of Fig. 3 is what is left of the upper part after smoothing. The average size of instantons found in ref. l1 is p w 0.36fm and their average separation is R = ( N / V ) - a w 0.89fm. Similar results have been obtained by other lattice groups using various techniques. A decade earlier the basic characteristics of the instanton ensemble were obtained analytically from the Feynman variational principle 12J3 and expressed through the only dimensional parameter A one has in QCD: p w 0.48/Am N 0.35fm, R w 1.35/Am N 0.95 fm, if one uses A m = 280 MeV as it follows from the DIS data. The theory of the instanton vacuum is based on the assumption that the QCD 'partition function' is saturated by large nonperturbative fluctuations of the gluon field (instantons), plus perturbative oscillations about them. It takes the form of a partition function of a liquid (like H2O) of N+ instantons and N - anti-instantons:
where Uint is the interaction depending on relative positions, sizes and orientations of instantons. Actually, it is a grand canonical ensemble of interacting 'particles' since their numbers N h are not fixed but must be found from the minimum of the free energy and ultimately expressed through A = f exp(- $) appearing through the 'transmutation of dimensions' from
1 57
integrating over perturbative gluons ( a is the UV cutoff, e.g. the lattice spacing). The numbers for p and R quoted above come from the study of this ensemble. a l27I3
3
How do instantons break chiral symmetry?
We now switch in light quarks into the random instanton ensemble. The basic property is that massless quarks are bound by ,instantons with exactly zero ‘energy’. These localized states are called quark zero modes, discovered by ’t Hooft lo. They have definite helicity or chirality: left-handed quarks are localized on instantons ( I ) and right-handed are on anti-instantons ( I ) . However, this is correct only for a single (anti)instanton. If there is a If pair, no matter how far apart, the degeneracy of the two would-be exactly zero modes is lifted owing to the overlap of their wave functions. If there are infinitely many 1 ’ s and ps, each of them brings in a would-be zero mode but, because of the quantum-mechanical overlap, the degenerate levels split and form a continuous spectrum, meaning the delocalization of the would-be zero modes. The effect is similar to the so-called Anderson conductivity: the appearance of the conductivity of electrons bound by random impurities. It can be shown mathematically that a finite density of quark states at zero ‘energy’ means spontaneous chiral symmetry breaking, and one can calculate the chiral condensate from the average overlap of the zero-mode wave functions and express it through the basic quantities characterizing the instanton ensemble, i.e. the average size of instantons and their density 3 . However, there is a simpler physical argument. Each time a quark ‘hops’ from one random instanton to another it has to change its helicity. Delocalization implies quarks make an infinite number of such jumps. An infinite number of helicityflip transitions generates a non-slash term in the quark propagator, i.e. the dynamically-generated mass M ( p ) , see Fig. 4. It implies the spontaneous chiral symmetry breaking. Two different formalisms have been developed in the 80’s to calculate hadron observables: (i) first computing an observable and then averaging it over the instanton ensemble and (iz) first averaging over the ensemble which leads to an effective low-energy theory, and then computing observables in the effective theory. Despite very different appearance the two formalisms give “The first study of the instanton ensemble on a qualitative level was performed by Callan, Dashen and Gross l4 and later on by Shuryak 15. Ilgenfritz and Mueller-Preussker l 6 were the first to study the instanton ensemble quantitatively by modelling the interactions by a hard-core repulsion.
158
Figure 4. Quarks hopping from instantons to anti-instantons and vice versa flip helicity (left). An infinite number of such jumps generates a dynamical mass M ( p ) , in MeV (right).
identical final results. Let me list a few of them:
< qq >= --const. R2p
N
-(255MeV)3,
N
-
M ( 0 ) = const. 7rP 345MeV, (3) R2 -
100 MeV vs. 94 MeV (exper),
const. m,, = -- 980 MeV vs. 958 MeV (exper) . .
ii
N
(4) (5)
where “const.” are computable numerical constants of the order of unity. Recently, the instanton mechanism of the SCSB has been scrutinized by direct lattice methods. At present there is one group l 9 challenging the instanton mechanism. However, the density of alternative ‘local structures’ found there explodes as the lattice spacing decreases, and this must be sorted out first. Studies by other groups 1 7 7 1 8 support or strongly support the mechanism described above. In particular, in a recent paper Gattringer l8 convincingly demonstrates that quarks in near-zero modes concentrate in the regions where the gluon field is either self-dual (1’s) or anti-self-dual (ps). Since near-zero modes are responsible for the SCSB it is a direct confirmation of the instanton mechanism. 17118~19
4
Baryons
There is a remarkable evidence of the importance of instantons for the baryon structure. In Ref. l1 the so-called density-density correlation function inside the nucleon has been measured both in the full vacuum and in the instanton vacuum resulting from the full one by means of smoothing. The correlation
159
(N)
0.01 0
0.5
1.5
1
x (fm)
Figure 5. Density-density correlation function in the nucleon. l 1 Filled circles are measurements in the full gluon vacuum (corresponding to Fig. 3a,b) while open circles are measured in the vacuum with instantons only (Fig. 3c,d). Despite that linear confining potential is absent in the instanton vacuum the nucleon structure seems to be very well reproduced.
in question is between the densities of u and d quarks separated by a distance x inside the nucleon which is created at some time and annihilated at a later time. The two correlators (‘full’ and ‘instanton’) are depicted in Fig. 5: one observes a remarkable agreement between the two, up to x = 1.7fm. It must be stressed that neither the one-gluon exchange nor the linear confining potential present in the full gluon vacuum survive the smoothing of the gluon field shown in Fig. 3. Nevertheless, quark correlations in the nucleon remain basically unaltered! It means that neither the one-gluon exchange nor the linear confining potential are important for the quark binding inside the nucleon. As a matter of fact, the same remark can be addressed to the lightest mesons r and p since the density-density correlators for these hadrons also remain basically unchanged as one goes from the full glue to the reduced instanton vacuum. l 1 Therefore, one must be able to explain at least the lightest T ,p, N on the basis of instantons only. The dynamics remaining in the instanton vacuum is the SCSB, the apearance of the dynamical quark mass M ( p ) , and quark interactions induced by the possibility that they scatter off the same instanton. Actualy these interactions named after ’t Hooft, are quite strong. They are in fact so strong that for quark and antiquark in the pion channel they eat up the 700 MeV of twice the constituent quark mass to nil, as required by the Goldstone theorem. In the vector meson channel ’t Hooft interactions are suppressed, and that is why the p mass is roughly twice the constituent quark mass. In the nucleon they are fully at work but in a rather peculiar way: instanton-induced interactions can be iterated as many times as one wishes in the exchanges between quarks, see Fig. 6 , left. It can be easily verified that the diagram in Fig. 6 , left, can be drawn as three continuous quark lines going from the 1.h.s of the diagram to its r.h.s., without adding closed loops. Therefore, that kind of interaction arises already in the so-called quenched approximation. At the same time, it 495
160
Figure 6. ’t Hooft interactions in the nucleon (left) essentially come to quarks interacting via pion fields (right).
yields plenty of Z-graphs absent in “valence QCD” but which are necessary to reproduce hadron properties. 2o Summing up all interactions of the kind shown in Fig. 6, left, seems to be a hopeless task. Nevertheless, the nucleon binding problem can be solved ezcactly when two simplifications are used. The first exploits the fact that in the instanton vacuum there are two lightest degrees of freedom: pions (since they are the Goldstone bosons) and quarks with the dynamical mass M . All the rest collective excitations of the instanton vacuum are much heavier, and one may wish to neglect them. Pions arise from summing up the qq bubbles schematically shown in Fig. 6, left. The resulting effective low-energy theory takes the form of the non-linear a-model: 4,21 ~ ~ = f [ig f - M e x p ( i ~ ~ ~q. ~ ~ ~ / ~ ~ ( )6 ) ] The absence of the explicit kinetic energy term for pions (which would lead to the double counting) distinguishes it from the Manohar-Georgi model. 22 Expanding the exponent to the first power in nA we find that the dimensionless pion-constituent quark coupling, M Qnqq = - M 4, (7)
Fn
is quite strong. The domain of applicability of the low-energy effective theory (6) is restricted by momenta p < 1/p = 600MeV, which is the inverse size of constituent quarks. At higher momenta one starts to feel the internal structure of constituent quarks, and the two lightest degrees of freedom of Eq. (6) become insufficient. However, the expected typical momenta of quarks in the nucleon are of the order of M M 345 MeV, which is inside the domain of applicability of the low-momentum effective theory. The chiral interactions of constituent quarks in the nucleon, following from the effective theory (6), are schematically shown in Fig. 6, right, where quarks are denoted lines with arrows. Notice that, since there is no explicit
161
kinetic energy for pions in Eq. ( 6 ) , the pion propagates only through quark loops. Quark loops induce also many-quark interactions indicated in Fig. 6 as well. We see that the emerging picture is rather far from a simple one-pion exchange between the constituent quarks: the non-linear effects in the pion field are essential. The second simplification is achieved in the limit of large N,. For N , colors the number of constituent quarks in a baryon is N , and ,all quark loop contributions are also proportional to N,. Therefore, at large N , one can speak about a classical self-consistent pion field inside the nucleon: quantum fluctuations about the classical field are suppressed as l / N c . The problem of summing up all diagrams of the type shown in Fig. 6 is thus reduced to finding a classical pion field pulling N, massive quarks together to form a bound state. 5
Chiral Quark-Soliton Model
Let us imagine a classical time-independent pion field which is strong and spatially wide enough to form a bound-state level in the Dirac equation following from Eq. ( 6 ) . The background chiral field is color-neutral, so one can put N , quarks on the same level in an antisymmetric state in color, i.e. in a color-singlet state. Thus we obtain a baryon state, as compared to the vacuum. One has to pay for the creation of this trial pion field, however. Since there are no terms depending directly on the pion field in the low-momentum theory (6) the energy of the pion field is actually encoded in the shift of the lower negative-energy Dirac sea of quarks, as compared to the free case with zero pion field. The baryon mass is the sum of the bound-state energy and of the aggregate energy of the lower Dirac sea. It is a functional of the trial pion field; one has to minimize it with respect to that field to find the self-consistent pion field that binds quarks inside a baryon. It is a clean-cut problem, and can be solved numerically or, approximately, analylically. The description of baryons based on this construction has been named the Chiral Quark-Soliton Model (CQSM). The model reminds the large-2 Thomas-Fermi atom where N , plays the role of 2. Fortunately, corrections to the model go as l/Nc or even as 1/N: and have been computed for many observables. In the Thomas-Fermi model of atoms corrections to the self-consistent (electric) field are of the order of l/aand for that reason are large unless atoms are very heavy. In the end of the 80’s and the beginning of the 90’s dozens of baryon characteristics have been computed in the CQSM, including masses, mag23724325
162
netic moments, axial constants, formfactors, splittings inside the mutliplets and between multiplets, polarizability, fraction of nucleon spin carried by quarks, etc. - see for a review and references therein. Starting from ’96 a new class of problems have been addressed, namely parton distributions in the nucleon at low virtuality. 27 Parton distributions are a snapshot of the nucleon in the infinite momentum frame. One needs an inherently relativistic model in order to describe them consistently. For example, a bag model or any other nonrelativistic model with three quarks in a bound state, being naively boosted to the infinite-momentum frame gives a negative distribution of antiquarks, which is nonsense. On the contrary, being a relativistic fieldtheoretic model CQSM predicts parton distributions that satisfy all general requirements known in full QCD, like positivity and sum rules constraints. Numerous parton distributions have been computed in the CQSM, mainly by the Bochum group. There have been a number of mysteries from naive quark models’ point of view: the large number of antiquarks already at a low virtuality, the ‘spin crisis’, the large flavor asymmetry of antiquarks, etc. The CQSM explains all those ‘mysteries’ in a natural way as it incorporates, together with valence quarks bound by the isospin-1 pion field, the negative-energy Dirac sea. Furthermore, the CQSM predicts nontrivial phenomena that have not been observed so far: large flavor asymmetry of the polarized antiquarks 29, transversity dictributions 30, peculiar shapes of the so-called skewed parton distributions 31 and other phenomena in hard exclusive reactions. 32 Baryon dynamics is rich and far from naive “three quarks” expectations. 26i6
27328929
6 Conclusions 1. The would-be linear confining potential of the pure glue world is necessarily screened by pion production at very moderate separations between quarks. Therefore, light hadrons should not be sensitive to confinement forces but rather to the dynamics of the spontaneous chiral symmetry breaking (SCSB). 2. Most likely, the SCSB is driven by instantons - large nonperturbative fluctuations of the gluon field having the meaning of tunneling. The SCSB is due to ‘hopping’ of quarks from one randomly situated instanton to another, each time flipping the helicity. The instanton theory of the SCSB is in agreement with the low-energy phenomenology (cf. the chiral condensate < qq >, the dynamical quark mass M ( p ) , F,, m,r ...) and seems to be confirmed by direct lattice methods. Furthermore, lattice simulations indicate that instantons alone are responsible for the properties of lightest hadrons r,P,N , ...
163
3. Summing up instanton-induced quark interactions in baryons leads t o the Chiral Quark-Soliton Model where baryons appear t o be bound states of constituent quarks pulled together by the chiral field. The model enables one t o compute numerous parton distributions, as well as ‘static’ characteristics of baryons - with no fitting parameters. 4. For highly excited baryons ( m = 1.5 - 3 GeV) the relative importance of confining forces us. those of the SCSB may be reversed. One can view a large-spin J resonance as due to a short-time stretch of an unstable string or, alternatively, as a rotating elongated pion cloud. 33 What picture is more adequate is a question to experiment. In the first case the dominant decay is on the average of the type Bar J + Bar, J / z Mes, J/2; in the second case T + Bar~-2 TT + ... Studying it is mainly a cascade BZJ + Barj-1 resonances can elucidate the relation between chiral and confining forces.
+
+
+
References
1. G. Bali, K. Schilling and A. Wachter, in Confinement 95, eds. H. Toki et al. (World Scientific, Singapore, 1995) p.82, hep-lat/9506017. 2. F. Karsch, E. Laermann and A. Peikert, Nucl. Phys. B605,579 (2001), hep-lat/0012023. 3. D. Diakonov and V. Petrov, Phys. Lett. B 147,351 (1984); Sou. Phys. JETP 62,204 (1985); ibid. 62,431 (1985); Nucl. Phys. B272,457 (1986). 4. D. Diakonov and V. Petrov, Spontaneous Breaking of Chiral Symmetry in the Instanton Vacuum, preprint LNPI-1153 (1986), in: Hadron Matter under Extreme Conditions, eds. G. Zinoviev and V. Shelest (Naukova dumka, Kiev, 1986) p.192. 5. D. Diakonov, in: Proc. of Enrico Fermi School, Course 130, eds. A. Di Giacomo and D. Diakonov (10s Press, 1996), hep-ph/9602375; T. Schafer and E. Shuryak, Rev. Mod. Phys. 70,323 (1998). 6. D. Diakonov and V. Petrov, in: At the Frontier of Particle Physics, ed. M. Shifman (World Scientific, Singapore, 2001) p.359, hep-ph/0009006. 7. L.D. Faddeev, Looking for multi-dimensional solitons, in: Non-local Field Theories (Dubna, 1976) p.207; R. Jackiw and C. Rebbi, Phys. Rev. Lett. 37,172 (1976). 8. A. Belavin, A. Polyakov, A. Schwartz and Yu. Tyupkin, Phys. Lett. 59, 85 (1975). 9. A. Polyakov, Nucl. Phys. B120,429 (1977). 10. G. ’t Hooft, Phys. Rev. D14, 3432 (1976).
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11. M.C. Chu, J.M. Grandy, S. Huang and J.W. Negele, Phys. Rev. D 49, 6039 (1994), hep-lat/9312071. 12. D. Diakonov and V. Petrov, Nucl. Phys. B245, 259 (1984). 13. D. Diakonov, M. Polyakov and C. Weiss, Nucl. Phys. B461,539 (1996), hep-ph/9510232. 14. C. Callan, R. Dashen and D. Gross, Phys. Rev. D17, 2717 (1978). 15. E. Shuryak, Nucl. Phys. B203, 93 (1982). 16. E.M. Ilgenfritz and M. Muller-Preussker, NucZ. Phys. B184, 443 (1981). 17. J. Negele, Nucl. Phys. Proc. Suppl. 73, 92 (1999), hep-lat/9810053. 18. T. DeGrand and A. Hasenfratz, Phys. Rev. D64, 034512 (2001), hep-lat/0012021; C. Gattringer et al., Nucl. Phys. B617, 101 (2001), hep-lat/0107016; T. Blum et aZ., Phys. Rev. D65 014504 (2002); hep-lat/O105006; R. G. Edwards and U. M. Heller, Phys. Rev. D65, 014505 (2002); hep-lat/0105004; I. Hip et al., Phys. Rev. D65, 014506 (2002), hep-lat/0105001; C. Gattringer, hep-lat/0202002. 19. I. Horvfith et al., hep-lat/0201008. 20. K.F. Liu et al., Phys. Rev. D59, 112001 (1999), hep-ph/9806491. 21. D. Diakonov, in: Advanced school on non-perturbative quantum field physics, (World Scientific, Singapore, 1998) p.1, hep-ph/9802298. 22. A. Manohar and H. Georgi, Nucl. Phys. B234, 189 (1984). 23. S. Kahana, G. Ripka and V. Soni, Nucl. Phys. A 415, 351 (1984); S. Kahana and G. Ripka, Nucl. Phys. A 429, 462 (1984). 24. M.S. Birse and M.K. Banerjee, Phys. Lett. B 136, 284 (1984). 25. D. Diakonov and V. Petrov, Sou. Phys. JETP Lett. 43, 57 (1986); D. Diakonov, V. Petrov and P. Pobylitsa, in: Proc. 21st PNPI Winter School (Leningrad, 1986) p.158; Nucl. Phys. B 306, 809 (1988). 26. C. Christov et al., Prog.Part.Nucl.Phys. 37, 91 (1996), hep-ph/9604441. 27. D. Diakonov et al., Nucl. Phys. B 480, 341 (1996), hep-ph/9606314; Phys. Rev. D 56, 4069 (1997), hep-ph/9703420. 28. P. Pobylitsa et al., Phys. Rev. D59, 034024 (1999), hep-ph/9804436. 29. B. Dressler, K. Goeke, M. Polyakov and C. Weiss, Eur. Phys. J. C14, 147 (ZOOO), hep-ph/9909541. 30. P. Pobylitsa and M. Polyakov, Phys. Lett. B 389, 350 (1996), hep-ph/9608434. 31. V. Petrov et al., Phys. Rev. D 57, 4325 (1998), hep-ph/9710270. 32. K. Goeke, M. Polyakov and M. Vanderhaeghen, Prog. Part. Nucl. Phys. 47, 401 (2001), hep-ph/0106012. 33. D. Diakonov and V. Petrov, Rotating chiral solitons lie on linear Regge trajectories, preprint LNPI-1394 (1988); see also D. Diakonov, Acta Phys. Polon. B25, 17 (1994).
THE STRANGENESS CONTRIBUTION TO THE FORM FACTORS OF THE NUCLEON F. E. MAAS FOR. T H E A4-COLLABORATION Johannes Gutenberg ClniversitZt Mainz, Institut f i r Kernphysik, J.J. Becherweg 45, 55299 Mainz, E-mail:
[email protected] We report here on a new measurement of the parity violating (PV) Asymmetry in the scattering of polarized electrons on unpolarized protons performed at the MAMI accelerator facility in Mainz. This experiment is the first to use counting techniques in a parity violation experiment. The kinematics of the experiment is complementary to the earlier measurements of the SAMPLE collaboration at the MIT Bates accelerator and the HAPPEX collaboration at Jefferson Lab. After discussing the experimental context of the experiments, the setup at MAMI and preliminary results are presented.
1
Strangeness
1.1 Strangeness in the nucleon The structure of the nucleon is often described in terms of three constituent quarks where these are understood as effective particles with a mass that arises dynamically from a sea of virtual gluons and virtual quark antiquark pairs. The contribution of the strange quarks to this sea is of special interest, since the mass value of the strange quarks is approximately equal to the scale of XQCD and lies inbetween the masses of the very light u and d current quarks and the mass of the much heavier quarks like c,b and t. There is a detailed discussion of the present understanding of the role of strangeness within the nucleon in the literature Unfortunately, the scalar strangeness density Fs does not couple directly to the electr+magnetic probe, therefore the answer on the question of how much strangeness is in the nucleon is not directly available. The analysis of the scattering amplitude in wN-scattering and the connection to the C, term and the scalar density matrix element < NI F s IN > gives a contribution of the strange quark antiquark pairs to the mass of the nucleon on the order of 130 MeV 3 . New data from wN-scattering suggest even a larger value up to 50 % of the proton mass. The observed charm production rate from deepinelastic neutrino nucleon scattering can only be explained if there is a 2% contribution of the strange quarks to the momentum of the nucleon. In polarized deep inelastic muon and electron scattering the axial matrix element
165
166
< NISypy5sIN > is measured. It is equal to the contribution of the strange quarks to the spin of the Proton C,. A value for C, of 0.12 f 0.1 has been extracted4. Our experiment aims at a measurement of the contribution of strange quark antiquark pairs to the elastic vector form factors of the nucleon. 1.2 Extracting the strangeness form factor contribution
The dynamic response of the nucleon structure to electron scattering via the exchange of virtual photons is described in terms of the four elastic form factors: the Dirac form factor F];'"(Q2) of proton and neutron and the Pauli form factor Fg'"(Q2) (another combination are the Sachs form factors, Gg"= FYI" - Fgl" and Gp,n Fg'"). It has been first noted by Caplan M = FP?" and Manohar 5 , that a flavor decomposition of the form factors into the three lightest quark flavors u,d and s can be obtained. This is obtained by combining the form factors of proton and neutron using isospin symmetry and electromagnetic and weak neutral current form factors. If one writes the electromagnetic (FT;;) and the weak form factors (PY;;)decomposed into the three lightest quark flavors:
+
Fp?"
~
Qu 1,z 1,2 = Qu
PP?"
"Fr," + Qd dFrF + Qs "F::," Qd 'F;,'; Qs "FC;
"Fc;+
+
(1) (2)
The left side of Eq. (1) and Eq. (2) represents the eight experimentally accessible electro-magnetic and weak form factors of the nucleon and on the right side are the 12 the unknown flavor contributions. The Q-factors are the electremagnetic and weak charges of the appropriate quark flavor, i.e the electric and the weak charge of quark flavor u,d and s. Isospin symmetry allows to eliminate one half of the unknown quark flavor contributions by replacing the u-quark contributions in the proton by the d-quark contribu-S Fll -+' F I , ~and , tion in the neutron ("F:,2 =d Fc2 -+u F I , ~SFP ) vice versa and to use one strangeness contribution for both proton and neutron. In addition the quark distributions are an intrinsic property of the nucleon and do not depend on the probe. This allows to use the same flavor form factor contributions in Eq. 1 and Eq. 2 (u1d9sF1,2=u9dis F I , ~ Therefore ). the number of unknown flavor contributions on the right side of Eq. 1 and Eq. 2 is now reduced down to 6 unknown flavor contributions u9d3sF1,2,which can be determined, provided the electremagnetic and weak neutral form factors are measured by experiment. The weak neutral form factors enter into the amplitude A4 for elastic scattering of electrons off protons which is described at lowest order (one boson exchange) by the sum of the Feynman diagrams given in Eq. 3: my and
167
mzo. The cross section is given by the square of the amplitude M M * and consists of three terms: the pure y-exchange (m,m;), the 7-Zo interference term (m,m>,) and the pure &exchange (mz,m>o).At the proton vertex the elastic electremagnetic and weak form factors enter and can therefore be measured in electron scattering.
e
e’
e
e’
P’
In elastic electron proton scattering at four momentum transfer in range of 0.1 Gev2 < Q2 < 1 GeV2 the cy-Zo interference term is about 5 orders of magnitude smaller than the pure y exchange. The direct measurement of the weak contribution to the cross section is therefore at present beyond experimental reach. But the parity violating coupling of the ZO gives a unique possibility to separate the pure cy exchange from the interference term. In a measurement of the parity violating asymmetry in elastic scattering of longitudinally polarized electrons on unpolarized protons the pure y exchange (m,ml;) vanishes and one measures directly the interference term. Therefore one has direct access to the weak form factors of the nucleon, since the electremagnetic form factors are known from other experiments. As we have seen above, the determination of the weak form factors is equivalent to a determination of the strangeness contribution to the vector form factors of the nucleon. The experimental quantity which is measured is the difference in the cross section in the scattering of left handed or right handed electrons on unpolarized protons divided by the sum of the two cross sections. This is a parity violating
168
symmetry which can be calculated in the framework of the standard model:
(1 - 4sirl28w) +
+ +
E G ~ G E r G p G" M 2 M 4 cGg2 r G L
€G',G& t rGLGft, cG; 2 + r G L 2
ere r = 4Mp2 Q2 and
E =
+
(1 2(1 + ~ ) t a n ~ ( ; ) and ) - ~t'
=
d ~ ( lr )+ ( l - c2)
sing the flavor decomposition of Eq. 1, the asymmetry in Eq. 5 can be ritten like Eq. 6 as the sum of three terms (7), (8) and (9). (7) contains .ndamental constants and the electremagnetic form factors only. (7) is 'ten referred to as 4. (8) contains the unknown strangeness contribution (9) contains the weak axial form 1 the vector form factors of the nucleon. ctor G A which is known only at Q2 = OGeV2 from neutron beta decay. In rward scattering (9) is strongly suppressed due to the kinematical factors. he sensitivity on the axial term is on the order of 1-2% for HAPPEX and A4 nematics. In the case of backward scattering the sensitivity to the axial form ctor is of the same order as the sensitivity to the magnetic form factor, the :termination of term (9) requires an additional measurement of the parity olating asymmetry Apv on deuterium. Any significant difference between e measured parity violating asymmetry A and Ao is in forward scattering direct measure of the strangeness contribution to the vector form factors of e nucleon. Experiments 1
Approaches
parity violation electron scattering one finds two experiment a1 difficulties d the existing experiments use different techniques to overcome these as
169 Table 1. The different experimental approaches t o separate inelastic from elastic scattering processes at the very high scattered particle flux have been optimized to meet the specific kinematical requirements of each of the experiments. Elastic++Inelastic Experiment S A M P L E 6 ~ 7 ~ 8 ~ 9 low energy, no .Ir-production HAPPEX11~'2~13~ l4ll5 magnetic spectrometer A416 crystal calorimeter (E) GOI8 time of flight (T)
Measurement of High Rate integrating, air Cerenkov integrating in focal plane counting, histogramming E counting, histogramming T
summarized in table 1. First difficulty is the size of the asymmetry without strangeness contribution A0 in Eq. 3 which is used as an estimate of the expected measured asymmetry. For the existing and planned experiments it is on the order of A0 M lop6. A significant determination of the strangeness contribution requires a measurement at a very high rate of elastic scattered electrons in order to determine the asymmetry in reasonable experimental time with an accuracy of a few percent. Second, in the applied Q2 range of the existing and planned experiments, one has inelastic channels like nonresonant .rr-electroproduction or excitations of nucleon resonances like the A . These inelastic channels have to be separated very well from the elastic scattering, since they have their own parity violating asymmetries which are a priori unknown.
2.2
The SAMPLE collaboration at the MIT-Bates accelerator
The SAMPLE collaboration has m e a s ~ r e dat~the ~ ~MIT-Bates ~~ accelerator under backward scattering angles between 130" and 170' using a large solid angle air Cerenkov detector. The beam energy of 200 MeV ensures, that inelastic scattering from .rr-electroproduction is negligible. The Cerenkov light produced by elastic scattered electrons is focused into a photomultiplier tube and the current of the photomultiplier tube is integrated and digitized. The systematic change of beam parameters with helicity are naturally more difficult t o control at the pulsed machine, but on the other hand the lack of any spectrometry or calorimetry makes the experimental setup simpler. The published experimental result for the a s ~ r n m e t r yon ~'~ the proton is:
AFp = -4.92 f0.61 f0.73ppm
( 10)
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The reported value for the quasielastic deuterium asymmetry' is:
A Y p = -6.79 f0.64 f0.55ppm
(11) The combination of the SAMPLE results from hydrogen and deuterium yield a value for the strangeness magnetic form factor contribution: (12) G&(Q2 0.1GeV2) = 0.14 & 0.29 -f 0.31 From the measurements on proton and deuterium it is possible to extract also a value for the isovector axial form factor:
G>(T = 1)
=
+0.22 f0.45 f 0.39
(13) which is in contrast to the calculated value of Zhu et.al.1° of G>(T = 1) = -0.83 f 0.26. In order to investigate this difference and the Q2-dependence of G2 the SAMPLE collaboration has proposed an additional measurement at even lower Q2 of 0.04 GeV2'. The measurement has been finished end of January 2002 and the analysis is in progress.
2.3 The H A P P E X collaboration at TJNAF The Hall A Proton Parity Experiment (HAPPEX) collaboration has measured parity violation in electron scattering at Jefferson Laboratory using the two spectrometers in Hall A. Both identical spectrometers have been used symmetrically and have been set to very forward scattering angles (6 = 12.3'). The scattered elastic electrons have been selected using a lucite-lead detector sitting in the focal plane of the spectrometer. The shape of the calorimeter has been adjusted to detect elastic scattered electrons only which are in the focal plane very well separated from the inelastic channels. The measured asymmetry isl1>l2
A,(Q2 = 0.477GeV2,6 = 12.3')
=
(-14.60 f 0.94 f 0.54) ppm
(14)
The experiment is sensitive to the combination GLt0.392GL t0.018G2. The contribution from the axial form factor had been estimated from calculation'' to ( - 0 . 5 6 f 0 . 2 3 ) p . The value of the strangeness contribution to the asymmetry has been normalized to the proton magnetic form factor and is: G& 0.392GL = 0.091 f 0.054 f 0.039 GLhP The HAPPEX collaboration is planning on two further measurements: A measurement at a lower Q2 of 0.1GeV213which then gives a different combination of G& and G&. The second proposal14 is a measurement with elastic scattering from 4He where all magnetic and axial contributions cancel giving a very clean measurement of G&.
+
171
pol. electron source P=80%, 1=20pA transmission
1022 PbF2-crystsls
Figure 1. A schematic overview on the principle of the A4 experiment is shown.
2.4
The A4 collaboration at the MAMI facility an Main2
The A4 collaboration16 has performed a measurement of the parity violating asymmetry in the scattering of longitudinally polarized 854.3 MeV electrons on unpolarized protons using counting techniques. This is the first time, that a parity violating asymmetry in electron scattering has been measured by counting individual, scattered particles. Particles scattered from the hydrogen target are detected between 30" < 8 < 40" (0.7 srad), resulting in a Q2 at 35" of 0.23 GeV2. The particle rate of elastic scattered electrons in the solid angle of the detector is about 10 MHz where the energy of the elastically scattered electrons is 734 MeV at 35" scattering angle. In addition there is an almost ten times higher background of about 90 MHz coming from other processes. Scattered electrons from pion production are closest in energy to elastic scattered electrons (610 MeV at 35"). Since the pion production has an unknown parity violating asymmetry by itself, the energy resolution of the PbFz-detector has to be good enough to separates these two processes at level better than 1%.Some of the photons from TO-decay can carry almost the energy of an elastic electron due to the three body m-production and additional
172
Figure 2. The left side shows a schematic of the mechanical setup of the lead fluoride calorimeter. The electron beam coming from the left is at about 2.2 m height. The right side is a schematic of the mechanical setup of the associated readout electronics which is in total about 3 m high.
boost17. Figure 1 shows the principle of the experimental setup. It can be divided in three different parts: 1. The electron source with the subsequent MAMI accelerator is the first and important part of the experiment. Helicity correlated changes of beam parameters cause trivial asymmetries in the PbF2detector and therefore need to be suppressed with substantial effort already at the electron source and within the electron accelerator. 2. The fast fully absorbing PbFz-Cerenkov calorimeter with the high power hydrogen target and the luminosity monitor detect the flux of particles and measure the particle energy. 3. In the associated experiment readout electronics the particles are registered and histogrammed with a dead time of 20 ns according to their deposited energy in order to separate elastic scattered electrons from other inelastic channels like n-production. Electrons from a high polarization strained layer GaAs crystal at a current of 20 p A and with a longitudinal polarization of about 80 % are accelerated within the three stages of the MAMI racetrack microtron up to an energy
173
22000L 20000
18000 16000 14000b
4000k
"0
&f 50
100
150
200
250
Figure 3. The datashow an energy spectrum of scattered particles from the hydrogen target as read directly from the hardware memory. The Number of counts per channel is displayed versus the ADC channel. The only correction comes from the differential nonlinearity of the ADC.
of 854.3 MeV. A fast reversal at about 25 Hz of the electron polarization is achieved by a Pockels-cell, which reverses the circular polarization of the laser light hitting the GaAs-crystal. An additional slow reversal of the electron polarization is done by putting in or out an additional X/Zplate in the optical system (GVZ). The electron current at the source is stabilized in a closed feedback loop by measuring the electron current in front of the high power hydrogen target and modulating the power of the laser light hitting the GaAs-crystal. Independently any difference in the electron current for the two different helicity states is controlled to a level of several ppm by adjusting the angle of an additional permanently installed X/2-plate. The energy of the electron beam is stabilized and controlled to a level of A E / E = by measuring the phase advance of the electrons in the last turn of the t h r d stage of MAMI by heterodyne methods and modulating the phase of the accelerating microwaves in the third stage linacs. In order to stabilize and control the position and the angle of the electron beam, the horizontal and vertical position of the electron beam is measured at two locations separated by 10 m in front of the hydrogen target by using position sensitive microwave cavities.
174 n
g20,
W
out
-20
in out out in out in 1
2
4
6
8
10
1
1
1
1
in out in out ,
12
1
1
1
1
1
1
1
14 16 Sample P
Figure 4. The measured decorrelated polarization corrected asymmetries are shown with X/2-plate in or out respectively as a function of the data sample.
The position signal is feedback to fast modulating coils, which then stabilize position and angle of the beam. The stabilization systems within the accelerator and the beam line have made it possible to efficiently suppress false asymmetries in the PbFz-detector. The mean of the helicity correlated variation of individual beam parameters over a data sample correspond to false asymmetries in the PbFz-detector which are less than 0.05 ppm or less than 1 % of the expected asymmetry in the PbFz-detector. The target system is a special new design, whch enforces turbulent flow in the target cell, so that the effective heat conductance is enhanced by transverse flow. The target can stand without boiling the full 20 p A of electron beam current also without any rastering of the electron beam. The left part of Fig. 2 shows a design drawing of the 1022 channel PbFz-Cerenkov calorimeter. For the measurements presented here, only half of the 1022 detector and electronics channels had been installed. The completion of the solid angle is in progress and almost completed. Scattered electrons coming from the left (electron beam height: 2.2 m) pass through the high power liquid hydrogen target. The scattered particles produce an electromagnetic shower in a cluster
175
of lead fluoride crystals. The crystals have a length of between 16-20 radiation lengths and a width of about $ of a Moliere radius so that the full electre magnetic shower of an elastic scattered electron is contained in a 3 x 3 crystal cluster. The Cerenkov light is read out by photomultiplier tubes. 8 waterCerenkov luminosity monitors are located &symmetrically under a scattering angle of 4-10" where the asymmetry from elastic scattering is negligible. The right part of Fig. 2 shows the mechanical setup of the associated 3 m high readout electronics, which consists of 1022 identical readout channels and which has been developed in the Institut fiir Kernphysik in Mainz. The photomultiplier signals of every 3 x 3 cluster are summed in a summation amplifier, integrated over 20 ns, digitized with a fast digitizer and stored in a fast first in - first out pipeline chip. A local maximum signal is derived by comparing the signal of the center crystal with the 4 direct neighbors. The additional requirement of an energy deposit above a threshold triggers the fast digitization. Any second particle hitting the same cluster or any direct neighboring cluster within the integration time of 20 ns would hinder the determination of the energy of the scattered particle and is therefore vetoed by the veto circuit. In this circuit the local maximum signals from the 5 x 5 cluster around the central 3 x 3 cluster need to be controlled. The distribution of the analogue and digital signals is done by a special bus structure where every detector module is connected to the 8 neighboring modules for the analogue signals and where every veto circuit is connected to the 24 neighboring modules for the digital signals. This requires also that the topology of the electronics is the same as the detector, i.e. neighboring detector modules go into neighboring electronics channels. The registered events in the pipeline are histogrammed in hardware memory in VMEbus based modules. The upper part of Fig. 2 right contains the analogue sum, the trigger and veto circuit and the digitization, the lower part contains the galvanically separated VME-bus based histogramming circuits. The whole lead fluoride detector is a completely new development and is used here for the first time. The whole system of electronics and detector achieves an energy resolution of 3.5 % at 1 GeV and a total dead time of 20 ns. The average rate per channel is about
500 k H z Fig. 3 shows a histogram of the scattered particle energies as read out from the histogramming memory of the data acquisition electronics. One can see the peak of elastic scattered electrons in the right part of the spectrum. There is a distinct valley between the elastic scattering and the A-excitation. At lower energies Moeller and Moeller-Mott scattering and excitation of higher resonances mixes together. The leftmost part of the spectrum is defined by the discriminator threshold.
176
There are at present 1022 histograms (511 for each polarization direction) per 5 minutes run which give at present a total of about 10,000,ooO histograms. These histograms together with the recorded beam parameters represent the data set for the analysis. The number of scattered elastic electrons is determined by integrating the histogram between the lower and the upper elastic cut. The number of elastic scattered events is then normalized to the luminosity signal. In a final step the correlation of the cross section with the change of electron beam parameters is analyzed by a standard multidimensional regression analysis in order to determine the measured asymmetry in elastic scattering. The polarization of the electron beam has been measured with a Moeller polarimeter in the hall of the 3-spectrometer setup, where the electron beam is antiparallel with respect to the A4 beam line. The Moeller polarimeter itself has a high accuracy of about 2 % per measurement. The fact that one has to interpolate between two measurements leads to a reduction in the knowledge of the polarization, which is reflected in an enlarged error on the polarization. Fig. 4 shows the final decorrelated, polarization corrected asymmetry as a function of the data sample. The data samples have been taken in a period from November 2000 until June 2001 and April 2002. The dependence of the combined decorrelated asymmetry value on different parameters which are used to select PbF2-spectra or to reject runs because of instable beam conditions etc. has been checked. It has been found that there is no significant variation of the asymmetry value on the different cut parameters. The combined preliminary result on the asymmetry from all data sets is:
Aemp= (-7.3 f0.5 f 0.8) x
lop6
(16)
The first error is the pure statistical error coming form the counting statistics of the scattered particles. The second error is the combined systematical uncertainty from the regression analysis and the uncertainty in the polarisation etc. The isolation of the individual electric or magnetic contribution is not possible with one measurement at this Q2 value only. The further program of the ACcollaboration involves the installation and commissioning of a laser backscatter Compton polarimeter and a transmission Compton polarimeter, which will reduce the uncertainty in the polarization down to possibly 2-3% from now 7 %. The completion of the missing 511 detector and electronics channels is also in progress and very important for the further measurement program. Due to the fact that we use crystals in the calorimeter the Q2 can be changed by changing the beam energy or by reverting the whole detector. This will make it possible to measure at a Q2 of 0.1 GeV2 in forward scat-
177
tering (8 = (35 f 5)") by lowering the beam energy to 570 MeV. In addition the statistical and systematical error at the Q2 value of 0.23 GeV2 will be further reduced. The present planning foresees, that the whole detector will be reverted, so that the scattering angle will be changed to backward scattering between 140" and 150'. We plan measurements at Q2 = 0.23 GeV2 and Q2 = 0.47GeV2 at this backward angle. In combination with the SAMPLE and HAPPEX measurements it will then be possible to make a full flavor separation at the three Q2 values in order to reveal the contribution of the strangeness to the vector form factors of the proton. Acknowledgments
Ths work has been supported by the Deutsche Forschungsgemeinschaft in the framework of the SFB 201, SPP 1034. We are indebted to K.H. Kaiser and the whole MAMI crew for their tireless effort to provide us with good electron beam. We are also indebted to the Al-Collaboration for the use of the Moeller polarimeter. References 1. Musolf et all Phys. Rep. 239,1 (1994).
2. D.H.Beck and B.McKeown, Phys. Rev. D 36,2109 (1987). 3. B.Borasoy and U.-G.Meissner, Ann.Phys. 254,192 (1997). 4. H.Lipkin and M.Karliner, Phys. Lett. B 461,280 (1999). 5. D.Kaplan and A.Manohar, NucI. Phys. B 310,527 (1988) 6. Mueller B.A., et al. Phys. Rev. Lett. 78, 3824 (1997) 7. Spayde D.T., et al. Phys. Rev. Lett. 84,1106 (2000) 8. Hasty R., et al. Science 290,2117 (2000) 9. Ito T., spokesperson. MIT-Bates Lab experiments 00-04 (2000) 10. Zhu S.L., et al. Phys. Rev. D 62,033008 (2000) 11. Aniol K.A., et al. (HAPPEX coll.) Phys. Rev. Lett. 82,1096 (1999) 12. Aniol K.A., et al. (HAPPEX coll.) 13. Kumar K., Lhuillier D., spokespersons. Jefferson-Lab experiment 99-115 14. Armstrong D., spokesperson. Jefferson-Lab experiment 00-114 (1999) 15. Beise E., spokesperson. Jefferson-Lab experiment 91-004 (1991) 16. von Harrach D., spokesp., Maas F.E. contact. MAMI exp. A4-01-93 17. S. Ong, M.P.Rekalo and J. Van de Wiele, Eur.Phys.J. A6, 215 (1999) 18. Beck D., spokesperson. Jefferson-Lab experiment 00-006 (2000)
E L E C T R O M A G N E T I C P R O D U C T I O N OF P I O N S I N THE R E S O N A N C E R E G I O N - T H E O R E T I C A L ASPECTS T. SAT0 Department of Physics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043 Japan E-mail:
[email protected] Theoretical approaches to investigate the structure of nucleon resonances from the pion electroproduction are briefly reviewed. Application of the dynamical approach on the &3(1232) region and the consequences on the y N + A transition form factors are discussed in comparison with the recent data.
+
1
Introduction
A challenging problem in nuclear physics is to understand the hadron structure and reactions in terms of QCD and investigate the role of confinement and chiral symmetry. One way to proceed is to test the predictions of QCD inspired models or lattice simulations using the data of resonance excitations by GeV electron. The baryon resonances in the meson-baryon continuum are excited from the resonant and non-resonant mechanisms. From the unitarity condition, resonance amplitude inherently contains both resonant and non-resonant mechanisms. Since most of the resonant parameters in hadron models are obtained by perturbative calculations of resonance decay, it is necessary to develop an appropriate reaction theory to separate the reaction dynamics to examine the predictions of the hadron models. The main objective of the dynamical approach developed by Refs.[l,2](SL model) is to extract electromganetic couplings of resonances and investigate the role of meson degrees of freedom from the pion photo and electroproduction with the meson-exchange model. The first place to carry out the program is the electromagnetic excitation of the A:p,(1232), which is isolated and almost elastic resonance. Here the interest is the Q2 development of the y N -+ A form factors. The electric and Coulomb quadrupole form factors are particularly interesting in connection with the deformation of the baryons and the helicity conservation law on the exclusive reaction at large Q2. Photon asymmetry data of pion phctoproduction at LEGS3 and Mainz4 have revealed a few % negative E2/M1. New precious and systematic data of pion electroproduction at JLAB5-', MIT-Bates'o>'', M a i n ~ ~ ~ and y'~ NIKHEF14 allow us to investigate the Q2 dependence of y N -+ A form factors and detailed test of the reaction dy-
+
+
178
179
namics, which will help to understand the mechanism of the quadrupole form factors. In this contribution, we briefly describe the existing theoretical a p proaches to extract resonance information form the data in section 2. A p plication of the dynamical approach for the pion electroproduction in the A33(1232) region and the consequence of the model in comparison with the recent data are discussed in section 3. 2
Theoretical Approaches
Essentially three theoretical approaches have been used to extract resonance parameters from the data in A region. One approach is based on the dispersion theory, which is applied for the A resonance region by Mainz group15. The other is effective Lagrangian appr~ach'"'~ based on the K-matrix unitarization with the tree approximation on the K-matrix. The last one is the dynamical approach of meson-exchange model, which has been investigated by several g r o ~ p s ~ - ~ Here , ~ ~we - ~briefly ~ . discuss the later two approaches. 2.1
Effective Lagrangian Approaches
Pion electromagnetic production can be described using Lippmann-Schwinger equation or Bethe-Salpeter equation with Green's function Go and driving term V as
T = V + VGoT, K
=V
+ Re(G0)K.
(1)
The on-shell T-matrix is expressed by only on-shell information of the Kmatrix. T-matrix is then given in the following matrix form for all possible open channels
In the effective Lagrangian approach, one approximates K-matrix by a driving term V evaluated by the Lagrangian model. Taking the first order perturbation of the electromagnetic interaction, T-matrix is approximated as
The first interaction Vp7 is meson production with electromagnetic current and the rest describes the meson-baryon scattering. One can reduce the number of unknown coupling constants of the model by evaluating the strong and
180
electromagnetic interactions V simultaneously with the Lagrangian model. In the Gies~en-GW”.’~works, the open channels are explicitly taken into account, where two pions channel is approximated by effective meson and resonances in the same partial wave can interfere with each other. If we restrict the intermediate state n in Eq. (3) by nN channel, one can obtain the formula of MAID18
<
T$ = (1 - i~PTon),N.,NV:g,
+
c
TT(BW),
(4)
T
with the non-resonant pion production mechanism V/zT,. Here one can replace the nN T-matrix by the scattering amplitude obtained from the phase shift analysis without referring the model. The resonance contribution is included using the Breit-Wigner form independent from non-resonant amplitude, where one introduces phenomenological phase to guarantee unitarity. One should keep in mind that the interpretation of the resonance parameters of the Giessen and MAID approaches might be different with each other beyond the A resonance, since in the latter approach only nN channel is explicitly treated and the resonance contributions are diagonalized.
2.2 Dynamical Approach We discuss the dynamical approach following the SL model. In the dynamical approaches pion photoproduction and electroproduction reactions are described in terms of photon and hadron degrees of freedom. We start from the Hamiltonian and electromagnetic current given as
+rBrttBM, + J L + J&+,BM.
H = HO J’” = J&B
(5) (6)
The interaction Hamiltonian rg,,+EM describes the creation and absorption of a meson ( M )by a baryon ( B ) .The electromagnetic currents include baryon current ( J & B ) , meson current(JL) and seagull current (Jg,++BM). Calculation of the reaction amplitudes from the above Hamiltonian is a nontrivial many body problem. To obtain a manageable reaction model, a unitary transformation method25 is used up to the second order of the strong interaction Hamiltonian. The unitary transformation is chosen to eliminate the ’virtual’ processes, which partially diagonalizes the single baryon state and rewrite the Hamiltonian in terms of the baryon dressed with meson cloud. Within the nN,A and yN Fock space, the effective Hamiltonian has the following form:
H,ff
= UtHU
181 = Ho
+ V,N + ~ A - , N ,
(7)
where V , N is non-resonant T N potential and delta excitation is described by r Q C r r r N . The effective electromagnetic current is given by using the same unitary transformation as
Jfff * E
= Ut J ' U . E
+
= vYrr ~ - , N - A ,
(8)
where vyT is non-resonant pion production interaction and the y N + A interaction is given by r 7 N - A . An important feature of this procedure is that the effective Hamiltonian and current are independent on the total energy of the system and hermitian, therefore the unitarity can be trivially satisfied. One can start from the Hamiltonian determined from the quark model of the hadron26, or one can fix the off-shell behavior of the strong interaction Hamiltonian by studying the T N reaction. In either case, it is noted that the effective current must be treated in a consistent way as the strong interaction Hamiltonian. A set of coupled equations for T N and y N reactions can be derived from the effective Hamiltonian in Eqs. (7) and (8). The pion photoproduction amplitude is written as
The non-resonant amplitude t,, is calculated from vYx by
t 7 , ( E ) = vuy, + ~
, N ( E ) G , N ( E ) ~ ~ ~ .
(10)
The dressed vertices in Eq. (9) are defined as r7N-A
=r7N-A
FQ+?rN
= [I
+~ K N + A G X N ( E ) V ~ T ,
+tlrN(E)GrN(E)]rA-+rrN.
(11) (12)
The A self-energy in Eq. (9) is then calculated from
ZA(E)=r?rN-AGrrN(E)PA+xN-
(13)
Important consequence of the dynamical model is that the influence of the non-resonant mechanisms on the resonance properties can be identified and calculated explicitly. The bare vertex r 7 N - A is modified by the non-resonant interaction vyT to give the dressed vertex ~ - , N + A , as defined by Eq. (11). Similar modification is also for the T N + A vertex. The resonance position of the amplitude defined by Eq. (9) is shifted from the bare mass mA by the self-energy CA ( E ).
182
It will be useful to compare the amplitudes of the effective Lagrangian approach and the dynamical approach. In the dynamical approach Eq. (9) can be rewritten as follows
s
In the effective Lagrangian approach, the second term K,NRe(Go)vT, is not included. Therefore the obtained resonance parameter r 7 N - A is considered to include non-resonant contribution effectively”. This non-resonant rescattering process gives non-trivial Q2 dependence as we shall see in the next section.
3
Pion Electroproduction in the A region
3.1 y
+N
+
A amplitudes
The helicity amplitudes of y N -+ A transition are obtained from the imaginary part of the multipole amplitude of (y,T ) , ’312 AM = clm(M;+ )
(15)
evaluated at the resonance energy where the multipole amplitudes are s u p posed to be pure imaginary. Similarly, electric AE and Coulomb A c quadrupole helicity amplitudes are obtained from E:? and Sl?. In the dynamical approach those amplitudes are decomposed as
F ~ N - A = ~-,N-+A + T T ~ - ~ G T ~ ( E ) v y T .
(16)
r
The ’dressed’amplitude is sum of the ’bare’ amplitude r and the rescattering contribution, which is the last term of the above formula. In SL model, the dynamical model described in the previous section have been applied to the pion-nucleon scattering, pion photoproduction and the pion electroproduction reactions. Most of the strong interaction parameters of the model are determined by studying the T N reaction at first. The analysis of the (y, T ) reaction determines the y N + A ’bare’ coupling constants GM and GE at Q2 = 0. Then for pion electroproduction we take simple assumption. Unknown Coulomb quadrupole Gc(0) is estimated from GE(O) using the long wave length limit approximation. All three bare y N -+ A form factors are assumed to follow the same Q2 dependence as Ga(Q2) = G a ( 0 ) G ~ ( Q 2 ) & ( Q 2 )
+
(17)
with R,(Q2) = (1 aQ2) exp(-bQ2) and Go(&’) is the dipole form factor of proton. Two constants a, b are determined by fitting the JLAB data at
183
.... ............................... .......
.....
........
I 0
1
2
3
4
g2[(Gev/c)*] Figure 1. Q2 dependence of the ratio between M1 form factor and dipole form factor of proton.
Q2 = 2.8 and 4 ( G e ~ / c on ) ~ the resonance energy5. Without any further fine tuning of the model parameters, our results on the other Q2and energy region are our predictions. Fig. 1 shows the Q2 dependence of the magnetic dipole amplitude ( I m ( M : p ) ) at resonance energy calculated by the SL model. The dressed amplitude(so1id line) is in good agreement with the extracted one from the previous works. The dressed amplitude drops faster than proton’s dipole form factor and the difference between bare(dashed curve) and dressed amplitude becomes smaller at higher Q2, which is due to the long range character of the rescattering mechanism. The ’bare’ magnetic dipole strength can be interpreted as the contribution of the quark core. About 40% pion cloud contribution at Q2 = 0 might explain the discrepancy between the predictions of hadron models and the ’empirical’ helicity amplitude. The Q2 dependence of the predicted quadrupole amplitudes I m ( E ; f ) and I m ( S ; f ) are shown in Fig. 2. In our model we need non-zero but small ’bare’ quadrupole strength. The pion cloud contribution enhances strongly these amplitudes but much less at high Q2. This non-resonant mechanism is mainly due to the loop correction of the pion current. Further measurement on the slope of the momentum dependence at low Q2 of those quadrupole amplitudes will test the meson cloud enhancement quantitatively. The ratio REM = I m ( E : f ) / I m ( M : p ) and RSM= Im(SFf)/Im(M,3!”) at resonance energy are shown in Fig. 3 compared with the recent extracted ’data’. The predicted REM and RSM generally follow the Q2 dependence of the extracted ones. In low Q2 region, where pion cloud plays role, our predicted ratios does not agree well with the ’data’. Clearly REM does not
184
Figure 2.
Q2
dependence of I m ( E ; f ) and Im($P).
Figure 3. Q2 dependence of R E M and R S M .
show pQCD limit yet in the current Q2 region. It is interesting to study how REMmay reach pQCD limit in the coming high Q2 investigations.
3.2 Comparison with the Data Unpolarized cross section of ( e ,e’r) reaction in one-photon-exchange approximation is given as23
where differential cross sections are function of pion scattering angle 0,) Q2 and center of mass energy of hadronic system W . 4, is off-plane scattering angle of pion. Longitudinal current can be best studied through the interference term between transverse and longitudinal current darldf2,. d u p / d R ,
185
a
a3
-
1 '
2.
8 . 4 '"
+
Figure 4. Angular distribution of structure functions UT coL(Left),ar (Middle) and op(Right) on p ( e , e ' r + ) reaction at W = 1230MeV. From top panel, Q2 = 0.3,0.4,0.5,0.6(GeV/~)~, respectively.
term essentially measures the same quantity as C of pion photoproduction. Systematic measurement of p(e,e'7r0) at JLAB' at 0.4 < Q2 < 1.8(G'eV/~)~allows separation of three unpolarized structure functions and multipole decomposition using Legendre polynomial. The SL model describes the data well up to the A resonance. This is consistent with the agreement of extracted RSM and SL prediction in this Q2 region. However there is a
186
-0.2 0
40
20
60
0, Figure 5. ATL ofp(e,e’no) reaction at W = 1232MeV and Q 2 = 0 . 1 2 6 ( G e V / ~ ) ~ .
indication of less agreement of our model with the data for the s-wave component of OLT. The model also gives reasonable description on the p ( e , e ’ r f ) reaction shown in Fig. 4 compared with preliminary data at JLAB7, where non-resonant mechanism plays more role than the neutral pion production. In the low momentum transfer region around 0.1 < Q2 < 0 . 2 ( G e V / ~ ) ~ , where the contribution of the pion cloud was essential on the resonant quadrupole amplitudes. ALT data from MIT-Bates”, which measures OLT, are compared with the prediction of SL model in Fig. 5. The double polarPz) are shown in ization with the special parallel kinematics at Mainz12 (Px, Fig. 6. At least for those observables which are the ratio of the matrix elements, prediction of the SL model is not far from the data in contrast to the disagreement of the SL model’s RSM from their reported values. As reported by Ref. 11, the absolute values of response functions in this Q2 region is not so well described in SL model. Further test of the reaction mechanism can be done form the single POlarization data, which measure the imaginary part of the interference between amplitudes and are sensitive to the non-resonant mechanism. The beamhelicity asymmetry measured at Mainz13 is compared in Fig. 7 with SL model, which is about 20% off the data. The JLAB data on polarized structure function’ will be important to further understand the reaction mechanism. 4
Summary
The dynamical model has been developed to investigate the structure of baryon resonance using the GeV electron reactions. The meson exchange model of SL could explain large number of the available data in spite of using the simple assumption on the momentum dependence of the bare form factors. The dynamical model shows the importance of the role of the meson cloud in
187
Pdpc
(“w
-10
20
-1 -20
0 0.2
0
e2(Gev/c)’
0.4
@ (GeV/c)’
Figure 6. Recoil polarization of p(Z, e’p3no reaction at W = 1232MeV.
understanding the y N -+ A form factors. It is however the complete quantitative description of the reaction is yet reached and there are indications on the need of further investigations. For the study of higher energy resonances,
0 -2
-
-4-
-6
-
-8
-
L
i
i
-10
0.1
0.2
0.3
@ (CeV/c)2 Figure 7. p
~ ofpp(Z, e’7r0) reaction at W = 1232MeV.
188
challenging and necessary problem is to develop dynamical model including the three body dynamics. This work was supported by the Japan Society for Promotion of Science, Grant-in-Aid for Scientific Research (c) 12640273.
References 1. T. Sat0 and T.-S. H. Lee, Phys. Rev. C 54, 2660 (1996). 2. T. Sato and T.-S. H. Lee, Phys. Rev. C 63,055201 (2001). 3. G. Blanpied et al., Phys. Rev. Lett. 79,4337 (1997). 4. R. Beck et al., Phys. Rev. C 61,035204 (2000). 5. V. V. Frolov et al., Phys. Rev. Lett. 82,45 (1999). 6. K. Joo et al., Phys. Rev. Lett. 88, 122001 (2002). L. C. Smith, these proceedings. 7. H. Egiyan, Private communication. 8. K. Joo, these proceedings. 9. J. Kuhn, these proceedings. 10. C. Mertz et al., Phys. Rev. Lett. 86,2963 (2001). 11. A. Bernstein, these proceedings. 12. Th. Pospischil et al., Phys. Rev. Lett 86,2959 (2001). 13. P. Bartsch et al., Phys. Rev. Lett 88,142001 (2002). 14. L. D. van Buuren, Nucl. Phys. A684, 324c (2001). 15. 0. Hanstein, D. Drechsel and L. Tiator, Nucl. Phys. A632 561 (1998). 16. R. M. Davidson, N. C. Mukhopadyay and R. S. Wittman, Phys. Rev. D 43 71 (1990). 17. T. Feuster and U. Mosel, Phys. Rev C 59, 460 (1999). 18. D. Drechsel, 0. Hanstein, S.S. Kamalov and L. Tiator, Nucl. Phys. A645 145 (1999). 19. C. Bennhold et al. Proceedings of NSTAR 2001, 109 (2001). 20. H. Tanabe and K. Ohta, Phys. Rev. C 31,1876 (1985). 21. S. N. Yang, J. Phys. G 11, L205 (1985). 22. S. Nozawa, B. Blankleider, and T.-S. H. Lee, Nucl. Phys. A513, 459 (1990). 23. S. Nozawa and T.-S. H. Lee, Nucl. Phys. A513, 511,543(1990). 24. S. S. Kamalov and S. N. Yang, Phys. Rev. Lett. 83 4494 (1999). 25. M. Kobayashi, T. Sato and H. Ohtsubo, Prog. Theor. Phys. 98, 927 (1997). 26. T. Yoshimoto, T. Sato, M. Arima and T. -S. H. Lee, Phys. Rev. C 61, 065203 (2000). 27. S. N. Yang et al, Proceedings of NSTAR 2001, 83 (2001).
HADRONIC PRODUCTION OF BARYON RESONANCES M. E. SADLER. FOR T H E CRYSTAL BALL COLLABORATION Departm.ent of Physics, Abilene Christian Vniversity, 320B Foster Science Building, Abilene, T X 79699-7963, LISA E-mail:
[email protected] The baryon spectroscopy program using the Crystal Ball detector at Brookhaven National Laboratory (BNL) is presented. Precise measurements for n-p and K - p interactions to neutral final states have been obtained. The measurements were performed in the C6 beam line at the BNL AGS, which has a maximum beam momentum of about 750 MeV/c. Data were taken at incident beam momenta as low as 150 MeV/c for pions and 500 MeV/c for kaons. New experiments have been approved that will extend the pion measurements t o even lower momenta and to obtain additional data with kaon beams.
1
Introduction
Data taken in 1998 by the new Crystal Ball Collaboration" have already res u l l e d in six p ~ b l i c a t i o m ~ ~ ~ f four ~ ~ . 5Ph.D. . 6 , dissertation^^^^^^^'^ and a dozen papers in the proceedings of international conferences. This experimental program is being conducted at the Alternating Gradient Synchrotron (AGS) at Brookhaven National Laboratory. The data pertaining to baryon and hyperon spectroscopy, namely, x-p Neutrals and K p + Neutrals, are summarized here. These are the results of AGS experiments E91311 and E91412. The motivation is to improve the determination of the masses, widths and decay modes of N*, A*, A* and C* resonances, to determine the Vn, VA and VC scattering lengths, and to measure the rare and not-so-rare 77 decays. ---$
"The new Crystal Ball Collaboration consists of A. Barker, C. Bircher, B. Draper, C. Carter, M. Daugherity, S. Hayden, J. Huddleston, D. Isenhower, J. Quails, C. Robinson and M. Sadler, Abilene Christian University, C. Allgower, R. Cadmau and H. Spinka, Asgonne Nationd Labomtory, J. Comfort, K. Craig and A. Ramirez, Arizona State University, T. Kycia (deceased), Bmokhaven National Labomtory, M. Clajus, A. Marusic, S. McDonald, B. M. K. Nefkens, N. Phaisangittisakul, S. Prakhov, J. Price, A. Starostin and W. B. Tippens, University of California at Los Angela, J. Peterson, Unzversity of Colorado, W. Briscoe, A. Shafi and 1. Strakovsky, George Washington Univeraity, H. Stalldenmaier, Unaverssitiit Karlsruhe, D. M. Manley and J. Olmsted, Kent State University, D. Peaslee, University of Maryland. V. Abaev, V. Bekrenev, N. Kozlenko, S. Kruglov, A. Kulbardis, and I. Lopatin, Pelersbusg Nuclear Physics Institule, N. Knecht, G. Lolos and 2. Papandreou, University of Regina, I. Supek, Rvdjer Boskovic Institute and A. Gibson, D. Grosnick, D. D. Koetke, R.Manweiler and S. Stanislaus, Valparaiso University
189
190
Figure 1. The Crystal Ball multiphoton spectrometer (cutaway view to show target, beam direction, veto barrel and crystal geometry).
2
The Crystal Ball
The Crystal Ball (CB) detector, designed and built at SLAC, is a highlysegmented, total-energy electromagnetic calorimeter and spectrometer that covers ~ 9 4 % of 47r steradians. A schematic is shown in Fig. 1. The ball proper is a sphere with an entrance and exit opening for the beam and an inside cavity with diameter of 50 cm for the target. It is constructed of 672 optically isolated NaI(T1) crystals that detect individual 7 ' s . Electromagnetic showers in the CB are measured with an energy resolution of 3-5% for gamma rays of 400-100 MeV. Directions of the 7 rays are measured with a resolution of 2-3" in the polar angle. An electromagnetic shower from a single 7 ray deposits energy in several crystals, called a cluster. The cluster algorithm sums the energy from the crystal with the highest energy with that from the twelve nearest neighbors.
191
The experiment utilizes the CB as a niultipholon spectrometer to measure the all-neutral final states that predominantly come from intermediate resonance production, na.mely, n-p
--+
(N*or A*)
--+
multiple 7 ' s
+ n,
(A* or C*)
--+
multiple 7 ' s
+ n,
and K-p
3
--+
Examples of the Pion Data
For pion beams at momenta up to 750 MeV/c, the neutral reaction cha.nnels that can be investigated are n-p w-p n-p n-p w-p n-p n-p
--+
--+
--+
-+ --+
--+ --+
yn Ton qn nonon nonoron noyn Tyn.
Preliminary data at 296.5 MeV/c are shown in Fig. 2. The GWU SM9913 phase shift solution agrees very well with these data over the full angular range, as expected at this momentum since the scattering amplitude is dominated by the well-known A(1232) resonance, Also shown are previous data'4~'5~16~'7 at nearby momenta. Preliminary Crystal Ball results at five momenta below and one momentum above the A(1232) are shown in Fig. 3. The data shown in Figs. 2 and 3 are at momenta where the electron conta.mination in the beam can be determined by timeof-flight information of the beam counters. Data taken at higher momenta have a more uncertain normalization due to the differcnt phase space of electrons in the beam. A gas Cherenkov counter was used to measure the electron contamination but was placed far downstream to minimize background. New runs are planned during 2002 to improve this normalization. An example of the results for n-p --+ 7r0nonis presented in Fig. 4. Shown are Dalitz plots at incident pion momenta from 0.40 to 0.75 GeV/c. There are two TO'S that may be combined with the neutron to form m2(non) along the horizontal axis, so each event is plotted twice, once for each combination. These plots all show an enhancement at the upper end of the
192 n p +no" Near the A( 1232) monance
-. SM99 0 Jembb (293 MeVk)
-1
4.8
4.6
4.4
A
JeneWqW2McVk)
0
B o s k d i n g (MI MeVk)
4.2
0
0.2
0.4
0.6
0.8
1
m m
Figure 2. Preliminary results at 296.5 MeV/c compared with existing data at nearby mcmenta. Only statistical errors are included for the Crystal Ball data.
kinematically allowed region for m2(noro). As explained in the caption, the dominant reaction mechanism is ostensibly n-p noAo 7r0non. This realization creates exciting possibilities for doing a partial-wave analysis for noAo channel in order to elucidate the branching fraction for the 7r-p 7roAo decay of the P11, S11 and D13 rcsonanccs. Such an analysis should improve the determinations for the mass and width of the Pll, which have a range of 1430-1470 MeV and 250-450 MeV, respectively, in the latest edition of the Review of Partzcle Physzcs.18 ----f
4
-.
Examples of the Kaon Data
For kaon beams at momenta up to 750 MeV/c, examples of the neutral reaction channels that can be investigated are
193
a p -+ aon Differential Cross Sections 4
3 2
I 0
-1
-0.5
0
0.5
1
cos(0) 143.7MevIc 6
8
* @@ Ball l
6
4
4
2 0
' C
2 -1
-0.5
0
0.5
1
0
1
-0.5
0
0.5
cos(e) 209.1Mevlc
1 c o w
236.2MevIc 10 7.5 5 2.5
0
-1
-0.5
0
0.5
0
1 cos(0)
-1
-0.5
0
1
0.5
CON@)
268.7Mevlc
321.5MevIc
Figure 3. Preliminary results at momenta below and above the A resonance.
-
K-p yA K - p -9 a o A K-p 7A K-p aoaoA K-p aoao7roA K - p -+ a°Co K-p I?%. ---f
---f
194
mZ(Iron)
mz(non)
m2(Iron)
m2(Iron)
Figure 4. Dalitz plots for m-p 4 momon. Each event is plotted twice, for each combination of m‘((n”n) along the horizontal axis. The vertical dashed line for each plot corresponds t o m2(Ao), or where the data would lie if the readion proceeded via 7r-p + *‘Ao, assuming the “correct” pio from A’ decay was combined with the neutron, and the A’ has zero width. The slanted d o t a a s h e d line indicates where the data would lie if the reaction proceeded via m-p 4 7roAo and the “wrong“ 7 r o were combined with the neutron. The slanted dotted line that bisects these two caws is the axis of symmetry expected if both combinations are plotted and the dominant readion mechanism were ( n - p ---f noAo with a Ao of finite width. The data are remarkably consistent with this hypothesis. ~
A striking example of the improvement in the world’s data that is derived from the CB program is the comparison shown in Fig. 5 and Fig. 6 for the K - p -+ 7711 reaction. The Crystal Ball data5 are shown in Fig. 5 and older data19,20321~22 are shown in Fig. 6. The Crystal Ball data have already been incorporated into a unitary, multichannel analysis6 to determine better parameters (mass, width and elasticity) for the A(1670);- resonance. The A polarization can be determined from the asymmetry of the A -+ Ton decay5?’. Preliminary results for the A polarization for the K - p + noA reaction at 761 MeV/c, taken from the thesis of Olmsted’, are compared with the prediction of the G 0 p a 1 ~partial-wave ~ analysis in Fig. 7. There are significant differences between the data and the analysis, indicating a need for new multichannel analyses of hadron production data from meson beams. 5
Conclusions and F’uture Plans
The obvious extension of this program is to use the Crystal Bail to measure n-p -+Neutrals and K-p --+ Neutrals with higher-momentum meson beams.
195
K-p +?A Crystal Ball data
Figure 5. Differential cross section for K - p 4 qA (Starcstin et aZ.) measured using the Crystal Ball. The curve shows the result of a unitary siuchannel fit assuming S-wave dominance. (Manley et d.). 2.c
0.E
0.c 1
166
1.67
1.68
1.69
1.70
W (GeV) Figure 6. Previously available data for K - p
4
qA.
An endcap would be needed to improve the acceptance at forward angles. Beam momenta of 2 GeV/c are needed to produce N* or A* at W = 2.1 GeV and A* or C* at 2.2 GeV. These data are needed to complete the original
196
-0.5
cos
e
Figure 7. Preliminary results by the Crystal Ball Collaboration for A yolarkation in K - p + a O A at P,- = 761 MeV/c. The curve is the Gopal 1977 partial wave analysis.
goals of OUT BNL proposals and to complement the K* program at Jefferson Laboratory. Present plans are to move the CB to Mainz for experiments with photon beams. If an opportunity to utilize higher-momentum meson beams with the CB becomes available we plan to be ready to take advantage of it. Three additional experiments have been approved at the BNL AGS. These are E927, Measurement of the K:3 Decay Rate and Spectrum24;E953, Neutral Hyperon Spectroscopy with the Crystal Balp5; and E958, Pion ChargeExchange Cross Sections at Low Energie26. E927 requires a significant hardware upgrade and is planned upon the completion of the Mainz program. E953 and E958 could be done with the existing setup but are in jeopardy because of the present funding situation and the difficult,yof running fixed-target experiments at the AGS in the RHIC era.
Acknowledgments This work has been supported in part by US DOE, NSF, KSERC (Canada), Russian Ministry of Sciences, Croatian Ministry of Science and 'z'echnology, and Volkswagen Stiftung.
197
References
1. S. Prakhov, et al., Phys. Rev. Lett. 84, 4802 (2000). 2. A. Starost,in, et al., Phys. Rev. Lett. 85, 5539 (2000). 3. W. B. l'ippens, et ul., Phys. Rev. Lett. 87 192001 (2001). 4. T. D. S. Stanislaus et al., Nucl. Inslrurn. Meth. A462 463 (2001). 5. A. Starostin et ul., Phys. Rev. C 64,055205 (2001). 6. D. M. Manley et al., Phys. Rev. Lett. 88 231101 (2001). 7. A . Sta.rost,in, Mefiwiremen.t of 7 ~ ~ 7 ~ ' production, an. the n.uclenr medium by ST- at 0.408 GeV/c, Ph.D. Dissertation, Petersburg Nuclear Physics Institute, Catchina, Russia, 2000. See Starostin, et aL2 a.bove. 8 . J . A. Olmsted, lhperzmental Study of th.e K - p noA Rmction., Ph.D. Dissertation, Kent State University, 2001. 9. N. Phaisangittisakul, First Measurement of the Radiative Process K - p +. AT at Beam Momenta 520-750MeV/c Using the Crystal Ball Detector, Ph.D. Dissertation, University of California at Los Angeles, 2001. 10. K. K. Craig, Double Neutral-Pion Production in Pion-Proton Interactions, Ph.D. Dissertation, Arizona State University, 2001. 11. AGS Experiment 913, M. E. Sadler arid W. B. Tippens, cospokespersons. 12. AGS Experiment 914, B. M. K. ISefkens, T. Kycia and H. M. Spinka, cospokespersons. 13. R. A. Arridt, el al., Phys. Rev. C 52, 2120 (1985). The PWA solutions presented were obtained from http://gwdac.phys.gwu.eduf . 14. R. F. Jenefsky, et al., Nucl. Phys. A290, 407 (1977). 75. F. 0. Rorcherding, IJCLA Thesis (1982). 16. J. C. Comiso, et al., Phys. Rev. D 12, 738 (1973). 17. W. Bayer, et al., Nucl. Inst. and Meth. 134,449 (1976). 18. D. E. Groom, et al., The European Physical Journal C15, (2000). 19. G. W. London, et al., Nucl. Phys. B89, 289 (1975). 20. D. F. Baxter, et al., Nucl. Phys. B67, 125 (1973). 21. R. Rader, et al., Nuovo Cimento SOC.Ital. Fis., A 16A, 178 (1973). 22. D. Berley, et al., Phys. Rev. Lett. 15, 641 (1965). 23. G. P. Gopal, et al., Nucl. Phys. B119, 362 (1977). 24. AGS Experiment 927, B. M. K. Nefkens and J . K.Comfort, cospokesper+ .
sons.
25. AGS Experiment 953, D. M. Manley, B. M. K. Nefkens and H. M. Spinka, cospokespersons. 26. AGS Experiment 958, J . R. Comfort and M. E. Sadler, cospokespersons.
BARYON RESONANCES AND STRONG QCD EBERHARD KLEMPT Institvt fur Strahlen- und Kernphysik der Uniuersitat B o n n Nvflallee 14 -16, 53115 B o n n , G e r m a n y E-mail:
[email protected] A new mass formula is suggested describing the spectrum of light baryons. The formula uses 3 baryon masses (N, A, 0)and the slope of meson Regge trajectories as input quantities and no free parameter.
1
Introduction
Baryon spectroscopy has played a decisive role in the development of the quark model and of flavor SU(3). The prediction of the R- carrying total strangeness S = -3 and its subsequent experimental discovery at the anticipated mass was a triumph of SU(3). From the demand that the baryon wave function be antisymmetric with respect to the exchange of two quarks, the need of a further quark property was deduced which later was called color and found to play an eminent dynamical role. The linear dependence of the squared masses of baryons on their total angular momentum led t o the Regge theory of complex angular momenta. The unsuccessful attempts to ’ionize’ protons and to observe free quarks was the basis for the confinement hypothesis. There is hence the hope that an improved understanding of the spectrum of excited baryons may reveal the underlying quark-quark interactions. 2
Quark models
Current baryon models differ in their basic assumptions on quark-quark and quark-antiquark interactions. Most models start from the hypothesis that chiral symmetry breaking of the (chiral symmetric) QCD Lagrangian generates constituent quarks with effective masses. Confinement is enforced by a potential which grows linearly with the distances between the quarks. The color-degrees-of-freedomguarantee the antisymmetry of the baryon wave function. The equation of motion is solved after the color-degrees-of-freedomhave been integrated out: color plays no dynamical role in the interaction. The confinement potential corresponds to the mean potential energy experienced by a quark at a given position, with a fast color exchange between the three quarks. Confinement does not exhaust the full QCD interaction: there are residual interactions which can be parameterized in different ways.
198
199
The celebrated Isgur-and-Karl model starts from an effective spin-spin interaction from one-gluon exchange the strength of which is adjusted to match the A(1232)-N mass difference. This requires a rather large value for as, certainly invalidating a perturbative approach. However, the one-gluon exchange is supposed to sum over many gluonic exchanges which in total carry the quantum numbers of a gluon. Now there is an immediate problem: with this large one-gluon exchange contribution, the spin-orbit splitting becomes very large, in contrast to the experimental findings. Isgur and Karl solved this problem by assuming that the Thomas precession in the confinement potential leads to a spin-orbit splitting which cancels exactly the spin-orbit coupling originating from one-gluon exchange. This assumption allowed to reproduce the low-lying baryon resonance masses and was a break-through in the development of quark models for baryons '. Later, this model was further developed and refined, relativistic corrections were applied and the full energy spectrum of the relativized Hamiltonian was calculated. Results of the latest variant of this type of model can be found in An alternative model was developed by Glossman and R i s k 3 . The model is based on the assumption that pions or, more generally, Goldstone bosons are exchanged between constituent quarks. The phenomenological success is impressing, in particular the low-lying P11(1440), the Roper resonance, is well reproduced. Cohen an Glozman emphasize the presence of parity doublets which they believe to signal chiral-symmetry restoration at high baryon masses 4. The group of Metsch and Petry developed a relativistic quark model with instanton induced two-body and three-body interactions 5 . The confinement forces - which in most models are defined only in a non-relativistic frame and given as linear potential in the three-particle rest frame - have a complex Lorentz structure. They solve the Bethe-Salpeter equation by reducing it to the Salpeter equation. The parity doublets are naturally explained by instanton interactions. Rijker, Iachello and Leviatan suggested an algebraic model of baryon resonances 6 . Their mass formula is similar to the one proposed here, but uses 10 parameters where most of them have no intuitive physical significance. On the other hand, wave functions are constructed and transition amplitudes can thus be calculated. A problem of all models is the large number of states predicted. The number of required states can be reduced dramatically in models in which the full three-particle dynamics is frozen into a diquark-quark picture But in
'.
'.
200
the meanwhile, there are more baryon resonances than a simple quark-diquark model can reproduce.
3
A mass formula for baryon resonances
In this contribution, we propose a mass formula for baryon resonances which reproduces most baryon masses given in the Review of Particle Properties 8 . The mass formula is given as
M2 = M i where
+ % . M i + a . (L + N) - Si . Isym,
(1)
M: = ( M i - M i ) ~i = ( M i - Mk)
n, number of strange quarks in baryon, L the total intrinsic orbital angular momentum. N + 1 is the principal quantum number; L+2N gives the harmonic-oscillator band (which we denote N ) . Isym is the fraction of the wave function (normalised to the nucleon wave function) antisymmetric in spin and flavor. It is given by Isym= 1.0 for S=1/2 and 8 E 56;
Isym= 0.5 for S=1/2 and 8 E 70; I, = 1.5 for S=1/2 and 1; Isym= 0 otherwise. M N , M A , M are ~ input parameters taken from PDG; for nucleon and A resonances, n,=O and eq. (1) describes the mass change with respect to the A mass. a = 1.142/GeV2 is the Regge slope determined from the series of light (isoscalar and isovector) mesons with quantum numbers Jpc = 1-- , 2++ l 3--, 4++, 5--, 6++. In the following, we motivate the above formula. 4
Spin-orbit forces
[t is well known that spin-orbit forces lead to at most small mass splittings n baryon spectroscopy. Baryons seem to form super-multiplets for which the ntrinsic orbital and spin angular momentum can be defined while their couding to the observed total angular momentum has no significant impact on the nasses. We give a few examples: we assign L = l and S=1/2 to the doublet of 1 resonances having J=1/2 and 3/2, A;;;? (1620) and A;;;? (1700); L is the ,otal orbital angular momentum, S the sum of the spins of the 3 constituent luarks. The number of *'s gives the overall status of the resonances as defined ~ythe Particle Data Group. To the triplet of states N;;;? (1650), Ngj;? (1700),
20 1
NgjqZ(1675) we assign L = l and S=3/2 coupling to J=1/2, 312 and 512. Note that there is very little splitting between these five masses. Similarly, there are eight states N;,2+(2100), N;j2+ (1900), N;j2+ (2000), N;j2+ (1990) and A;;;: (1910), A;;;: (1920), A;j;:(1905), A;;;: (1950) in which L=2 and S=3/2 couple to J=7/2, 512, 3i,2, and 112. We thus assume that spin-orbit splittings are small and that intrinsic orbital and spin angular momenta of baryon resonances can be defined. A group of resonances with different J but identical L and S is called a super-multiplet.
3 ‘312‘ ‘lE+ ‘!jJ2+ (1950) (1895) (1935) (1895) ‘712’
N7/2+
N5/2’
(1990)
(2000) (1900)
N3/2i
Y
N
I
I
-4
+
1
I
t
I
T
i
‘3/2-
‘112-
N5E-
(1700)
(1620)
(1675) (1700) (1650)
N312-
‘1/2-
0 Figure 1. A and N resonances assigned to super-multiplets with defined spin and orbital angular momentum. Shown is the increase in mass square above the A(1232) [in units of a=1.142 GeV2]. Upper panel: N’ and A* with L=2 and S=3/2 coupling to 5(7/2+,5/2+,3/2+,1/2+). Lower panel: A * with L(1) 3(1/2) = j ( 3 / 2 - , 1/2-) and N’ with Z(1) 3(3/2) = j(5/2- ,3/2- ,1/2-) In this and the following Figures, A’s are represented by squares, nucleons by circles. Open symbols characterize even, full symbols odd parity.
+
+
202
5
Regge trajectories
The smallness of spin-orbit couplings allows us to plot the squared masses of baryon resonances as a function of the intrinsic orbital angular momentum L, and thus to combine baryons with positive and negative parity in a single Regge trajectory. Fig. 2 shows the masses of selected N* and A* resonances. A resonances of lowest mass are plotted for spin S=1/2 and S=3/2 and J=L+S. We call this the leading resonance of a super-multiplet. Positive-parity A resonances (A3/2+(1232), &/2+ (1950), (2300), and A1512+(2950)) have S=3/2, negative-parity resonances (A3/2-(1720), A7/2- (2220)) have S=1/2. Both series’ lie on the same Regge trajectory even though the spin-spin interaction changes sign. In the A spectrum, spin-spin interactions obviously do not contribute significantly to baryon masses; we conclude that they can neither be responsible for the N-A splitting. N* resonances with intrinsic spin S=3/2 also fall onto the same Regge trajectory as A*%.
I
0
1
2
3
4
5
6
7
8
. . orbital . pigure 2. Regge trajectory of N and A resonances as a function of their in+rinsic ingular momentum. Shown are resonances of lowest mass and maximum J for a given L vith J=L+S. For N resonances, the intrinsic spin is S=3/2, for A resonances, the intrinsic .pin is 3/2 for L even and 1/2 for L odd. The errors are defined in section 9.
203 6
Resonances with S=l/2
We now discuss nucleon resonances with spin 1/2. In Fig. 3, we compare the squared masses of positive- and negative-parity nucleon resonances to our standard Regge trajectory. All resonances are lower in mass compared to the
cJ-9
as
N13/2* (2700K,
CM
N11/2' N
F ^(1720)
0
1
2
3
4
5
6
7
8
Figure 3. The N* masses (with intrinsic spin 3=1/2) lie below the standard Regge trajectory. They are smaller by about 0.6 GeV2 for N* in the 56-plet, and by 0.3 GeV2 for N* in the 70-pIet.
trajectory. The mass shifts are visualized by arrows with a length denned by the A(1232)-N mass splitting; for nucleons with odd angular momentum, the length of the arrow is divided by 2. The horizontal lines represent the expected masses, deduced from the trajectory and a squared-mass shift calculated from
Si =
T2 ^(1232)
1VT2 1V1
nucleon-
(2)
Even-parity baryon resonances have masses which are systematically lower than expected even though no resonance is off by more than 2cr. We note that nucleons with spin S=l/2 are shifted in mass, nucleons with S=3/2 not. A excitations do not have this spin-dependent mass shift. The mass shift occurs only for baryons having spin and isospin which are both antisymmetric w.r.t. the exchange of two quarks. This is the selection rule for instanton
204
induced interactions which act only between pairs of quarks which are antisymmetric w.r.t. their exchange in spin and isospin. We consider the even-odd staggering of Fig. 3 as most striking experimental evidence for the role of instanton interactions in low-energy strong interactions. We note that the octet - decuplet mass splittings (in squared masses) between C - C" and E - E* are compatible with eq. (2).
7
Radial excitations
Some partial waves show a second resonance at a higher mass. The best known example is the Roper resonance, the N,p+(1440). Its mass is rather low compared to most calculations since, in the harmonic oscillator description of baryon resonances, it is found in the second excitation band (N=2). In mass squared, the difference between Roper resonance and the nucleon is 1.19 GeV2. We compare this to the mass squared difference between the A3/2+ (1600) and the A3/2+ (1232) (which is 1.04 GeV2), the A l p + (1600) and the A l p + (1112) (which is 1.32 GeV2), the C1/,+(1660) and the C1p+(1193) (which is 1.33 GeV2), the E(1690) - which we identify with the first radial excitation - and the E1/2+(1318) (which is 1.19 GeV2). Likewise, the mass square difference between the A1/2- (1900) and the All2- (1620) is 0.99 G e V . We conclude that the radial excitation energy is, in mass square, of the order of (1.05f0.09) GeV2 (the spread (I given as 'error'), in the same range as a single step 6L = 1 on the Regge trajectory. Also in meson spectroscopy, radial excitations do not have a mass shift corresponding to two units of orbital angular momentum. Based on a large number (- 100) of radial excitations, Bugg concluded that the mean increase in squared mass per radial excitation is 1.143f0.009GeV2. These observations motivate the L+N dependence in the mass formula. 8
Multiplet structure of N* and A* resonances
The mass formula (1) uses values for the intrinsic orbital and spin angular momenta while only the total spin J is measured. In the sections above, we have shown how we assign L and S to specific states. Of course, resonances of defined J can have an admixture of several wave function components. To give an example: the A3/2+ (1920) can have contributions from (L=2,S=3/2) which we believe to be dominant, from (L=O,S=3/2) or (L=2,S=1/2); contributions from other shells are also possible. The mixing with other states must however be different for the individual states in the series AIp+(1910), &/2+(1920), Asp+ (1905), and &/2+(1950). In particular the two lower-spin states can mix with L=O components, the two
205
Baryon
N1/2+(939) N l / 2 + (1440) N1/2+(1710) N1/2+(2100)
6M2 (GeV2)
Baryon
SM2 (GeV2)
(1232) A3/2+(1600) A3/2+ (1920)
1. 1.04
2 . 1.08
A3/2- (l7Oo) A3/2- (1940)
1 ‘0.87
A3/2+
1 . 1.18 2 . 1.02
3 . 1.18
A l p (1620) A1/2- (1900)
1 .0.99
A,/,- (2150)
2 . 1.00
N1/2- (1530)
N3/2- (1520)
Nl/2-
2.1.01
(2090)
2 . 1.01
N3/2N3p- (2080)
A1/2+(1115) All2+ (1600) All2+ (1810)
1 . 1.24
&/2+ (1193) C1/2+(156O)
1 . 1.04
2 .0.98
C1/2+(1880)
2 . 1.06
N1/2-
Table 1. Radial excitations of baryon resonances
higher-spin states with L=4. The J=3/2 state can mix with the second radial excitation; the J=3/2 and J=5/2 states can mix with states having L=2 and S=1/2. But all four states have masses falling into a f 2 3 MeV mass interval. Hadronic effects like coupling t o decay channels have an impact on the masses which is likely much larger. We conclude that the effect of configuration mixing on baryon masses cannot be decisive for the interpretation of the spectra. These effects could be important for decays where small amplitudes can be important due to interference with larger amplitudes. In Table 2 we give the quantum numbers we assign t o N* and A* resonances. We note that, experimentally, there is no need for a 2O-plet, and for any set of quantum numbers there is only one 56-plet or 70-plet. Negativeparity states in a 56-plet require N = l radial excitation. These are empirical selection rules governing the observed states. Note that even with these restrictions there is a large number of missing resonances, the lowest-mass N* resonances being expected t o have masses at about 1780 and 1860 MeV. The two positive-parity states at 1860 MeV are required to complete the 70-plet started with the four N’ states in the 1900 to 2000 MeV mass range. The existence of the negative-parity states at 1780 MeV is required by the triplet
206
of negative-parity A* at 1950 MeV. The masses must be lower than 1900 for the same reasons for which the N 1 p - (1535) and N 3 p (1520) have a lower mass than the states N1/2- (1650), N3/2- (1700) and N512- (1675). 9
Comparison of mass formula and data
For a quantitative comparison between data and eq. (l), masses and errors need to be defined. The Particle Data Group lists ranges of acceptable values; we use the central value for the comparison. In some cases the range of the acceptable values is rather large; in these cases our error can be too small. We do not include the acceptable range in the error definition, since otherwise poorly known states (for which no acceptable range is known) would gain more weight than well established states. Our error contains two parts, a model error of 30 MeV and a width-dependent error. The model error avoids extremely large x2 contributions from the octet ground-state particles. The second error allows for mass shifts of resonances due to hadronic effects, like virtual decays. We estimate this effect to be of the order of one quarter of the width, and use I'/4 as second error contribution. The two errors are added quadratically. The widths of the resonances are often not well determined and for less established baryons, no width estimate is given. We parameterize all widths using the formula r = Q(3) 4 where Q is the largest momentum accessible in hadronic decays of the resonance. With this error definition, most baryon resonances are rather well described. The Particle Data Group lists 103 baryon ground states and resonances; three masses are used to define the model, three have masses which are incompatible with (1) for any set of quantum numbers. These three are the C(1560), E(1620) and the R(2380). None of them has a known spinparity; they were discovered as bumps in some mass distribution. For the remaining 97 states, x2=117. A detailed comparison between data and model is presented elsewhere g . Here we discuss only resonances deviating from (1) prediction by more than 2 standard deviation. The h1/,+(1750) and C7/2-(2100) are 1* resonances, and the discrepancy does not need to be a failure of the model. For the h1/2+(1600) and A1/2+(1810), both 3* resonances, the errors given by F/4 are underestimated; the mass of the A1/,+(1600) falls into the range from 1560 to 1700 MeV, the predicted mass is 1565 MeV. The Allz+ (1810) should have a mass in the
207
56
1=3/2;L=O;N=0,1,2,3 S=3/2;L=O;N=0,1,2,3
70
S=1/2 S=3/2 S=1/2 S=1/2 S=3/2
L=l L=l L=l L=l L=l
N=O N=O N=O N=l N=l
S=1/2 S=3/2 S=1/2
L=l L=l L=l
N=2 N=2 N=2
S=1/2 S=3/2 S=1/2
L=2 L=2 L=2
N=O N=O N=O
S=3/2 S=1/2
L=2 L=2
N=O N=O
S=1/2 S=3/2 S=1/2
L=3 L=3 L=3 L=3
N=O N=O N=O N=l
56 70
56 70
70
56
S=1/2
N1/2+(939) A3/2+ (1232)
N i p + (1440) A3/2+ (1600)
N i p + (1710) A3/2+ (1920)
N i p (1535) Ni/z- (1650)
N3/2-(1520) N3/2- (1700)
Allz- (1620) N1/2A l p (1900)
A3/2- (1700)
Ni/2-
(2090)
N i p + (2100)
N5/2- (1675)
A3/2- (1940)
A5/2- (1930)
N3/2- (2080) N3/2-
N5/2-
Nl/z+
N3/2-
N3/2+ (1720) A3/2+(1920) N3/2+ N3/2+ (1900) A3/2+
N5/2+(1620) A5/2+ (1905) N5/2+ N5/2+(2000) A5/2+
N5/2N5/2- (2200)
N7/2N7/2- (2190)
A5/2N5/2-
A7/2-
(2200)
N7/2-
1530 1631 1631
N3/2P
A i / - (2150) A1/2+(1910)
MBS MeV
A7/2+(1950) N7/2+(1990)
N Q / ~(2250) -
1779 1950 2151 2223 2223 1779 1950 1866 1950 1950 2151 2223 2223 2334
Table 2. Nucleon and A resonances. The masses on the right side are calculated from the mass formula. There are no known resonances with L > 3 which need to be assigned to a 70-plet .
208
1750 to 1850 range; the predicted value of 1895 MeV is still larger but now compatible within the model error. The two resonances E(2250) and R(2380) have no known spin-parities; it is therefore difficult to appreciate the meaning of the discrepancy. It is not excluded that in baryon resonances with two or three strange quarks, heavy-quark physics is starting to take over, that gluon exchange begins to be effective and that the extrapolation of the mass formula to Z and R states is not justified. Clearly, there is not sufficient experimental information to clarify this point in a phenomenological description of data. The C3/2- (1580) and C3/2- (1670) are more critical. The C3/2- (1670) is a 4* resonance with a well-measured mass. It would perfectly fit, with the (1620), as (70,’ 8)l instead of (70,48)1resonance. But then, the 2* state C 3 p - (1580) would have no slot. If we remove it, the total x’ contribution would go down from 34.69 to 23.05 (for now 24 degrees of freedom). A 2* resonance should perhaps not be ’talked away’. But the experimental situation is certainly not clear enough to reject the model because of these two C states. 10
Interpretation
The mass formula (1)suggests that the dynamics of baryon resonances is governed by the formation of constituent quarks carrying color and that the interaction between these colored constituent quarks can be reduced to quasi two-body interactions between colored (constituent) quarks and diquarks carrying anti-color. One-gluon exchange between the colored quark clusters plays no important role. Instanton-induced interactions are, however, important and lead to the well-known N-A mass splitting.
209
References
1. N. Isgur and G. Karl, Phys. Rev. D 18 (1978) 4187, [Erratum-ibid. D 23 (1979) 8171, D 19 (1979) 2653. 2. S. Capstick and N. Isgur, Phys. Rev. D 34 (1986) 2809. 3. L. Y. Glozman, W. Plessas, K. Varga and R. F. Wagenbrunn, Phys. Rev. D 58 (1998) 094030. 4. T. D. Cohen and L. Y. Glozman, Phys. Rev. D 65, 016006 (2002). 5. U. Loring, K. Kretzschmar, B. C. Metsch and H. R. Petry, Eur. Phys. J. A 10 (2001) 309. U. Loring, B. C. Metsch and H. R. Petry, Eur. Phys. J. A 10 (2001) 395. U. Loring, B. C. Metsch and H. R. Petry, Eur. Phys. J. A 10 (2001) 447. 6. R. Bijker, F. Iachello and A. Leviatan, Annals Phys. 236 (1994) 69. R. Bijker, F. Iachello and A. Leviatan, Annals Phys. 284 (2000) 89. 7. D. B. Lichtenberg, Phys. Rev. 178 (1969) 2197. 8. D. E. Groom et al. [Particle Data Group Collaboration], Eur. Phys. J. C 15 (2000) 1, and 2001 update. 9. E. Klempt, “Baryon resonances and strong QCD,” arXiv:nuclex/0203002.
SPIN STRUCTURE FUNCTIONS IN THE RESONANCE REGION R. DE VITA Istituto Nazionale d i Fisica Nucleare, via Dodecaneso 33, 16146 Genova, Italy E-mail:
[email protected] Spin structure functions in the deep inelastic region have been extensively measured over the past three decades. On the contrary much less is known in the region of the nucleon resonances and at low t o intermediate Q 2 . A large experimental program is in progress at Jefferson Lab t o study this kinematic region using polarized electrons impinging on polarized proton, deuteron, and helium-3 targets. Preliminary results on the first moment of the spin structure function g1 and on the Gerasimov-DrellHearn integral for proton and neutron are presented. In addition, first double polarization data on exclusive pion production are discussed.
1
Introduction
The understanding of the spin structure of the nucleon is one of the main issues in hadronic physics. The relation between the macroscopic properties of the nucleon, as spin and magnetic moment, and its microscopic constituents, quark and gluons, is a fundamental problem which has driven the experimental and theoretical activity for many years. In the last three decades extensive studies of the spin properties of the nucleon have been carried out in various kinematical domains. Measurements of the spin-dependent structure functions g1 and g2 have been performed in several facilities as SLAC, CERN, and DESY in the DIS region, while at Q2 = 0 measurements of the helicity dependence of the photo-absorption cross section have been performed at Mainz and Bonn 2 . 3 . One of the most surprising resuits was obtained in 1989 by the EMC collaboration which measured the structure functions g1(z) for the proton and derived its first moment ry. A constraint on the value of this integral had already been introduced in 1974 by Ellis and Jaffe in the framework of the parton model, assuming negligible contribution from strange sea quarks. The EMC result showed that this sum rule was violated and led to the conclusion, in the naive quark parton model, that the total quark spin constitutes a rather small fraction of the nucleon spin. This result was confirmed by later experiments and recent analysis have attested that only 20-25% of the nucleon spin is carried by quarks. The same measurements have been extended also to the neutron and to the proton-neutron difference which is important to test the
210
21 1 % 0.15 0.125
p
........... 0
0.1
:
..................
;03
%
L
I"
0.15
................................ /
0
0.1
0.075 0.05
0.05
0.025 0
0
-0.025 0
05
I
13
-0.05
Q2(CeV')
I
I
I
05
I
13
Q' (GV')
Figure 1. First moment of the spin structure function g1 for the proton (left) and for the proton-neutron difference (right). Data points are from SLAC and HERMES. At large Q 2 , the solid curves show the pQCD evolution of the measured rl integral for the proton and of the Bjorken sum rule. At low Q2 the slope given by the GDH sum rule and chiral perturbation theory calculation (dashed-dotted) [lo] are indicated. The dashed and dotted lines are model predictions from Burkert and Ioffe [13] and Soffer and Teryaev [14].
Bjorken sum rule. This sum rule, derived in 1966 on the basis of current algebra, relates the difference of the first moments of the proton and neutron structure function g1 to the weak axial coupling constant g A :
This sum rule applies at infinite momentum transfer Q 2 , but have been evolved to finite Q 2 in perturbative QCD up to the order of a;, and verified experimentally at the 5% level. On the other extreme of the kinematical domain, an important constraint is provided by the Gerasimov-Drell-Hearn sum rule which relates the difference in the helicity-dependent total photoabsorption cross sections to the anomalous magnetic moment K. of the the nucleon '3*
where uo is photon energy at pion threshold and M is the nucleon mass. This sum rules is based on very general assumptions, as gauge invariance, causality,
212
and analyticity, and has been studied for photon energies up to 850 bIeV at Mainz 2 , while is currently being tested up to more than 2 Gel1 at ELSA 3 . Even if derived for very different kinematics, the Bjorken and GDH sum rules can be connected by the observation that lim
Q2+0
Q2 rl = 2h12 IGDII.
(3)
As a consequence of this relation, the rl integral is expected to reach zero at the photon point with a slope which is fixed by the GDH sum rule. This implies strong constraints on the Q2 dependence of rl. The proton integral (see figure l),which was found to be positive in the DIS regime, must in fact undergo to a dramatic change at lower Q 2 , approaching zero with negative slope. To understand the mechanisms which drive this transition, it is necessary to study in details the Q 2 dependence of the GDH and rl integrals both from the theoretical and experimental point of view. A rigorous extension of the GDH integral at finite Q2 has been introduced by J i and Osborne lo, relating the virtual-photon forward Compton amplitude to an integral of the g1 structure function. While the latter can be measured experimentally, the former is a calculable quantity. In particular, operator product expansion and pQCD techniques can be used to extend the DIS expectation to Q2 values of the order of 0.5 - 1.0 GeV2, while, at the other extreme, chiral perturbation theory has been used to extend the GDH sum rule up to Q2 of 0.1-0.2 Ge\J2. As pointed out in ref. 12, chiral perturbation theory may be extended to somewhat larger Q2 in the case of the proton-neutron difference, and eventually connected with the pQCD evolution. However presently there is still a window which is not covered by any fundamental theory and is lacking of experimental data. Even if this gap is rather small, physically it is very interesting since this is the regime in which the transition between hadronic and partonic degrees of freedom occurs and allow to understand at which distance scale pQCD and twist expansion will break down and the physics of confinement will dominate. In this intermediate region, non-perturbative phenomena as resonance excitation play a fundamental role and can have strong impact on the Q2 dependence of l?l 1 3 . For this reason, the study of the helicity structure of the nucleon excited states and the measurement of spin observables in inclusive and exclusive reactions in this kinematical domain, becomes fundamental to reach a deep understanding of the mechanisms which dominate this region and to complete our picture of the nucleon spin structure from small to large distance scales.
213 N
1 0.8
, +
0.6 0.4
0.2 0 -0.2 -0.4
-0.6 -0.8
-1 1
1.5
2
1
W(GeV)
1.5
2
W(GeV)
Figure 2. Asymmetry A1 + qA2 for the proton (left) and the deuteron (right) at Q2 = 0.5 GeV2. The CLAS data (squares) are shown in comparison with the SLAC results (circles). The grey band shows the systematic uncertainty. The line is a model calculation used for radiative corrections and to extrapolate at small x.
2
Spin Physics at Jefferson Lab
An extensive physics program that covers these topics is in progress at Jefferson Lab involving the three experimental Halls of the facility. Experiments to study the neutron spin structure using polarized electrons impinging over a high pressure longitudinally and transversally polarized 3He target have been completed and others are planned in Hall A. A first measurement performed in 1998 focused on the evaluation of the generalized GDH integral at low Q2 (0.1-1 GeV2) 15, while two experiments were completed in 2001 aiming at high precision measurements of the spin asymmetry A; l 6 and of the neutron structure function g 2 ( 2 , Q 2 ) 17. In addition to these experiments which are in various stages of the analysis, other two measurements 1 8 ~ 1 9 are planned in the close future. Measurements of spin observables in inclusive and exclusive reactions have been performed in Hall B with the CEBAF Large Acceptance Spectrometer (CLAS) 21 using a longitudinally polarized NH3/ND3 target. The large acceptance of the CLAS detector allowed the simultaneous study of several processes in a large kinematic domain which cover the whole resonance region
214 h
5
ao”
0.2 0 -0.2 0.2 0 -0.2 0.2
0 -0.2 0.2
0 -0.2
0 - 0 . 2 1 ,
,
, ,
,
0.06 0.070.0BD.090.1
, 0.2
_43__1
0.3
0.4
0.5
,
,
,
,
0.6 0.7 0.8 0.9
X
Figure 3. Preliminary results on gi(x) for the proton obtained by CLAS. The grey band shows the systematic uncertainty. The line is a model calculation used for radiative corrections and to extrapolate at small I.
for Q2 between 0.05 to 3 GeV2 22123,24,25. A first data set recorded in 1998 is in the final stage of the analysis and the results will be discussed in the next section, while a second run was completed in 2001 and is now being analyzed. Finally, an experiment to measure the spin asymmetries A1 and A2 in the resonance region was performed in Hall C in the first months of this year using polarized electron beam and a longitudinally and transversally polarized NH3/ND3 target 26. In the following section I will discuss recent results from Jefferson Lab in inclusive and exclusive reactions. For details on the Hall A and Hall B data, see also the talks presented by J. P.Chen, T. Forest, and J.Kuhn in the parallel sessions.
215
Figure 4. First moment of the structure function 91 for the proton. The open circles are the CLAS data integrated over the measured region, while the full circles include the DIS contribution. The SLAC data (open squares) at Q 2 of 0.5 and 1.2 GeV2 are shown for comparison. At large Q2, the solid curve shows the pQCD evolution of the measured integral, while at low Q2 the slope given by the GDH sum rule and chjral perturbation theory calculation (dashed-dotted) [lo] are indicated. The dashed and dotted lines are model predictions from Burkert and Ioffe [13] and Soffer and Teryaev [14].
3 Preliminary results for proton and neutron The inclusive electron-nucleon cross section can be written as
{ + c a L + P, ptaT [m~~ cos 11, + J
da = rv aT dRdE’
~ sin
$1 } A (4)
where 11, is the angle between the target polarization and the virtual photon, 6 is the virtual photon polarization, and UT and U L are the total absorption cross section for transverse and longitudinal virtual photons. The structure function A1 is the virtual photon helicity asymmetry,
A1
=
IA1/2I2
- IA3/2I2
IA1/2I2
+ IA3/2I2’
216
Figure 5. First moment of the structure function g1 for the neutron. The Hall A preliminary results are shown in comparison with previous measurements from SLAC and HERMES. The bands above and below the horizontal axis represent respectively the experimental systematic errors and the errors due to extrapolation for the high energy (W > 2 GeV) contribution.
while A2 is a longitudinal-transverse interference term. These asymmetries are related to the spin structure function g1 and g2 by gi(a,Q2)=
& [ai(z,Q2)+ -A2(2,Q2) fi 1 Fi(s,Q2), 1
7
92(2,Q2)
=
1+7[&A1
(2, Q2)
(6)
+ A2(2, Q 2 ) ] Pi (2,Q 2 ) ,
where F1 is the usual unpolarized structure function. Experiments typically use targets polarized in the direction parallel or perpendicular to the incoming electrons, measuring the quantities
All = D(Ai + ~
Ai
4 2 ) ~
= d(A2 - U
i),
(7)
where D,q,d,<depends on the kinematics on the the ratio R = uL/uT. Figure 2 shows the asymmetry A1 + vA2 for the proton and the deuteron at Q2 = 0.5 GeV2 measured with CLAS. For both targets, the asymmetry shows a strong W dependence which reflects the resonance structure. The photon helicity asymmetry A1 is in fact extremely sensitive to the structure of the excited state. The asymmetry is strongly negative in the region of the
217
Figure 6. Generalized GDH integral for 3He and neutron. The bands around the horizontal axis represent the experimental systematic errors and the errors due to extrapolation for the high energy (W > 2 GeV) contribution.
-
&(1232) where one expects A1 -0.5, but becomes positive in the second and third resonance region where the contributions of higher mass states as the s11(1535) and the &(1520) are positive. Using a parameterization of the world data on 3’1 and A2 , g1 (z,Q2) was extracted from eq. 6 . Preliminary results on g1(z, Q2) are shown in fig. 3. Clearly at low Q 2 ,g1 is dominated by the &3(1232) state, whose contribution drives the integral of g1 towards negative values. These graphs show also a model parameterization of g1(z, Q 2 ) which was used to extrapolate to z + 0. The extrapolation is necessary to evaluate the first moment I‘1(Q2). The results for r:(Q2) are shown in fig. 4. The open circles are the CLAS data integrated over the measured W region, while the full circles include the DIS contribution. For comparison, the SLAC data at Q2 of 0.5 and 1.2 GeV2 are shown. The characteristic feature is the strong Q2 dependence for Q2 < 1 GeV2, with a zero crossing around 0.3 GeV2. The I’l integral for the neutron is shown in figure 5. The circles are the Jlab/Hall A preliminary results in comparison with the SLAC and HERMES data. The bands around the horizontal axis show the systematic uncertainty associated with the analysis procedure and the extrapolation in the DIS region. With respect to the proton, the neutron integral is smoother and remains
218
;-, 0.2
%.
L 0.15
0.1
0.05
n Jlab/CI.AS Hall A SLAC Ei Bjorken sum rule evolution st O(a:) ~
0
0.25
0.5
0.75
1
135
1.5
1.75
QZ(GeV’)
Figure 7. Preliminary results for the Bjorken sum rule. The solid band shows the combined CLAS and Hall A results.
negative through the whole Q2 range. The GDH integrals for the 3He and the neutron are also shown in figure 6. The integral was evaluated over the region from the pion threshold (on a free neutron) to W = 2 GeV, to cover the resonance region. Nuclear correction were applied, using the prescription of Ciofi degli Atti and Scopetta 2 7 . The higher energy contribution, for W 2 from 4 to 1000 GeV2, was estimated using the parameterization of Thomas and Bianchi 28. The final integral is large and negative in whole Q2 range explored by the measurements, in contrast with the small values observed fro Q2 > 1 GeV2. The CLAS data on rl for the proton and the Hall A data on the neutron were combined to obtain the Bjorken integral. The result is shown by the solid band in figure 7. The band width represents the combined proton and neutron systematic errors. The SLAC data for Q 2 of 0.5 and 1.2 GeV2 are shown for comparison. At large Q 2 the dashed band shows the pQCD evolution of the Bjorken sum rule including the theoretical uncertainty. The GDH slope and chiral perturbation theory calculation from reference lo are shown at Q2 = 0, while the dashed and dotted-dashed lines are the model calculation by Burkert and Ioffe l 3 and Soffer and Teryaev 14.
219
1.6<W< 1.72GeV
0
0.5
1
1.50
0.5
1
1.5
C!'(GeV')
+
Figure 8. Q2 dependence of the double spin asymmetry (A1 vA2)/(1+ E R )for the nn+ channel. The error bars show the statistical error while the shaded bands represent the systematic uncertainty. The data are compared with the pure resonance contribution (dotted line) predicted by the A 0 model, with the MAID(dashed line) and A 0 (solid line) full calculations.
Double spin asymmetries in exclusive reactions have been measured for $(I?,e'p)ro, $(Z, e'r+)n, G(Z, e ' r - ) p in Hall B with the CLAS detector. A complementary technique has been used in Hall A measuring the recoil proton polarization in p(< e'p37ro at the invariant mass of the &(1232) resonance 20. These measurements are fundamental for the understanding of the helicity structure of baryonic resonances, whose study has been so far limited to unpolarized measurements. Here I discuss briefly the nr+ channel where final results have been obtained. Figure 8 shows the asymmetry (Al+qA2)/(1+&) for the n r t in comparison with model calculation based on the analysis of unpolarized data The dotted curve represents the pure resonance contribution as predicted by the A 0 model, while the solid and dashed lines are, respectively, the A 0 and MAID calculations including non-resonant ampli30131.
220
tudes. In the &(1232) niass region, the asyrnmctry is strongly affected by non-resonant processes, leading to small and positive values in spite of the negative asymmetry expected for the P33(1232) statc and observed in the inclusive asymmetry. At larger W , in agreement with the niodel predictions, the asymmetry becomes larger, indicating that in this range the reaction is ruled by the helicity-1/2 amplitude. 4
Summary and Outlook
Extensive rneasurcments of spin observables in inclusive and cxclusivc channels in the resonance region have been performed at Jefferson Lab. The results show large contribution from resonance excitation and allow for the first time a detailed study of this transition region, not explored by previous experiments. The measurement of the structure function g1 (x)for the proton shows a strong Q' dependence with the dominance of the P33 (1232) contribution a t low Q 2 . This results in a dramatic change with Q2 of the first moment of the structure function that in fact changes sign at Q2 0.3 Gel?'. On the contrary the l?l integral for the neutron is negative through the whole range explored by the experiment and shows a smooth Q2 dependence. Nearly final results for the generalized GDH integral on the neutron have been presented. The double spin asymmetry in 7r+ electroproduction has been measured for the first time. The asymmetry is large in the resonance region and, with increasing Q', tends to approach rapidly the dominance of helicity-1/2 production. New data have been taken both on hydrogen and deuterium with nearly 10 times more statistics and an improved kinematical coverage. These will allow to cover a Q' range from 0.05 to 4.5 GeV2, and a larger part of the deep inelastic region than our previous data. An extension of the neutron measurement performed in Hall A is also in progress. The GDH integral for the neutron will be measured down to Q2 = 0.02 GeV2 using quasi-real photons, while high precision measurements of the asymmetry A1 at large x and of the structure functions g1 and g2 are under way.
-
Acknowledgments
I am grateful to the many members of the Hall A and CLAS Collaborations whose work I have reported here. The Southeastern Universities Research Association (SURA) operates the Thomas Jefferson National Accelerator Facility for the United States Department of Energy under contract DE-AC0584ER40 150.
22 1
References
1. For a recent review see: B. W. Filippone and X. D. Ji, hep-ph/0101224 (2001). 2. J. Ahrens et al., Phys. Rev. Lett. 87, 022003 (2001). 3. T. Michel, talk at his conference. 4. EMC, J . Ashman et al., Phys. Lett. B206, 364 (1988), and Nucl. Phys. B328, l(1989). 5. J. Ellis and R. L. Jaffe, Phys. Rev. D9 (1974) 1444; D10 (1974) 1969. 6. J . D. Bjorken, Phys. Rev. 148, 1467 (1966). 7. S. B. Gerasimov, Sov. J . Nucl. Phys. 2, 430 (1966). 8. S. D. Drell and A. C. Hearn, Phys. Rev. Lett. 16, 908 (1966). 9. X. D. Ji and J. Osborne, Phys. Lett. . 10. X. D. Ji et al., Phys. Lett. B472, 1 (2000). 11. V. Bernard et al., hep-ph/0203167 (2002). 12. V. D. Burkert, Phys. Rev. D63, 097904 (2001). 13. V. D. Burkert and B. L. Ioffe, Phys. Lett. B296, 223 (1992); J. Exp. Theor. Phys. 78, 619 (1994). 14. J. Soffer and 0. V. Teryaev, Phys. Rev. Lett. 70, 3372 (1993), Phys. Rev. D51, 25 (1995). 15. JLab E94-010, Spokesperson G. Cates, J . P. Chen and Z. E. Mcziani. 16. JLab E99-117, Spokesperson J. P. Chen, Z. E.Meziani and P. Souder. 17. JLab E97-103, Spokesperson T. Averett and W. Korsch. 18. JLab E97-110, Spokesperson J . P. Chen, A. Dew and F. Garibaldi. 19. JLab E01-012, Spokesperson J . P. Chen, S. Choi, and N. Liyanage. 20. JLab E91-011, Spokesperson S. Frullani, J. Kelly, and A. Sarty. 21. W. Brooks, Nucl. Phys. A663, 1077c (2000). 22. JLab E91-023, Spokesperson V. D. Burkert, D. G. Crabb and R. Minehart. 23. JLab E93-009, Spokesperson S. E. Kuhn, G. E. Dodge and M. Taiuti. 24. JLab E93-036, Spokesperson M. Anghinolfi, R. Minehart and H. Weller. 25. JLab E94003, Spokesperson P. Stoler, R. Minehart and M. Taiuti. 26. JLab E01-006, Spokesperson 0. Rondon-Aramayo. 27. C. Ciofi degli Atti and S. Scopetta, Nucl. Phys. B404, 223 (1997). 28. E. Thomas and N. Bianchi, Nucl. Phys. B82, 256 (2000). 29. R. De Vita et al. (The CLAS collaboration), Phys. Rev. Lett. 88, (2002). 30. V. Burkert and Z. Li, Phys. Rev. D47, 46 (1993). 31. D. Drechsel et al., Nucl. Phys A645, 145 (1999).
QUARK-HADRON DUALITY SABINE JESCHONNEK The Ohio State University, Physics Department, Lima, OH 45804 USA E-mail: jeschonnek. 1 @om.edu
J. W. VAN ORDEN Jefferson Lab, Newport News, VA and Old Dominion University, Norfolk, VA, USA Quark-hadron duality and its potential applications are discussed. We focus on theoretical efforts to model duality.
1
What is Duality?
In general, duality implies a situation in which two different languages give an accurate description of Nature. While one may be more convenient than the other in certain situations, both are correct. If we are interested in hadronic reactions, the two relevant pictures are the quark-gluon picture and the hadronic picture. In principle, we can describe any hadronic reaction in terms of quarks and gluons, by solving Quantum Chromodynamics (QCD). While this statement is obvious, it rarely has practical value, since in most cases we can neither perform nor interpret a full QCD calculation. In general, we also cannot perform a complete hadronic calculation. We will refer to the statement that, if one could perform and interpret the calculations, it would not matter at all which set of states - hadronic states or quark-gluon states - was used, as ” degrees of freedom” duality. However, there are cases where another, more practical form of duality applies: for some reactions, in a certain kinematic regime, properly averaged hadronic observables can be described by perturbative QCD (pQCD). This statement is much more practical than the ”degrees of freedom” duality introduced above. In contrast to full QCD, pQCD calculations can be performed, and in this way, duality can be exploited and applied to many different reactions. Duality in the latter form was first found by Bloom and Gilman in 1970 in inclusive, inelastic electron scattering Duality in this reaction is therefore commonly referred to as Bloom-Gilman duality. Recently, it was impressively confirmed to high accuracy in measurements carried out at Jefferson Lab ’. Duality also appears in the semileptonic decay of heavy quarks 3 , 4 , in the reaction e+e- -+ h a d r o n s 5, in dilepton production in heavy ion reactions 6 , and in hadronic decays of the T lepton 7.
’.
222
223
Why should one be interested in duality? It is not only a rather interesting and surprising phenomenon, but also has many promising applications, e.g. for experiments probing the valence structure of the nucleon '. In inclusive electron scattering, duality establishes a connection between the resonance region and the deep inelastic region. Measurements in the resonance region have higher count rates than measurements in the deep inelastic region, and duality might be able to open up previously inaccessible regions. New duality experiments have been completed or are currently carried out at Jefferson Lab and there will be a large duality program at the 12 GeV upgrade of CEBAF lo. Examples of duality and possible applications of duality will be discussed in the next section. In order to use duality confidently to extract information from experimental data, a good understanding of duality is necessary. We need to know where it holds and how accurate it is. Our current understanding of duality is still limited. The theoretical efforts focus on modelling duality, and are discussed in Section 3. 938,
2
Applications and Examples
Our main focus is duality in electron scattering. We will briefly review duality in other reactions, before turning to the main subject of the talk. 2.1
Duality in various reactions
For semileptonic decays of heavy quarks, duality implies that the decay rate for hadrons is determined by the decay rate of the underlying quark decay. For perfect duality, the quark decay rate b -+ clvl is equal to the sum over all hadronic decays, B X & , where X , stands for the ground state D meson and its excited states. For infinitely heavy masses of the b and c quarks, duality was shown to hold exactly. In the realistic case of heavy, but not infinitely heavy quarks Mq, the various observables pick up correction terms of order and The precise form of the correction, in particular the -+
& &. question if & corrections exist at all, was the subject of much debate in the
literature, see e.g. ll. It seems that this matter was resolved recently in 4 , where it was shown that the form of the correction depends on the observable. The reaction e+e- + hadrons is a famous example of duality l2l5. Using the optical theorem, the cross section for the process can be described as the imaginary part of the forward elastic scattering amplitude, where the latter either contains a sum over all possible hadrons, i.e. the vector mesons, or a
224
sum over quark loops, including interactions with hard and soft gluons. For high enough center of mass energies, the ratio of the hadronic cross section to the e+e- -+ p+p- cross section is equal to N , C , eg, where N , is the number of colors and e, is the electric charge of a quark of flavor q. This clearly shows that at these energies, one may use either the quark degrees of freedom or hadronic degrees of freedom. More surprising, even at low center of mass energies where the resonance bumps can be seen clearly, the "quark result" N , C , eg, describes the average of the ratio. The production of dilepton pairs is the inverse reaction to e+e- 4 hadrons. One prominent feature of the dilepton production rate is the broadening of the resonance peaks in the spectrum, which gave rise to the explanation that the vector meson masses drop in the medium "dropping pmass". This phenomenon has also been interpreted as a quark-hadron duality induced effect Just as the resonance peaks vanish for masses larger than 1.5 GeV and below the J/* threshold (i. e. when the only active flavors are u, d , and s), the resonance peaks vanish in the dilepton production. Here, this vanishing occurs at lower masses already, which was interpreted as an in-medium reduction of the quark-hadron duality scale of 1.5 GeV for active u,d, and s flavors. Calculations working with hadronic degrees of freedom and quark-gluon degrees of freedom produce the same effect. 1396.
2.2 Duality in inclusive electron scattering
The cross section for inclusive electron scattering is given by
+
2)
=
aM&(w2 2Wl tan2 , where f f M & c( QP4. Therefore, the cross section for high Q2 is dropping off rapidly. Traditionally, the region where W , the invariant mass of the final state, is smaller than 2 GeV, is called the resonance region, and W > 2 GeV is referred to as the deep inelastic region. This distinction is rather artificial, and one key point of quark-hadron duality is that these two regions are actually connected. It is clear that duality in inclusive electron scattering must hold in the scaling region, for Q2 -+ m, as perturbative QCD is valid there, and therefore will describe the hadronic reaction. In deep inelastic scattering, the kinematics are such that the struck quark receives so much energy over such a small space-time region that it behaves like a free particle during the essential part of its interaction. This leads to the compellingly simple picture that the electromagnetic cross section in this kinematic region is determined by free electron-quark scattering, i.e. duality is exact for this process in the scaling region. The really interesting question is if duality will be valid approximately at lower Q 2 ,in a region where the cross section is dominated by resonances, which are strongly interacting
225 0.45 0.4 0.35
03
0 Q’= 1.7 (GeVlc)’
0.25
e:
0.2 0.15
0.1 0.05
“0.1
0.2
0.3
0.4
0.5
5
0.6
0.7
0.8
0.9
1
(e) loam Nicutsrcu OZ/OZ/W
Figure 1. Experimental data for F2(<,Q 2 ) = vW2(<,Q 2 ) from Jefferson Lab is plotted versus Nachtmann’s variable <.
2.
The data
hadrons, after all. The experimental data, see Fig. 1, show that duality holds even at very low Q2 = 0.5 GeV2 2 . One can see clearly that the resonance data follows the scaling curve, as given by the NMC parameterization evolved to Q2 = 5 GeV 2 . In principle, one should compare the resonance results to the pQCD results evolved to the same Q2 at which the resonance data were taken. As the resonance Q2 values are too low for this, choosing 5 GeV2 is a very reasonable approach. Finite energy sum rules formed for the scaling (pQCD) curve and the resonance regime further quantify the validity of duality, for details see Also, moments of the data have been considered 14. The most striking feature of the moments is that they flatten out at rather low Q2 M 2 GeV ’. If duality holds very locally, i.e. for just one resonance, instead of the whole resonance region, then one may use it to extract information on the resonance region from the deep inelastic region, and vice versa. A benchmark for applying duality in this, very local, way is the extraction of the magnetic form factor of the proton from the scaling curve 17J5. The result is shown
’.
226
- t ; -p~L' . m. ' e' .L" r i z a t G 7
u
Data subtraction (w/NMC 10) .
M
I - ' ' , I , - , - I - ," ~" .
1 0
u
.'-
u
U
U
10
1
:
U
I,.,,I,,.,I..,.IIII.I...II,..,I....I...I
0
05
1
15
2
2.5
3
35
4
4.5 X
Figure 2. Left panel: Extracted values for the magnetic form factor of the proton, from 15. Right panel: Data from SLAC for the polarization asymmetry of the neutron, A?, and projected data for the Jefferson Lab experiment E01-012 16.
in Fig. 2. The qualitative agreement is very good, and quantitatively, one sees that the duality extraction undershoots the form factor parameterization somewhat. This result may give us a good idea where we are in our understanding of duality, and in our ability t o extract information from the data. One important caveat in this case is that here, G L was extracted from the Fz data, and a constant ratio of 2.79 was assumed for the ratio of G M to G E . As we know from recent Hall A data from Jefferson Lab 18, this is not a decent assumption, and may introduce a sizable error. The good news is that new data for Fl have recently been taken at Jefferson Lab, and an extraction of G M can be performed without any assumptions on the ratio G M I G E ,as in elastic scattering, the electric form factor does not enter into the purely transverse Fl . Now, while extracting GM from deep inelastic data is a good check of our methods, this is not necessarily the "direction1' we want to take. From a practical point of view, it is very interesting to learn about the deep inelastic region from the resonance data. The valence quark region, i.e. the region of X B close ~ to 1, is of particular interest. However, data there are scarce, as the count rate in this kinematic region is very low. This can be seen immediately by inspecting Fig. 3, and recalling that (TM& 0; Q-4. If one wants to measure
227
1
Resonance Region
0.8
s
0.6
x
0.4
Deep Inelastic Region
0.2 0
0
5
10
15
20
Q2 (GeV2) Figure 3. The kinematic plane. The line indicates that W = 2 GeV. The region below it corresponds to W > 2 GeV (deep inelastic region), the region above it corresponds t o W < 2 GeV (resonance region).
in the deep inelastic region at large X B ~ one , necessarily has a very large Q 2 . However, if one is interested in a measurement at the very same value of X B ~ in the resonance region, the Q2values may be very small, and the count rate may therefore be much larger. One interesting, but currently not very well known quantity is the polarization asymmetry of the neutron, AT. For X B + ~ 1, it contains information about the valence quark spin distribution functions. There exist various, widely differing predictions for this quantity, for a review, see 19. If one believes that duality holds very locally, one may predict A? from form factor data ' O . As can be seen from Fig. 2, the currently existing data from SLAC (open symbols) are plagued by very large error bars, and do not reach the region of high ~ g relevant j for the valence quarks. The filled symbols represent projections €or data that are currently taken at Jefferson Lab, exploiting duality '. This means that data would be taken in the resonance region, and then properly averaged to obtain information on the deep inelastic region. As can be seen, the data taken in this way would have a much higher precision than the presently existing SLAC data, and would be deep in the valence
228
quark regime of high X B ~ . However, before we can apply such a "duality procedure" to data from the resonance region, we must understand where exactly duality holds, how exact it is, and which averaging procedure needs to be applied. The latter is especially important for polarized measurements, as one will need to take care to average only over resonances with the correct quantum numbers. Currently, we do not yet have such a firm and quantitative understanding of duality. There are several groups working on improving our theoretical understanding of duality, which is the topic of the next section.
3
Search for the Origins of Duality
The main questions that need to be addressed from the theoretical side are: Why do we observe duality? How can we see precocious scaling in a region where the interactions are strong? And, very relevant to applications of duality: For which observables in which kinematic regimes can we apply quark-hadron duality, and how precise are our results going to be? Theoretical efforts can be divided into two categories: refinement of the data analysis, e.g. use of various scaling variables, Cornwall-Norton vs Nachtmann moments, target mass corrections, averaging and modelling I will focus on the latter for the rest of my talk. When modelling duality, the first goal is to gain a qualitative understanding of the phenomenon. Obviously, the situation as observed in nature is very complicated, necessitating various simplifications. Nevertheless, the goal is to incorporate the essential physical features into a model. The general approach is to choose a solvable model for hadrons, calculate the relevant observables, and compare these results to the - hypothetical - free quark results. At this point, all models assume that after the excitation from the ground state to an excited level N , the quark will remain in its excited state,i.e. the produced resonance will not decay. The results obtained for the transition of the quarks to a bound, excited state are summed over and compared to the case where in the final state, the binding potential is switched off, and the quark is "free". The latter case corresponds to the pQCD situation. A schematic view of the modelling is given in Fig. 4. All models for duality must fulfill the following criteria: 21914922,
23124325,26.
1. The model must reproduce scaling. In addition, the scaling curve for the transition from the quark's ground state to the excited state must lead to the same scaling curve as the transition from the ground state to a free quark state. 2. The calculated moments must flatten out for large Q2, as observed in the data.
3. The resonance region results should oscillate around the scaling curve.
229
d
free quark
EN I
Figure 4. Schematic view of the model calculations. The left panel shows the bound-bound transition, the right panel shows the bound-free transition.
Let me now turn to one particular model, which was introduced in The approach in this work was to construct a model with just a few underlying basic assumptions, which could be extended to the more realistic case. In we assumed that it is sufficient to incorporate relativity and confinement in a valence quark model. We also treated the quarks as scalars - while spin is crucial in nature, we assumed that for duality to be observed, it would not be necessary. In principle, we are interested in nucleon targets, i.e. in a three-body system. As this poses some technical difficulties, we assumed that only one quark would carry charge and therefore interact with the photon, the other two quarks form a spectator system. One may think of them either as an anti-quark or as a diquark. In order to further simplify the task, we also assumed that the spectator system has infinite mass. This means that instead of solving the Bethe-Salpeter equation for the two-body problem, we have to solve only a one-body equation. As we are dealing with scalar quarks, the Klein-Gordon equation needs to be solved. We model the confinement using a scalar, linear potential, V a T . As the potential enters the Klein-Gordon equation as V 2, the resulting equation resembles the Schrodinger equation for the non-relativistic harmonic oscillator. This has the advantage that the wave functions obtained in the solution are exactly the wave functions obtained for the non-relativistic harmonic oscillator, whereas the energy spectrum is given by EN a which leads to a much higher density of excited states than in the non-relativistic case, where E 7 n - r e 10; N . A comparison between the relativistic and the non-relativistic solutions is easily feasible in this case. A nice feature of this model is that the solutions can be obtained analytically. 23924.
231241
a,
230
The two parameters needed for this model are the constituent quark mass, m = 0.33 GeV and the string tension, which takes a value of 0.16 GeV2. None of the results depend crucially on these precise values, and we have checked that variation of these values gives reasonable results, e.g. we obtain the free case in the limit of the sting tension going t o zero. While all particles, including beam and exchange particles, were treated as scalars in 23, only the quarks were treated as scalars in 24. In the latter case, with spin 1/2 electrons and spin 1 photons, one deals with a conserved current. The first requirement of duality that must be fulfilled by a model is scaling of the bound-bound transition, i.e. scaling for the case where only resonances are in the final state. Before investigating the scaling behavior, i.e. the behavior for large Q2, we need to establish which quantity ought to scale, and which scaling variable to use. Bjorken’s variable X B = ~ and scaling function F2 = vW2 are designed for the region of Q2 >> M y Duality was observed to hold at much lower values of Q2, where the target mass M is about as large as Q2, and the constituent quark mass, which is the relevant quantity at the considered low Q2, is not negligible compared to Q2. This situation demands a different scaling variable and scaling function. Bloom and Gilman used the ad hoc variable x‘ = , and later on 27, a variable that treats target mass and constituent quark mass on the same footing was - v)(1 , and was derived derived. It reads xCq= for the case of free quarks with a momentum distribution. When deriving a scaling variable, it turns out that it is intimately connected to a scaling function, which for our case (scalar quarks), reads S2,,¶ = lflW2. Note that all scaling variables and scaling functions must reduce to Bjorken’s variable X B and ~ F2 in the limit of high Q2. The results for the scaling in the bound-bound case are shown in Fig. 5. It is clear from the figure that scaling is present: once Q2 is high enough, the curves for different Q2 practically coincide. Analytically, it was shown m 2 u % jexp (Eo-musj)’ p2 and that this is the same result 24 that S2,,¶ =
F’
+Q
+ d-)
( d w
(-
T~PEO
),
which one obtains for the bound-free transition. It is interesting to note that the scaling function obtained in the all scalar case - where again, the boundbound and bound-free transitions lead to the same scaling function - has a exp ( E o - m up2 Bj)2 . In the slightly different analytic form: S,, =
(-
4iTT ~
E o
)
former case, one obtains that the scaling function goes to zero for the scaling variable approaching zero, as expected for valence quarks. However, we do not observe the behavior 0: fi,as predicted by Regge theory 28. With our simple model, this was not to be expected, though, and it is interesting to
231
-0
1
2
4
3
5
U
Figure 5 . Scaling of the bound-bound transition for Q2 -+ 0.6
1.4
1.2 -
N h
2 I
1
-
Q
5
v
00.
0.4
v
0.8
Y
0.4
v
0
Q?
0.2
0.2 0
1
3
2 U
4
5
0
1
2
3
4
U
Figure 6. Duality at low Q2 for the electromagnetic current (left panel), and the all scalar case (right panel). The solid lines show the result for large Qz, the short dashed lines show Q2 = 0.5 GeV2, the long-dashed lines show Q2 = 1 GeV2, the dotted lines show Q2 = 2 GeV2, and the dash-dotted lines show Q2 = 5 GeV2.
observe how introducing the proper spin for the beam and exchange particles leads to a more realistic description. he moments flatten out at large Q 2 , as required, and duality at low Q2 is shown in Fig. 6 for the all scalar case (right panel) and the electromagnetic case (left panel). A similar model is discussed in 2 5 . These authors consider a scalar probe and scalar quarks, and start from the semi-relativistic Hamiltonian 'H = Jp'2 f i r , where the quarks are massless. The solutions obtained in
+
232
this approach are purely numerical. When considering scaling with respect to the many-body variable ij = u - 14, scaling and local duality are observed. The authors also address the interesting question of contributions to sum rules from the time-like region, which may appear due to the binding of the quarks. The results in 25 differ in one important aspect from the results discussed previously the bound-bound and bound-free transitions do not lead to the same scaling curves, they differ by about 30 %. This difference apparently stems from the different wave equations used for the two models. 23124:
4
Summary and Outlook
We have shown that duality appears in many reactions, is experimentally very well established, and has interesting and useful applications. Duality can be modelled, and with just a few basic assumptions, one can qualitatively reproduce all the features of duality. In the future, we will see more data exploring duality in various reactions - unpolarized and polarized reactions, and meson production. Theory will progress to more realistic models, including the spin of quarks and explicitly modelling the decay.
Acknowledgments We gratefully acknowledge discussions with F. Close, R. Ent, R. J. Furnstahl, N. Isgur, C. Keppel, S. Liuti, I. Niculescu, W. Melnitchouk, M. Paris, and R. Rapp. This work was supported in part by funds provided by the National Science Foundation under grant No. PHY-0139973 and by the U S . Department of Energy (DOE) under cooperative research agreement No. DEAC05-84ER40150.
References 1. E. D. Bloom and F. J. Gilman, Phys. Rev. Lett. 25, 1140 (1970); E. D. Bloom and F. J. Gilman, Phys. Rev. D 4, 2901 (1971). 2. I. Niculescu et al., Phys. Rev. Lett. 8 5 , 1182 (2000); 85, 1186 (2000); R. Ent, C.E. Keppel and I. Niculescu, Phys. Rev. D 62, 073008 (2000). 3. N. Isgur and M. B. Wise, Phys. Rev. D 43,819 (1991). 4. R. Lebed and N. Uraltsev, Phys. Rev. D 62, 094011 (2000). 5. E. C. Poggio, H. R. Quinn, and S. Weinberg, Phys. Rev. D 13, 1958 (1976). 6. R. Rapp, hep-ph/0201101. 7. M. A. Shifman, arXiv:hep-ph/0009131.
233
8. Jefferson Lab experiment E01-012, spokespersons J.-P. Chen, S. Choi, and N. Liyanage; Jefferson Lab Experiment E93-009, spokespersons G. Dodge, S. Kuhn and M. Taiuti. 9. Contributions of E. Christy, C. Keppel, and I. Niculescu to these proceedings. 10. The Science driving the 12 GeV upgrade, edited by L. Cardman, R. Ent, N. Isgur, J.-M. Laget, C. Leemann, C. Meyer, and Z.-E. Meziani, Jefferson Lab, February 2001. 11. N. Isgur, Phys. Lett. B 448,111 (1999). 12. see e.g. F. Halzen and A. D. Martin, "Quarks & Leptons: An Introductory Course in Modern Particle Physics", John Wiley & Sons, 1984. 13. see e.g. R. Rapp and J. Wambach, Adv. Nucl. Phys. 25,1 (2000). 14. C. S. Armstrong, R. Ent, C. E. Keppel, S. Liuti, G. Niculescu and I. Niculescu, Phys. Rev. D 63,094008 (2001). 15. R. Ent, C. E. Keppel and I. Niculescu, Phys. Rev. D 64,038302 (2001). 16. N. Liyanage, private communication. 17. A. DeRujula, H. Georgi, and H. D. Politzer, Ann. Phys. (N.Y.) 103 315 (1977). 18. see e.g. Ed Brash, these proceedings. 19. N. Isgur, Phys. Rev. D 59,034013 (1999). 20. W. Melnitchouk, Phys. Rev. Lett. 86,35 (2001). 21. I. Niculescu, C. Keppel, S. Liuti and G. Niculescu, Phys. Rev. D 60, 094001 (1999); S. Liuti, R. Ent, C. E. Keppel and I. Niculescu, arXiv:hepph/0111063. 22. S. Simula, Phys. Lett. B 481, 14 (2000); Phys. Rev. D 64,038301 (2001). 23. N. Isgur, S. Jeschonnek, W. Melnitchouk, and J. W. Van Orden, Phys. Rev. D 64, 054005 (2C01). 24. S. Jeschonnek and J. W. Van Orden, Phys. Rev. D 65, 094038 (2002). 25. M. W. Paris and V. R. Pandharipande, Phys. Lett. B 514 361 (2001); M. W. Paris and V. R. Pandharipande, Phys. Rev. C 65,035203 (2002). 26. F. Close and Q. Zhao, hep-ph/0202181. 27. R. Barbieri, J. Ellis, M. K. Gaillard, and G. G. Ross, Phys. Lett. 64B 171 (1976); R. Barbieri, J. Ellis, M. K. Gaillard, and G. G. Ross, Nucl. Phys. B117 50 (1976). 28. R. G. Roberts, "The Structure of the Proton", Cambridge University Press, 1990.
FIRST RESULTS FROM SPRING-8 T. NAKANO FOR THE LEPS COLLABORATION RCNP, Osaka University, 10-1 Mihogaoka, Ibaraki, Osaka 567-004 7, JAPAN
E-mail: nakanoOrcnp. Osaka-u.ac.jp The GeV photon beam at Spring-8 is produced by backward-Compton scattering of laser photons from 8 GeV electrons. Polarization of the photon beam will be ~ 1 0% 0 a t the maximum energy with fully polarized laser photons. We report the status of the new facility and the prospect of hadron physics study with this high quality beam. Preliminary results from the first physics run are presented.
1
LEPS FACILITY
8 GeV
-
0 ExperimentalHutch
10 20m
Figure 1. Plan view of the Laser-Electron Photon facility at Spring-8 (LEPS).
The Spring-8 facility is the most powerful third-generation synchrotron radiation facility with 62 beamlines. We use a beamline, BL33LEP (Fig. l), for the quark nuclear physics studies. The beamline has a 7.8-m long straight section between two bending magnets. Polarized laser photons are injected from a laser hutch toward the straight section where Backward-Compton scat-
234
235
tering (BCS) of the laser photons from the 8 GeV electron beam takes place. The BCS photon beam is transferred to the experimental hutch, 70 m downstream of the straight section. The maximum energy of the BCS photon is expressed by
where kl is the energy of the laser photon, Ee is the energy of thc electron, and me is the electron mass. For a 351-1lrn (3.5 eV) Ar laser and a 8-GeV electron beam, the maximum energy is 2.4 GeV well above the threshold of &phtoproduction from a nucleon (1.57 GeV). If laser lights are 100 % polarizcd, a backward-Compton-scattered photon is highly polarized at the maximum energy. The polarization drops as the photon energy decreases. However, an energy of laser photons is easily changed so that the polarization remains reasonably high in the energy region of interest. The incident photon energy is determined by measuring the energy of a recoil electron with a tagging counter. The tagging counter locates at the exit of the bending magnet after the straight section. It consists of multi-layers of a 0.1 mm pitch silicon strip detector (SSD) and plastic scintillator hodoscopes. Electrons in the energy region of 4.5 - 6.5 GeV arc detected by the counter. The corresponding photon energy is 1.5 - 3.5 GeV. The position resolution of the system is much better than a required resolution. The energy resolution (RMS) of 15 MeV for the photon beam is limited by the energy spread of the electron beam and an uncertainty of a photon-electron interaction point. The operation of the BCS beam at Spring-8 started in July, 1999. Ar laser at 351-nm wave length is used, and the intensity of the beam is about 2.5 x lo6 photons/sec for a 5 W laser-output. 2
DETECTOR
The LEPS detector (Fig. 2) consists of a plastic scintillator to detect charged products after a target, an aerogel Cerenkov counter with a refractive index of 1.03, charged-particle tracking counters, a dipole magnet, and a time-of-flight T O F wall. The design of the detector is optimized for a 4 photo-production at forward angles. The opening of the dipole magnet is 135-cm wide and 55-cm height. The length of the pole is 60 cm, and the field strength at the center is 1 T. The vertex detector consists of 2 planes of single-sided SSDs and 5 planes multiwire drift chamber, which are located upstream of the magnet. Two sets of
236
Figure 2. The LEPS detector setup.
MWDCs are located downstream of the magnet. The identification of momentum analyzed particles is performed by measuring a time of flight from the target to the T O F wall. The start signal for the T O F measurement is provided by a R F signal from the 8-GeV ring, where electrons are bunched at cvery 2 nsec with a width (a)of 16 psec. A stop signal is provided by the TOF wall consisting of 40 2m-long plastic scintillation bar with a time cross resolution of 150 psec. The physics run with a 3-cm long liquid H2 target wad carried out during December, 2000 to June, 2001. The trigger required a tagging counter hit, no charged particle before the target, charged particles after the target, no signal in the aerogel cerenkov counter, at least one hit on the T O F wall. A typical trigger rate was about 20 counts per second. Figure 3 shows a prelim-
237
inary mass distribution of charged particles reconstructed from momentum and TOF informat ion.
~~
U o r e n t u m rcnge
--1
0
<1
1
2
3
Uoss/Charge (GeV/c')
Figure 3. A mass distribution of charged particles reconstructed from momentum and TOF information.
3
PRELIMINARY RESULTS
4 photopmduction near threshold Since a 4 meson is almost pure ss state, diffractive photo-production of a 3.1
meson off a proton in a wide energy range is well described as a pomeronexchange (multi gluon-exchange) process in the framework of the Regge theory and of the Vector Dominance Model (VDM) 2; a high energy photon converts into a q5 meson and then it is scattered from a proton by an exchange of the pomeron while the meson-exchange is suppressed by the OZI rule. However, at low energies other contributions arising from meson ( T , 71)-exchange 5 , a scaler (O++ glueball)-exchange 6 , and ss knock-out are possible. These contributions fall off rapidly as the incident y-ray energy increases, and can be studied only in the low energy region near the production threshold. Linearly polarized photons are an ideal probe to decompose these contributions. For natural-parity exchange such as pomeron and O++ glueball exchanges, the 37415
238
decay plane of K f K - is concentrated in the direction of the photon polarization vector. For unnatural-parity exchange processes like T and 77 exchange processes, it is perpendicular to the polarization vector. LEPS will greatly contribute to this field. Figure 4 shows the events of 4 mesons, which are successfully identified through the reconstruction of the K f K - invariant mass.
15
Figure 4. A two-kaon invariant mass distribution. The 9 peak is clearly identified.
3.2 K f photoproduction Recent measurements for K f A photoproduction at SAPHIR indicated a structure around W = 1.9 GeV in the total cross-section '. It attracted theorist's interest to study missing nucleon resonances in this process. Mart and Bennhold showed that the SAPHIR data can bc reproduced by inclusion of a new Dl3 resonance which have large couplings both to the photo and the K A channels according to the quark model calculation l o . Although it is difficult to draw a strong conclusion on the existence of Dl3 resonance from the cross-section measurements, the photon polarization asymmetry is very sensitive to the missing nucleon resonance. The LEPS collaboration measure the asymmetry in the photon-beam energy region of 1.5-2.4 GeV 1 1 , while the measurement below 1.5 GeV has been carried out at GRAAL 1 2 .
239
3.3 A(1405) photoproduction from proton and nuclei The mass of the A(1405) resonance is just below K N threshold. And it is well described by a chiral unitary model l 3 where the resonance is generated by meson-baryon interaction. The model predicts a drastic change of the decay width of the resonance in a nucleus because of its meson-baryon molecular nature. It also predicts that a decay shape depends on a decay mode. Photoproduction of the A(1405) from a proton and a nucleus will elucidate the nature of the A.
400
ii
i
300
200
100
0
1
I
I
I
12
1.4
1.6
Missirg mass for p(7.K')
18
(GeV/c2)
Figure 5. A missing mass distribution of (7, K f ) reactions.
Figure 5 shows a missing mass distribution of the (7, K + ) reactions. The A and C peaks are clearly identified, but the A(1405) is not separated from the
C(1385). The separation of two resonances are possible by requiring charged C in the missing mass spectrum of (7, K+n*) because about 2/3 of A(1405) particles decay into charged nC pairs while C(1385) particles predominantly decay into neutral nC pairs. The invariant m a s plots of the C n pairs are shown in the figure 6 where the C is identified by the missing mass technique. This method is not applicable to the case of nuclear target. A timeprojection chamber to identify the A(1405) in the invariant mass of a charged C n pair is under construction.
240 u) Q
c
Q)
40
w L
0 30 L Q)
a
E
20
3
z
10
0
1.3
1.4
1.5
1.6
1.7
1.8
M(x+I-)(GeV/cZ) m
Q
c
Q)
60
-
W L
0 L
40
-
a,
13
$
20
-
Z
0
1
1.3
1.4
1.5
1.6
l h 1.7
1.8
M(xCZ') (GeV/c2) Figure 6. Invariant mass distribution of the K + C C - (left) and a - C + (bottom). The C was identified in the missing mass spectrum of (7, K + & ) reactions. No xceptance correction was applied.
3.4 w photoproduction Missing nucleon resonances could couple to the 7r-nucleon channel weakly but couple to the w-nucleon channel strongly 14. The LEPS can measure a forward proton from backward w photoproduction. In this kinematic region u-channel and s-channel contributions dominate and the effects of missing resonances would be large. The old differential cross section data for backward w photoproduction l5 shows a structure around u = -0.15 GeV, which is very hard to be reproduced by model calculations 1 6 . New precise measurements are awaited to confirm the structure. Figure 7 shows a missing mass distribution of the ( y , p ) reactions. The w, q, and q' peaks are observed.
241
-0
14
x
v
m c
5
12
0
10
8
6
4
I
2
0
Figure 7. A missing mass distribution of ( 7 , reactions. ~)
References
1. R.H. Milburn, Phys. Rev. Lett. 10, 79 (1963). 2. J.J. Sakurai, Ann. Phys. 11, 1 (1960); J.J. Sakurai, Phys. Rev. Lett. 22, 981 (1969). 3. T.H. Bauer et al., Rev. Mod. Phys. 50, 261 (1978). 4. A. Donnachie and P.V. Landshoff, Nucl. Phys. B267, 690 (1986). 5. M.A. Pichowsky and T.-S. H. Lee, Phys. Rev. D56, 1644 (1997). 6. T . Nakano and H. Toki, in Proc. of Intern. Workshop on Exciting Physics with New Accelerator Facilities, Spring-8, Hyogo, 1997, World Scientific Publishing Co. Pte. Ltd., 1998, p.48. 7. A.I. Titov, Y. Oh, and S.N. Yang, Phys. Rev. Lett. 79, 1634 (1997); A.I. Titov, Y. Oh, and S.N. Yang, Phys. Rev. C58, 2429 (1998). 8. M.Q. Tran et al., Phys. Lett. B 445, 20 (1998). 9. T. Mart and C. Bennhold, Phys. Rev. C61, (R)012201 (2000). 10. S. Capstick and W.Roberts, Phys. Rev. D58, 074011 (1998). 11. R.G.T. Zegers, in these proceedings. 12. A. d’hngelo, in these proceedings.
242
13. J.C. Nacher, E. Oset, H.Toki, A. Ramos, Phys. Lett. B 455 (1999) 55; N. Kaiser, P.B. Siegel, W.Weise, Nucl. Phys. A 594 (1995) 325. 14. Y. Oh, A.I. Titov, and T.-S. H. Lee, Phys. Rev. C63, 025201 (2001); Q. Zhao, Phys. Rev. C63, 025203 (2001). 15. R.W. Clifft e t al., Phys. Lett. B 72 (1977) 144. 16. T.-S. H. Lee, private communication.
HYBRID BARYONS P. R. PAGE Theoretical Division, M S B283, Los Alamos National Laboratory, Los Alamos, N M 8'7545, USA E-mail:
[email protected] We review the status of hybrid baryons. The only known way to study hybrids rigorously is via excited adiabatic potentials. Hybrids can be modelled by both the bag and flux-tube models. The low-lying hybrid baryon is N f + with a mass of 1.5 - 1.8 GeV. Hybrid baryons can be produced in the glue-rich processes of diffractive 7 N and aN production, @ decays and p p annihilation.
1
Introduction
We review the current status of research on three quarks with a gluonic excitation, called a hybrid baryon. The excitation is not an orbital or radial excitation between the quarks. Hybrid baryons have also been reviewed elsewhere. The Mercedes-Benz logo in Fig. 1 indicates two possible views of the confining interaction of three quarks, an essential issue in the study of hybrid baryons. In the logo the three points where the Y-shape meets the boundary circle should be identified with the three quarks. There are two possibilities for the interaction of the quarks: (1) a pairwise interaction of the quarks represented by the circle, or (2) a Y-shaped interaction between the quarks, represented by the Y-shape in the logo.
'
2
Why does one consider hybrid baryons?
(1) You cannot avoid them. This is because excited glue is predicted by QCD (see the lattice QCD hybrid meson excited adiabatic potentials later), so that hybrid baryon degrees of freedom should be part of baryon spectroscopy. (2) Gluonic excitations are qualitatively new. While systems with more degrees of freedom than quarks are qualitatively new, the most promising place to study gluonic excitations does not appear to be hybrid baryons. Glueballs (made from gluons) and hybrid mesons (a quark and antiquark with a gluonic excitation) are more promising since they can be Jpc exotic, meaning that there are no mesons in the quark model with these J p c , or there are no local quark-antiquark currents with these J p c . Hybrid baryons have half-integral J and no C , and there are no J p exotics: all J p can be
243
244
LD
9
0 v)
500
c
3 0 1.5 2.0 2.5 M (q'n-)(GeV/c2) Figure 1. Mercedes-Benz logo (left) and number of events (per 50 MeV bin) as a function of V'T- invariant mass (right).
constructed for baryons in the quark model. In fact, a JPG = 1-+ exotic isovector meson at 1.6 GeV has recently been reported in IT-. In this analysis the exotic partial wave is in fact the dominant one. If one were shown the event shape (Fig. 1) a few decades ago when the p was discovered, it would be easy to conclude that a new resonance has been discovered. The exotic meson is currently thought t o be a hybrid meson. (3) Hybrid baryons are a test of intuitive pictures of Quantum Chromodymanics (QCD). As we will shortly detail, current lattice QCD data indicate that the interaction between three quarks is indeed a Y-shaped potential, which is expected to arise from three gluon flux-tubes meeting at a junction (see Fig. 2). Excitations of these gluon flux-tubes is expected to be very sensitive to the way that the flux-tubes connect (in this case in a Y-shape): hence the importance of hybrids for our intuitive pictures of QCD. The gluon self-interaction has no analogue in the Abrikosov-Nielsen-Olesen flux-tubes of QED. As promised, let us sketch current lattice QCD data. In Fig. 2 we define the three lengths 11, Z2 and l 3 as the distances from the quarks (the blobs) to the equilibrium position of the junction of the Y-shaped linearly confining flux-tube system. Define Lmin = ZI Z2 Z3. The quenched lattice potential for the three quarks as a function of Lmin is plotted in Fig. 2. At large Lmin the potential is proportional to Lmin. The potential was parameterized by a Coulomb and Y-shaped confining term
+ +
245
1.5
1 O(i, i,k) 0(0.1. k)
g 10
......
-
05 00
A=0.1316(62) 0=0.1528(27) C=0.9140(201) 20
4.0
60
80
L,," Figure 2. Definition of
11,12
and
13
(left) and lattice potential
(right).
and the string tension D = 0.1528(27) GeV2 was found to be similar to the value measured between a quark and an antiquark, albeit somewhat smaller. A possible reason for this is a cancellation of chromo-electric fields at the junction of the Y-shaped flux-tube. The value of the string tension is consistent with the value of 0.15 GeV2 extracted from the experimental baryon spectrum by Capstick and Isgur. It is found that x 2 / d . o . f . = 3.99 for the Y-shaped confinement potential versus and 10.9 for pairwise confinement, so that Y-shaped confinement is clearly preferred. Another lattice work concludes that pairwise confinement is preferred over Y-shaped confinement, but imposes the constraint that D for baryons must be identical to D for mesons, an assumption which is unjustified. 3
What are hybrid baryons?
Hybrid baryons can be defined in two ways: (1) Three quarks and a gluon. If states are rigorously expanded in Fock space, one can discuss hybrid (three quark - gluon) components of such an expansion, which can be accessed in large Q 2 deep inelastic scattering. Historically a low-lying hybrid baryon was defined as a three quark - gluon composite. However, from the viewpoint of the Lagrangian of QCD this definition is non-sensical. This is because gluons are massless, and hence there is
246 rha=6.162 GeV-I
V-H-V-B
fHybrid - Baryon1 P o t e n t i a l
IGeVl
Figure 3. Difference between hybrid and conventional baryon adiabatic potentials as a function of the quark positions (parametrized in terms of the Jacobi coordinates p , X and 8, with p fixed in this case.) 32
no reason not t o define a hybrid baryon, for example, as a three quark - two gluon composite. Neither is one possibility distinguishable from the other, since strong interactions mix the possibilities. Moreover, sometimes the definition becomes perilous. A case in point is recent work on large N , hybrid baryons, where their properties depend critically on the fact that the gluon is in colour octet, and hence the three quarks in colour octet, so that the entire state is colour singlet. * The bag model circumvents the objections raised against this definition, since gluons become massive due to their confinement inside the bag. 9,10,11,12,13 (2) Three quarks moving is an excited adiabatic potential. One can always evaluate the energy of a system of three fixed quarks as a function of the three quark positions, called the adiabatic potential. There is a ground-state adiabatic potential, corresponding to conventional baryons, and various excited adiabatic potentials, corresponding to hybrid baryons. The three quarks are then allowed to move in the excited adiabatic potential. This can be a perfectly sensible definition from the viewpoint of QCD. The caveat is that this definition is only exact for (1) very heavy quarks (for some potentials), or (2) for specific simplified dynamics, particularly that of three non-relativistic quarks moving in a simple harmonic oscillator potential. l4 In the latter case
247
10
5
-5
0
1
2
3
4
r/@r& Figure 4. Adiabatic potentials as a function of QQ separation.
33
the definition is exact even for up and down constituent quarks if one redefines the adiabatic potential suitably. l4 For the linear potentials of the flux-tube model is was noted that “For light quarks almost all corrections may be incorporated into a redefinition of the potentials. Mixing between [new] potentials is of the order of 1%”. l5 If mixing between the (redefined) adiabatic potentials is this small one can sensibly talk about hybrids even for light quarks. The redefinition depends on the quark masses, so that one would ideally start with very heavy quarks on the original adiabatic potential, and then gradually move to the quark masses of interest by redefining the adiabatic potential. An example of an adiabatic surface in the flux-tube model appears in Fig. 3.
248
The potential peaks at small p and X and the uneven rim corresponds to the transition from a Y-shaped flux-tube to a two-legged flux-tube (when the angle between two of the quarks is more than 120’). 4
How are hybrid baryons modelled?
To answer this question it is best to understand how hybrid mesons can be modelled. The quenched lattice QCD hybrid meson adiabatic potentials are shown in Fig. 4. (Note that at large QQ separation, linear confinement should break down due to qtj pair creation. For low-lying hybrids this effect can be incorporated as a higher order effect, i.e. as loop corrections to masses.) At small QQ separation, the adiabatic bag model (where quarks are stationary) gives a reasonable description of the lattice data. l6 At large QQ separations, a constituent gluon model (related to the bag model) is not applicable, l7 but a Nambu-Goto string (flux-tube) picture instead One hence needs a combined phenomenology of the “old bag” model and the flux-tube model to model hybrid mesons, and by implication hybrid baryons. This is a somewhat unhappy marriage, as the two models describe glue very differently. The exact way the glue is modelled is critical, e.g. in the flux-tube model Yshaped confinement for low-lying hybrid baryons has been shown to be wellapproximated by motion of the junction of the Y-shape. ’’ The dynamics is critically dependent of what the nature of the excitation is. We now summarize model estimates for masses of hybrid baryons. QCD sum rules estimates the low-lying N f + hybrid at 1.5 GeV. 2o The bag model obtains the lightest hybrid, Nf’, at 1.55 GeV, between the N(1440) (Roper) and N(1710). Higher mass N and A hybrids are at 1.5- 2.5 GeV. In the flux-tube model the N hybrids are at 1.87(10) GeV and the A hybrids at 2.08(10) GeV. l9 Hybrids with strangeness have surprisingly low mass, particularly a flavour singlet A at 1.65 GeV in the bag model. l 1 ~ l 2 What are the quantum numbers of hybrid baryons? The good quantum
’*.
-
N
9710911
9,10711
-
Table 1. Quantum numbers in the flux-tube model.
I Mass I
I Light Light Heavy
I
1
Flavour Spin J p I
N N A
I
I
-
-1 2
1 2
-3 2
I+ 2
3+
’ 5
2
z+ 7 2
2
‘ 2
L+
I+ g+ 2+ ’ 2
1
l9
249 Table 2. Quantum numbers in the bag model.
9,10,11
/%/I". I Flavour 1 Spin I
I
Jp
I
' 2
-
1+
2
2
s+
' 2
numbers are flavour (to the extent that isospin is a good symmetry), J and P . The non-relativistic spin of the three quarks is also important in (nonrelativistic) models, but is not a good quantum number. Table 1 lists the quantum numbers of the low-lying hybrids in the flux-tube model. The total angular momentum J is obtained by adding the spin (either $ or $) to unit orbital angular momentum L. The four N hybrids are the lightest, and the five A hybrids heavier, as previously remarked. Although hybrids contain the quantum numbers of the conventional N and A, one never obtains a full multiplet of conventional baryons like this in the quark model, even for excited conventional baryons. It is, however, possible to have L p = 1+ for conventional baryons, as is the case for hybrids. The quantum numbers of hybrids in the bag model is shown in Table 2. These differ from the flux-tube model in the last two rows: The spin $ and is exchanged, with corresponding changes in J . In the bag model the Nf+is the lightest, then the Nf+, N%+ and Nf', then the A;+ and A$+ with N $ + the heaviest. The bag model has the same number of low-lying states as in flux-tube model. When good quantum numbers are considered, the only difference is that the J p = $ + state is a A in the flux-tube model and a N in the bag model. In both models this is one of the highest lying states, so that the low-lying hybrids are identical. In fact, N $ + is amongst the lightest hybrids in both models, and, as previously noted, is light in QCD sum rules as well. For hybrids with strangeness, the Af+ and A$+ were predicted in the bag model, with the A$+ the lighter state. l 1 y l 2 Recently, masses and quantum numbers of hybrid baryons have been reported in a dispersion relation technique. 21
z
5
How does one find hybrid baryons?
There are currently two approaches:
250
Comparison with models (which are themselves callibrated against lattice QCD and experiment on glueballs and hybrid mesons). Comparison to generic expectations for glue-rich hadrons. Hybrid baryons can be found by (1) Observing more states than the conventional baryons. This approach is very difficult in practice, and has only proved useful in the Jpc = O++ (scalar) isoscalar meson sector, which has led to the identification of a gluonic excitation: the glueball. To see how difficult this approach is for hybrid baryons, look at Fig. 5. Nowhere in the spectrum does one observe an excess of quark model (conventional) baryons above those known experimentally. There is hence no need to posit hybrids. Another possible way to identify hybrids in the spectrum is to compare the behaviour of experimental states relative to properties conventional baryons are known to have. Examples of such properties is the hypothesis that the high-lying conventional baryons occupy chiral multiplets 22 or that conventional baryons follow Regge trajectories 23. (2) Diffractive y N and nN production. The detection of the hybrid meson candidate ~(1800)in diffractive wN collisions by VES 24 may indicate that hybrid mesons are producted abundantly via meson-pomeron fusion. If this is the case, one expects significant production of hybrid baryons via baryonpomeron fusion, i.e. production in diffractive y N and n N collisions. (3) Production in $ decays. Naive expectations are that the gluon-rich environment of $ decays should lead to dominant production of glueballs, but also signifant production of hybrid mesons and baryons. The large branching ratios 25 Br($ + plsw, ppr') may indicate hybrid baryons. Recently a J p =' f 2 0 peak at mass 18342:; MeV was seen in D ! + p m . 26 (4) Production in p p annihilation. The fact that the scalar glueball is strongly produced in this process, although not dominantly, may make it a promising production process. (5) Studying hybrid baryon decays. Except for a QCD sum rule motivated suggestion that the N' f hybrid baryon has appreciablea decay to N a , 2r and a bag model calculation which predicts a N ; + with large AA decay and minute n N decay, l 3 no decay calculations have been performed. However, decay of hybrid baryons to N p and Nw is a priori interesting since it isolates states in the correct mass region, without contamination from lower-lying conventional baryons.
-
"They find that ro/rtot = only 10% (modulo phase space), consistent with the Roper, although ru is still much larger than for other resonances.
25 1 2200 I
I
N experiment2 ind model states below 2200 MeV I
PDG mass range
-
light hybrids
N=0,1,2 bands
1700
u Nr amp1 I
l
0
5 _>lOMeV1
l
1500
1400
1300
lux) N1/2+
N3I2’
N7/2+
NlR
N3n
NSlf
Figure 5. Model (conventional and hybrid) and experimental N baryons. For each set of quantum numbers, the mass spectrum is indicated (in MeV). The thin bars indicate quark model predictions for conventional baryon masses. The four fully filled thin bars around 1870 MeV are the flux-tube model hybrids. l9 The large rectangular blocks are the mass ranges of known experimental states.
(6) Electroproduction. In the flux-tube model, which is an adiabatic picture of a hybrid baryon, there is the qualitative conclusion that “ep + e X should produce ordinary N*’s and hybrid baryons with comparable crosssections”. 28 However, the conclusions obtained from the three quark - gluon picture of a hybrid baryon is different. For large Q2 electroproduction, the Q2 dependence of the amplitudes is summarized in Table 3. Since the photon has both a transverse and longitudinal component, the amplitude for a conventional baryon is expected to dominate that of the hybrid baryon as Q2 becomes large. For small Q2 the conclusion agrees with the large Q2 result for transverse photons, but is more dramatic for longitudinal photons: the
’
252 Table 3. Q2 dependence of amplitudes for the electroproduction of conventional or hybrid baryons with transverse or longitudinal photons, valid at large Q2.
II Conventional I Hybrid I Transverse Longitudinal
l/Q3 l/Q4
l/Q5 l/Q4
amplitude vanishes. It has accordingly been concluded that the (radially excited) conventional baryon is dominantly electroproduced (depending on the details of the calculation), with the hybrid baryon subdominant relative to the resonances S11(1535),013(1520) and A as Q2 increases. 29 The Q 2 dependence of the electroproduction of a resonance can be measured at Jefferson Lab Halls B and C and an energy upgraded Jefferson Lab. A hybrid baryon is expected to behave different from nearby conventional baryons as a function of Q2. One needs to perform partial wave analysis at different Q2. For large Q 2 cross-sections are small, which would make this way of distinguishing conventional from hybrid baryons challenging. 29730
Various characteristics of the N(1440) (Roper) have been argued to be consistent with its being dominantly a hybrid baryon: Its mass is consistent with bag model lo and QCD sum rule 2o estimates, it is suppressed in large Q2 electroproduction 29 and the width ratio ra/I'totis consistent with QCD sum rule decay calculations 27. The A( 1405) (J = and A(1520) (J = have recently been proposed to be hybrid baryons based on the idea that this hypothesis solves a J ordering problem in this system: for hybrid baryons the ordering in a constituent gluon model is as observed, while it is opposite in (most) quark models. 31 We highlight current experimental searches for hybrid baryons. Photoand electroproduction efforts at Halls B and C at Jefferson Lab (Newport News) can isolate hybrid baryons in y N -+ hybrid -+ ( p , w , q)N at masses less than 2.2 GeV. As previously remarked, the higher mass decay channels are of most interest. Similar searches at the Crystal Barrel and SAPHIR detectors at ELSA (Bonn) is under way. Particularly, at Crystal Barrel hybrid baryons is planned to be isolated in y N -+ hybrid -+ (7, no) Sll(l535) + (7, r o )q N . Hybrid mesons in flux-tube model decay strongly to P S-wave mesons and not to S+S-wave mesons. If this is also true for hybrid baryons, decay to a Pwave baryon ( 4 1(1535)) and an S-wave meson ( q or r o )should be prominent. In Q production hybrid baryons are searched for at BES at BEPC. Searches for hybrid baryons in ! I ! + hybrid i j -+ pfj (q,rO) have been undertaken.
3)
z)
+
253
Acknowledgments
This research is supported by the Department of Energy under contract W7405-ENG-36. References
1. T. Barnes, contribution at the COSY Workshop on Baryon Excitations (May 2000, Julich, Germany), nucl-th/0009011. 2. E.I. Ivanov et al., Phys. Rev. Lett. 86, 3977 (2001). 3. T.T. Takahashi, H. Matsufuru, Y. Nemoto and H. Suganuma, Phys. Rev. Lett. 86, 18 (2001); ibid., Proc. of “Int. Symp. on Hadron and Nuclei” (February 2001, Seoul, Korea), published by Institute of Physics and Applied Phyics (2001), ed. Dr. T.K. Choi, p. 341; ibid., T. Umeda, Nucl. Phys. Proc. S. 94, 554 (2001). 4. Yu. A. Simonov, these proceedings; D.S. Kuzmenko and Yu. A. Simonov, hep-ph f 0202277. 5. S. Capstick and N. Isgur, Phys. Rev. D 34, 2809 (1986). 6. C. Alexandrou, Ph. de Forcrand and A. Tsapalis, Phys. Rev. D 65, 054503 (2002). 7. C.E. Carlson and N.C. Mukhopadhyay, Phys. Rev. Lett. 67,3745 (1991). 8. C.-K. Chow, D. Pirjol and T.-M. Yan, Phys. Rev. D 59, 056002 (1999). 9. T . Barnes, Ph. D. thesis, California Institute of Technology, 1977; T. Barnes and F.E. Close, Phys. Lett. B 123, 89 (1983). 10. E. Golowich, E. Haqq and G. Karl, Phys. Rev. D 28, 160 (1983). 11. C.E. Carlson, Proc. of the 7th Int. Conf. on the Structure of Baryons (October 1995, Santa Fe, NM), p. 461, eds. B. F. Gibson et al. (World Scientific, Singapore, 1996). 12. C.E. Carlson and T.H. Hansson, Phys. Lett. B 128, 95 (1983). 13. I. Duck and E. Umland, Phys. Lett. B 128, 221 (1983). 14. P.R. Page, Proc. of “The Physics of Excited Nucleonsn (NSTAR2000) (February 2000, Newport News, VA). 15. J. Merlin and J. Paton, J. Phys. G 11,439 (1985). 16. K.J. Juge, J. Kuti and C.J. Morningstar, Nucl. Phys. Proc. S. 63, 543 (1998). 17. E.S. Swanson and A.P. Szczepaniak, Phys. Rev. D 59, 014035 (1999). 18. T.J. Allen, M.G. Olsson and S. Veseli, Phys. Lett. B 434, 110 (1998). 19. S. Capstick and P.R. Page, Phys. Rev. D 60, 111501 (1999). 20. L.S. Kisslinger et al., Phys. Rev. D 51,5986 (1995); Nucl. Phys. A 629, 30c (1998); A.P. Martynenko, Sou. J. Nucl. Phys. 54, 488 (1991).
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21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.
S.M. Gerasyuta and V.I. Kochkin, hep-ph/0203104. T.D. Cohen and L.Ya. Glozman, Phys. Rev. D 65, 016006 (2002). E. Klempt, these proceedings. A.M. Zaitsev (VES Collab.), Proc. of ICHEP’96 (Warsaw, 1996). D.E. Groom et al. (Particle Data Group), Eur. Phys. J. C 15,1 (2000). H. Li (BES Collab.), Nucl. Phys. A 675,189c (2000); B.-S. Zou et al., hep-ph/9909204. L.S. Kisslinger and Z.-P. Li, Phys. Lett. B 445, 271 (1999). N. Isgur, Phys. Rev. D 60, 114016 (1999). Z.-P. Li et al., Phys. Rev. D 44, 2841 (1991); 46, 70 (1992). T. Barnes and F.E. Close, Phys. Lett. B 128,277 (1983). 0. Kittel and G.F. Farrar, hep-ph/0010186. P.R. Page, Proc. of <STdInt. Conf. on Quark Confinement and Hadron Spectrum” (Confinement 111), (June 1998, Newport News, VA). K.J. Juge, J. Kuti and C.J. Morningstar, Nucl. Phys. Proc. S. 63,326 (1998).
255
Gerry Miller, David Emst, Hall Crannell, and Mike Finn
Ed Brash and Garth Huber
Nucleon Electromagnetic Form Factors
E.J. Brash Department of Physics, University of Regina, 3737 Wascana Parkway, Regina, SK SdS OA2, Canada E-mail: brash @uregina.ca
The electromagnetic form factors of the proton and neutron contain all the information about the charge and current distribution of these baryons, and thus provide strong constraints on the fundamental theory of strong interactions. Indeed, over the last several years, there have been a number of high profile experiments which aim to measure the nucleon form factors at increasingly large momentum transfers, which corresponds t o probing the nucleon at very small distance scales. At the same time, there has been a monumental effort on the theoretical front t o develop a coherent picture which would account for the observed behaviours. In this paper, I will present the current state of experimental knowledge of the nucleon form factors, as well as discuss the theoretical and phenomenological efforts in this area. .
1
Introduction
It has long been known that the proton and neutron are not point-like particles. The fact that the static magnetic moments of the nucleons differ significantly from the predictions of Dirac for spin-; fermions was the first and perhaps the strongest evidence which pointed t o a finite spatial size of the nucleon; this result was discovered almost 70 years ago. Moreover, finite spatial size is strongly coupled to substructure, which, for the nucleons, is embodied in the QCD description of the quark and gluon degrees of freedom within the nucleon. Within such a description, the moving charged quarks give rise to charge and magnetization current densities, which are characterized by the electromagnetic form factors of the nucleon. Thus, the elastic electromagnetic form factors are crucial to our understanding of the nucleon’s internal structure. From an experimental standpoint, the differential cross section for elastic eN + eN scattering is described completely in terms of the Dirac and Pauli form factors, Fl and F2, respectively, based solely on fundamental symmetry arguments. Further, the Sachs form factors, G E and ~ G M ~which , are simply derived from FI and Fz, reflect the distributions of charge and magnetization current within the nucleon.
256
257
2
2. I
Electromagnetic Form Factors of the Proton Rosenbluth Separation Experiments
Until recently, the form factors of the proton have been determined experimentally using the Rosenbluth separation method 3 , in which one measures elastic ep cross sections at constant Q2, and varies both the beam energy and scattering angle to separate the electric and magnetic contributions. In terms of the Sachs form factors, the differential cross section for elastic e p scattering has traditionally been written as
where r = Q2/4M; and 8, is the in-plane electron scattering angle. For elastic e p scattering, the so-called nonstructure cross section, uns is given by
where aemis the electromagnetic coupling constant, and E’(E) is the energy of the scattered (incident) electron. From the measured differential cross section, one typically derives a ‘keduced cross section”, defined according to
+
where t: = (1 2(1 + r )tan2(6,/2>}-’ is a measure of the virtual photon polarization. Equation 3 is known as the Rosenbluth formula, and shows that fits to reduced cross section measurements made at constant Q2 but varying E values may be used to extract both form factors independently. With increasing Q” the reduced cross sections are increasingly dominated by the magnetic term Gil.lp;at Q2 = 3 GeV’, the electric term contributes only a few percent of the cross section. Experimentally, this makes the extraction of the electric form factor exceedingly difficult at large momentum transfers. for the electric and magnetic In Fig. 1, we show the world data form factors of the proton extracted from e p elastic scattering cross section measurements, prior to 1998. Several features are noteworthy. In general, over the momentum transfers probed in these experiments, it was found empirically that the form factors followed an approximate dipole form, consistent with an exponential charge distribution, viz. 4~5767778~9710
258
For the magnetic form factor, the agreement with the dipole form is apparent up to Q2 x 5 GeV2. Above Q2 x 15 GeV2, the deviations from the dipole form are much larger. In the case of the electric form factor, the difficulty of the experiments at large momentum transfers is evident. For Q2 > 1 GeV’, not only are the error bars large, but the data from different experiments are not consistent with one another. It is clear that a tremendous effort has gone into the analysis of these difficult experiments, however, one is forced to speculate that some of the experiments have underestimated the systematic errors. For example, the Rosenbluth experiments apply radiative corrections to their data at leading order, i.e. one hard photon emitted, which can vary significantly with 6 depending on the specific experiment. However, higher order radiative corrections, i.e. involving more than one photon, could in fact change the slope of the reduced cross section versus 6 plot, and thus have an impact on the extracted form factors. 1.4
1.4
1.o
1.o
<
$
0.5
0.5
0
8
0
1 Q2
2 3 4 (GeV’)
5
0
1 Q2
2 3 4 (GeV’)
5
Figure 1: Published world data (prior to 1998) for G E p / G D and G M p / p G D . The error bars shown are the result of combining systematic and statistical errors in quadrature.
2.2 Recoil Polarization Measurements Due to the fundamental nature of the quantities at hand, a more robust method for measuring the proton electromagnetic form factors is certainly desirable. Over the last few years, focal plane polarimeters have been installed in hadron
259
spectrometers in experimental facilities at Bates, Mainz, and Jefferson Lab. Specifically, one makes use of the polarization transfer method l1>l2, in which one measures, using a focal plane polarimeter, the transverse (P t ) and longitudinal (Pe)components of the recoil proton polarization in 'H(e', e'fi scattering, using a longitudinally polarized electron beam. The proton form factor ratio is given simply by
Here, E, (Eet)is the incident (scattered) electron energy. The polarization transfer method offersa number of advantages over the traditional Rosenbluth separation technique. Using the ratio of the two simultaneously measured polarization components greatly reduces systematic uncertainties. For example, a detailed knowledge of the spectrometer acceptances, something which plagues the cross section measurements, is in general not needed. Moreover, it is not necessary to know either the beam polarization or the polarimeter analyzing power, since both of these quantities cancel in measuring the ratio of the form factors. The dominant systematic uncertainty is the knowledge of spin transport, although in comparison to the size of the systematic uncertainties in cross section measurements, this too is small. Finally, the most recent theoretical calculations verify the assertion that the form factor ratio is unaffected by radiative processes at the momentum transfers involved here.
2.3 Eaperimental Measurements The first experimental measurement of the proton electromagnetic form factor ratio, r , using the recoil polarization technique, was carried out by Milbrath et al. at MIT-Bates 13; they measured the ratio at Q2 = 0.38and0.5 GeV2. Subsequently, at Mainz, Dieterich et al. l4 carried out a similar lower momentum transfer measurement, at Q2 = 0.4 GeV2. The results of these experiments were consistent with the results of previous Rosenbluth separation experiments, and in particular the MIT-Bates experiment gave the community confidence in the recoil polarization technique. Through the use of a focal plane polarimeter (FPP) installed in one of the two high resolution spectrometers (HRS) in Hall A at Jefferson Lab, the JLab FPP collaboration has carried out a series of measurements since 1998, which span the momentum transfer range 0.5 < Q2 < 5.6 GeV2'y2>l5. This collective set of measurements represent the results of two dedicated experiments, E93027 and E99007, as well as results from other experiments, most notably a series of photoproduction experiments, which use the e p elastic scattering reaction as a background subtraction technique.
260
To extract the proton form factor ratio from the ratio of transferred polarization components in ep elastic scattering, one begins by measuring the ratio of normal to transverse polarization components at the focal plane of the proton HRS. The polarization components are related to the azimuthal (4) distribution of the scattered events according to f*=l++:sincp+c;coscp,
(6)
where the f refers to the two helicity states of the longitudinally polarized electron beam and
Thus by taking the difference between the two helicity states, the difference spectrum becomes fdiff = diff - , / i f f coscp. +z (8) The tremendous advantage of working with the difference spectrum is that instrumental asymmetries in the polarimeter, which are dominantly uncorrelated with electron beam helicity, will cancel in taking the difference between helicity states. Moreover, in evaluating the ratio of polarization components, one sees that it is not necessary to have any knowledge of the precise values of the electron beam polarization, P,, and the analyzing power of the second scatterer, Ay(6). Following the extraction of the polarization components at the focal plane, one determines the corresponding components at the target scattering vertex using the well-determined spin precession matrix of the electromagnetic elements of the HRS (quadrupole and dipole magnets). The form factor ratio is then determined directly from Eq. 5 above. In Fig. 2a, we show as filled symbols the data from the polarization transfer measurements for the ratio, r = p p G ~ , / G ~together ,, with data from Rosenbluth separation measurements. The polarization transfer measurements have revealed the somewhat surprising result that the form factor ratio decreases with increasing Q2.As well, the JLab results are in considerable disagreement with the Rosenbluth separation results at large momentum transfers. 2.4
Discussion of Proton Form Factor Results
The first issue that will be addressed is the notable discrepancy between the JLab data and the Rosenbluth separation results, in particular the data of Andivahis et al., who measured the form factor ratio at large momentum transfers at SLAC. According to Eq. 1, the electric part of the e p cross section decreases
26 1 1.5
__
.. ,
.
,
..
1 .o
I" a
B 2
0.5
0.0
3)
1 0' (GeV')
10
1 0' (&$)
10
Figure 2: (a) Published world d a t a for r = p p G ~ p / G ~ open p ; symbols indicate Rosenbluth separations while filled symbols indicate polarization transfer measurements In the case of the Rosenbluth data, the error bars shown are the result of combining systematic and statistical errors in quadrature. For the polarization transfer measurements, the error bars shown are statistical only; the systematic uncertainties are in general a small fraction of the statistical error in these experiments. The dot dash line is the parameterization from ref. l 6 t o the cross section data, which indicates r M 1. (b) Fit to polarization transfer measurements from Jefferson Lab 18. Included are the most recent data a t large QZ from E99007'. Also shown are calculated ratios from recent published fits to the electromagnetic form factors by Lomon l7 within the Gari-Kriimpelmann framework. 495,6,7,8,9
1,2,13714715.
with increasing Q 2 . Based on the new JLab data, which are of high quality both from a statistical and a systematic viewpoint, we have calculated the contribution of the electric part to the total ep cross section, and show the results in Fig. 3. One sees that in fact the electric part accounts for only about 5% of the total ep cross section at Q2 = 3 GeV2, and is a mere 1%at Q2 = 5 GeV2. Given the difficulty in controlling systematic uncertainties in the Rosenbluth separation experiments, where absolute cross sections must be measured to better than 5%, it is not surprising that the ratio results from the Rosenbluth separation experiments begin to diverge, both from one another and from the JLab data, a t about Q2 = 3 GeV2, precisely where the electric contribution to the total cross section becomes comparable in size to the systematic uncertainties of the experiment. The JLab results for the form factor ratio have motivated a tremendous number of theoretical calculations. In Fig. 4a, we show a sample of such
262
0
2
4
6
8
Q‘ [GeVi
Figure 3: Contribution of the electric term to the total e - p elastic scattering cross section.
c a l c ~ l a t i o n s ” compared ~ ~ ~ ~ ~ to ~ ~the ~ ~JLab ~ ~ data. ~ ~ ~ The ~ , feature of the new breed of calculations that appears most important at this point is the inclusion of relativistic effects. In addition, although the various theoretical treatments, e.g. the solition model, di-quark model, constituent quark model, etc., view the problem of nucleon stucture from apparently different viewpoints, an important commonality is that the dominant interaction is non-perturbative, or “soft”, at these momentum transfers. All indications are that at the momentum transfers involved in the JLab experiments, we are, perhaps not suprisingly, still far away from the perturbative region. This is most notably demonstrated in Figure 4b, where we show the ratio F2,/FlP, which can be extracted directly from the experimentally determined ratio G E ~ / G M ,scaled , by a factor of Q2. Theoretical analyses of the hard-scattering process, which must dominate at very large Q2, show that this scaled ratio should reach a constant value. The new JLab data clearly demonstrate that this is not yet the case. In Figure 4c, we again show F2,/FlP, now scaled by a single factor of Q. It is an experimental fact that this ratio reaches an approximately constant value at Q2 2 GeV2,and remains constant up to the maximum momentum transfer that has been measured. Ralston et al? have argued that this behaviour corresponds to the pQCD expectation if one takes into account contributions to the proton quark wavefunction from states with non-zero orbital angular momentum. In a different approach which again points to the importance of N
263 2.0
1.5
1.5
9
p 1.0
& 5?
5
1.0
0-
9 0.5
0.5 0
J h b 99-027
s slab
*-am
JLab 03-02?
a llrb
89-007
0.0
0.0 0.0
20
4.0
6.0
8.0
Q2 in GeV2
10.0
Q2 in GeV2
Q2 in GeV2
Figure 4: (a)Jefferson Lab data for r = ~ A ~ G E ~ / Gcompared , U ~ , to various theoretical models. (b) Jefferson Lab data for Q 2 F z p / F ~ p(c) . Jefferson Lab data for Q F z p / F l p
relativistic spin-dependent effects, Miller and Fra@ have calculated Fzp/F1, within the context of a relativistic constituent quark model. They show that the requirement of Poincark invariance of the proton wave function leads to a violation of the helicity conservation rule, because the non-perturbative wavefunction is a mixture of different helicity states. Their treatment results in a scaling of QFzp/Flp,in good agreement with the new JLab data.
3
Electromagnetic Form Factors of the Neutron
A detailed understanding of the electromagnetic structure of the neutron is equally important as for the proton. Indeed, most modern theoretical efforts seek a consistent description of all four of the elastic nucleon form factors simultaneously. As well, the neutron form factors represent essential ingredients for both measurements and calculations of a host of other fundamental physical observables. Perhaps most notable among these are the nuclear electromagnetic form factors. Interestingly, at a momentum transfer of 5 GeV', GE,, and G E should ~ be approximately equal to one another, based on currently available data and predictions, and thus in principle, one would desire to know the neutron electric form factor to a comparable level of accuracy to that of the proton in order to have an accurate description of deuteron form factors at these momentum transfers. In addition, knowledge of the neutron electromagnetic form factors is currently the largest and limiting systematic uncertainty for experiments which seek to extract the strange electric and magnetic form factors of the nucleon in parity-violating electron scattering.
264
Unfortunately, our knowledge of the electromagnetic form factors of the neutron is much poorer than for the proton. This is, of course, a direct result of two undeniable facts - the charge of the neutron is zero, and there are no free neutron targets. From an experimental standpoint then, neutron form factor measurements are fundamentally extremely challenging. However, one can also take the viewpoint that since the electric form factor of the neutron is approximately zero at all momentum transfers, deviations from zero represent a sensitive measure of more complicated dynamical effects. At very low Q2, the slope of G E ~ ( Qis~well ) known from the scattering of thermal neutrons from atomic electrons. At higher momentum transfers, measurements had proceeded always in the past from inclusive unpolarized e -2 H scattering. Of course, performing the Rosenbluth separation for these experiments is difficult, just as in the case of the proton form factor measurements, due to the now familiar magnetic/electric imbalance. In addition, the proton subtraction which is necessary when one uses a deuteron target adds another level of difficulty, due to both experimental systematic uncertainties which arise, as well as the required detailed theoretical knowledge of the target wavefunction. Over the last several years, a host of experiments have been carried out at Bates, NIKHEF, Mainz, and JLab which have measured the neutron electric and magnetic form factors at ever increasing momentum transfers. In an attempt to address some of the systematic problems that plagued the previous Rosenbluth separation measurements, in many cases these experiments have carried out double-polarization measurements, where one makes use of a polarized electron beam, together with either the use of a polarized target or the measurement of the scattered neutron polarization. With the technology available today, these two methods have comparable figures of merit. Moreover, the systematic uncertainties involved are different, and thus a crosscomparison of the results is very informative. In Fig. 5, we show a compilation of the most recently available world data for the neutron electric form factor It is important to note that at this time, the final results for the two JLab experiments are not available, and thus the central values of the data points have been placed on the Galster parametrization 27 curve. In both cases, the error bars shown are those obtained from the experiment spokespersons. In addition, both of these groups have reported at this conference that their prelimary analyses indeed fall within one standard deviation of the Galster curve. 28729*30~31932~33734735.
265 0.12
0.1
0.08
5 CY
0.06
0.04
0.02
0
I 0.5
0'
(dd)
1.5
2
Figure 5: World data for the neutron electric form factor, GE,,.The dashed curve is the Galster parametrization 2 7 . The solid curve is the most recent phenomenological GariKrumpelmann type fit by Lomon 17.
4
Summary
The last several years have seen remarkable progress in our experimental knowledge of the electromagnetic form factors of the nucleon. At the same time, major advances have been made on the theoretical front, and now it appears that we have a much better understanding of the relevant degrees of freedom at the momentum transfers currently attainable. Recent calculations have shown that the inclusion of relativistic effects are crucial in understanding the proton form factor ratio data, but still suggest that the constituent quarks, as opposed to the current quarks of perturbative QCD, are the relevant objects in this energy regime. In Fig. 6 , we show the currently available world data for all four elastic nucleon form factors. In particular, we draw attention to the blue and red curves in each panel. These curves are the Gari-Krumpelmann model fits of Lomonl7, prior to and after inclusion of the JLab proton form factor ratio and neutron electric form factor data, respectively. Clearly, while such phenomenological model fits are useful, especially when trying to develop a self-consistent understanding of all four form factors, their predictive power is somewhat limited, as the model parameters depend strongly on the data sample used. The tremendous flurry of recent theoretical activity in this area, together with the limited predictive ability of phenomenogical models noted above, strongly underscores the need for the next generation of experiments which
266
Q2 [ GeV2 1
Q2 [
GeV2 I
Figure 6: World data for the elastic nucleon electromagnetic form factors. In all panels, the blue and red curves are recent phenomenological Gari-Kriimpelmann type fits by Lomon,'l as discussed in the text. The green curves in the proton form factor plots are the recent empirical parametrizations of Brash et al. l a . The dashed magenta curve shown in the proton magnetic form factor plot is the parametrization of Bosted 16, and the dashed curve shown in the neutron electric form factor panel is the Galster parametrizationz7.
seek to extend the current measurements to higher momentum transfers. Indeed, the next five years will see new experiments carried out at JLab which will measure the proton form factor ratio to a Q2 of 9 GeV2,and the neutron form factor to a momentum transfer of 3.2 GeV2,nearly doubling the current range in both cases. In addition, the planned energy upgrade of the CEBAF accelerator to 12 GeV will allow to measure these fundamental quantities to even higher momentum transfers, thus providing crucial constraints on the most advanced theoretical efforts. Acknowledgments
I wish to thank C.F. Perdrisat, V. Punjabi, M.K. Jones, and 0. Gayou for their assistance in the preparation of the transparencies used in the presentation and material used in this manuscript. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). References
1. M.K. Jones et al., Phys. Rev. Lett. 84, 1398 (2000)
267
2. 0 Gayou et al., Phys. Rev. Lett. 88, 092301 (2002). 3. M.N. Rosenbluth, Phys. Rev. 79, 615 (1950). 4. L. Andivahis e t al., Phys. Rev. D 50, 5491 (1994). 5. W. Bartel et al., Nucl. Phys. B 58, 429 (1973). 6. Ch. Berger et al., Phys. Lett. B 35, 87 (1971). 7. J . Litt et al., Phys. Lett. B 31, 40 (1970). 8. L.E. Price et al., Phys. Rev. D 4, 45 (1971). 9. R.C. Walker et al., Phys. Rev. D 49, 5671 (1994). 10. T. Jannsens et al., Phys. Rev. 142, 922 (1966). 11. A.I. Akhiezer and M.P. Rekalo, Sov. J. Part. Nucl. 3, 277 (1974). 12. R.G. Arnold, C.E. Carlson, and F. Gross, Phys. Rev. C 23, 363 (1981). 13. B. Milbrath et al., Phys. Rev. Lett. 80, 452 (1998), Phys. Rev. Lett. 82, 2221(E) (1999). 14. S. Dieterich et al., Phys. Lett. B 500, 102 (2001). 15. 0. Gayou et al., Phys. Rev. C 64, 038202 (2001). 16. P.E. Bosted, Phys. Rev. C 51, 409 (1995). 17. Earle L. Lomon, Phys. Rev. C 64, 035204 (2001). 18. E.J. Brash et al., Phys. Rev. C 65, 051001R (2002). 19. A.F. Sill et al., Phys. Rev. D 48, 29 (1993). 20. M. De Sanctis et al. Phys. Rev. C 62, 025208 (2000). 21. D.H. Lu et al., Phys. Rev. C 57, 2628 (1998). 22. R.F. Wagenbrunn e t al., Phys. Lett. B 511, 33 (2001). 23. G. Holzwarth, 2. Phys. A 356, 339 (1996). 24. F. Cardarelli, S. Simula, Phys. Rev. C 62, 065201 (2000). 25. J . Ralston et al., in Intersections between Particle and Nuclear Physics, AIP C o d . Proc. No. 549 (AIP, Melville, NY, 2000), p. 302; (private communication). 26. G. Miller and M. Frank, Los Alamos Preprint, nucl-th/0201021. 27. S. Galster et al. Nucl. Phys. B 32, 221 (1971). 28. T. Eden et al. Phys. Rev. C 50, R1749 (1994). 29. M. Ostrick et al., Phys. Rev. Lett. 83, 276 (2001); C. Herberg et al., Eur. Phys. J . A 5, 131 (1999). 30. J . Becker et al., submitted to European Physics Journal. 31. D. Rohe et al., Phys. Rev. Lett. 83, 4257 (1999). 32. I. Passchier et al., Phys. Rev. Lett. 82, 4988 (1999). 33. D. Day and I. Sick, spokespersons, JLab Experiment E93-026. 34. R. Madey and S. Kowalski, spokespersons, JLab Experiment E93-038. 35. R. Schiavilla and I. Sick, Phys. Rev. C 64, 041002 (2001).
VIRTUAL COMPTON SCATTERING H. FONVIEILLE for the Jefferson Lab Hall A and VCS Collaborations Labomtoire de Physique Corpusculaire IN2P3-CNRS Universite' Blaise Pascal Clermont-II, F63177 Aubibre Cedex, Fmnce E-mail:
[email protected] Virtual Compton Scattering off the proton: y * p 4 'yp is a new field of investigation of nucleon structure. Several dedicated experiments have becn performed at low c.m. energy and various momentum transfers: yielding specific information on the proton. This talk reviews the concept of nucleon Generalized Polarizabilities and the present experimental status.
Virt,ual Compbon Scat,t,ering (VCS) off t.he prot,on: y * p ~p has emerged within t.he last. t.en years as a powerful tool t.0 sbudy the int,ernal structure of the nucleon, bringing forward exciting new concepts and observables. The field can be subdivided according to different c.m. energy domains. At. high energy (s >> At&) and large momenbum t.ransfer (Q2 >> A{&), QCD factorizat,ion allows t.he use of t,he VCS process t.0 access: i) t.he nucleon Generalized Part,on Distributions (GPDs) via Deep VCS at, small t ; ii) the nucleon Distribution Amplitudes via hard Compton scatt,ering at large t '. At. low energy, t,he VCS process gives access t,o the nucleon Generalized Polarizabilities or GPs, which are t.he main focus of this t,alk. The basic concepts are introduced and an experimental review is given of the experimenbs performed in t,he t,hreshold regime (& 5 ( M N AtT)) and resonance region. --f
+
1
Concept of Generalized Polarizabilities
These are t,he generalizat,ion to a non-zero Q2 of the polarizabilities int,roduced in Real Compton Scatt,ering (RCS). Let, us recall t.hat.polarizabilit,ies measure how much t.he internal st,ructure of a composit,e particle is deformed when an external EM field is applied. The description of the RCS process at low energy involves six polarizabilities ( a ,p, and ~ i , i= 1 , 2 , 3 , 4 ) which parametrize the unknown part of nucleon structure, due t.0 its internal EM deformation (see ref.3 and references therein). Performed since the sixties, RCS experiments have measured the prot,on electric and magnetic polarizabilities ( Y E and 3, the results of which can be summarized as: i) t.he proton is a rather rigid object (polarizabilities are
268
269
ep-, amplitude
-
+ P _ _ _ _ _ _ _ __.__ _. _ .I L .________________.,_..___.__________ I -l“-Il
..,’
Compton Born
~
Compton Non-Born
Berhe-Heirler
Figure 1. Decomposition of the photon electroproduction amplitude into: Born (s and u channels), Non-Born, and BH contributions.
y p center-of-mass
:
Figure 2. VCS kinematic variables.
small), ii) p~ is smaller than a ~due , to a cancellation between its paramagnetic and diamagnetic contributions. These observables can be generalized t.0 any Q 2 ,such t,hat in VCS a t low energy one probes the nucleon polarizability locally inside the particle, with a distance scale given by Q 2 . Equivalently, VCS can be seen as elast.icscattering on a nucleon placed in an applied EM field, and hence the GPs can be seen as a measurement of “distorted” form factors. In all cases these observables are intrinsic characteristics of the particle, and provide a valuable and original test of models describing nucleon structure. 1.1
Photon electroproduction amplitude
VCS is accessed by photon electroproduction ep 4 em , which is the coherent sum of the Compton process and the BetheHeitler (BH) process, or electron bremsstrahlung; see Fig. 1. The main kinematic variables are defined in Fig. 2: the initial and final photon threemomenta q and q’ and the final photon angles , 8 and #, in the (yp) center of mass. The (ep + em)kinemat,ics is fully defined by these four variables plus the virt,ual photon polarisation c. The low-energy behavior of the amplitude Tee?has first been worked out
270 Tablc 1. The six lowest order Generalized Polarizabilities (also called dipole GPs. due to 1‘ = 1). find y
initial y*
h.I 1
hiI 1 M2
M1
S proton spin-flip 0 1 0 1 1 1
by P. Guichon et a1 ‘. Only a brief summary is given here, and more det.ails can be found in ref.5. The Compton amplitude decomposes int,o a Born t,erm, characterized by a prot,on in the intermediate st,at.e, and a Non-Born term cont,aining all ot,her int,ermediat,est,at,es. The BH and Born amplitudes are ent,irely calculable, wit,h prot,on EM form factors as input,s. The Non-Born amplitude T N Bcont,ains t,he unknown part of bhe nucleon st,ructure. Below pion threshold a Low Energy Theorem (LET) allows to expand TNBin powers of q’ ; t,he first, t,erm of t.he expansion is a known analytical funct,ion of six independent GPs, which are the goal of t.he measurements. These GPs are derived from a multipole expansion of T N B .One defines mut,ipole amplitudes HFi”’)’ according to t,he t,wo involved EM transit,ions: p ( p ’ ) st,ands for inibial (final) photon polarization st.ates (0,1,2 = longitudinal, magnetic, electric), 1 (1’) is t.he t,ot’alangular momentum of the init,ial (final) transibion, and S = (0), 1 stands for proton (non)spin-flip. The H N B mukipoles depend on photon momenta q and q’ . The GPs are defined (up t,o dimensional factors) as t,he limit of H N B when q’ + 0 , i.e. in the limit of a st,at,icEM field; they are denoted P(P’”P’)’ and depend only on q. Table 1 summarizes the notations for the two scalar ( S = 0) and the four spin GPs ( S = l),and also shows their continuity to the real photon point, (Q2= 0). Below pion threshold, the VCS amplit,ude is purely real; above pion threshold it becomes complex, and resonances can be produced on-shell. One may say that the GPs are conceptually linked t,o the contribution of virtual resonant int,ermediat,est,at,es,ext’rapolat,eddown to q’ = 0 . 1.2 Photon electroproduction cross section The photon electroproduction cross section is evaluated from the relat.ion: ITeey12= I T B H + B , ,-t ~ ~ ~R~~ ( T B H x+ TBN~B~) ~ I T N B.~Below ~ pion
+
27 1
threshold, I T N B (can ~ be neglected and thus the GPs are extracted via the interference term (BH+Born)(NB).The LET leads to the following expression for the unpolarized cross section: a d U ( e m ) = duBH+Born
(P.S.) x
[
+
211( P L L ( q )
-
where (P.S.) is a phase space factor and t1,t2, are known kinematic coefficients ’. The t,wo st,ruct,ure functions (PLL- ~ P T T and ) PLT are linear combinations of t,he GPs, given e.g. by t,he following choice: PLL(q) = - 2 d
hfjV
G E ( & ~P(O1’O1)O ) (4)
$
PTT(q) = -3 G M ( Q ~ ) X PLT(q) =
fi
Q
[
P(ll”l)l(q) -
G E ( Q 2 )P ( l l > l l ) O ( q+ )
Jz&
32
P(01”2)1(q)]
& GM(Q2)P ( o l , o l ) l(4) . 40
’.
no.
where Q2, 0 are specific kinematic variables So in an unpolarized experiment performed at fixed q and E , one measures two structure functions: (PLL- ~ P T , ) sensitive to the electric GP a ( Q 2 ) P(O1,ol)O , and PLT sensitive to the magnetic GP p(Q2) P(llill)O . N
N
1.3 Methods to extract GPs Two methods are presently used to extract GPs from absolute (em)cross sections. Method 1 is based on the LET, and only works below pion threshold. In bins of photon angles (Ocm,q5), one forms the quantity (dneZpduBH+BoTn)/(P.S.) measured at finite q f , and extrapolates it to q‘ = 0 to obtain the term in brackets in eq. 1. Present experimental data suggest that, at least in most of the phase space, the extrapolation can be done assuming that the 0 ( q f 2 ) contribution in eq. 1 is negligible. The bracketed term is then easily fitted as a linear combination of the two structure functions (PLL- ~ P T T and ) PLT a t fixed q and E. Method 2 is based on the formalism of Dispersion Relations (DR) and works below pion threshold as well as in the first resonance region. In this model the imaginary part of the VCS amplitude is given by the sum of T N intermediate states, computed from y * N ---t T N data (MAID model), plus adcr is a short notation for the fivefold differential cross section d 5 0 / d a y dk’lab dQcm P’ ’ bThe important notion is that Q2is equivalent to q.
272 Table 2 . VCS experiments.
I
II
experiment
JLab E93-050 Batcs E97-03 Batcs E97-05
Q2
(GeV2) 0.33 1.0:1.9 0.05 0.12
cncrgy fi < ( A ~ N All,) < 1.9 GeV
p cone
taking 1995+97
+
6'. ' 3 2000
status (a end 2001) published final stage analysis analysis
higher order cont,ribut,ionswhich are not const,rained by the model. The lat,t,er have t,o be fit.t,edt.o t.he VCS dat,a, under t.he form of t,wo free paramet,ers A, and Ap describing t,he Q2-dependence of t.he scalar GPs a and ,b. The knowledge of t,he paramet,ers at. a given value of Q2 t,hen yields t,he model predict,ion for t.he st,ruct,urefunctions PLL , PTT and PLT at. t.his moment,um t.ransfer.
1.4
GP effect on cross sections
Figure 3-left. shows the various component,s of t.he phot,on electroproduction cross sect,ion, in and out, of t,he leptonic plane, for select,ed kinemat.ics. The Bet.heHeit,ler peak is dominant. around t,he incident, and scat.tered electron direcCions; as one goes out-of-plane it fades away, giving a smoot,her cross sect.ion behavior. Figure %right shows t,he expected effect,of GPs on the cross section, as given by t.wo different calculat,ions: the lowest. order (or bracket,ed) t,erm of eq. 1, and t,he full DR prediction. Out-of-plane, the GP effect is roughly const,ant,,of t,he order of -10 %. In-plane the GP effect has a more complicat.ed pat,t,ern, due to the BH interference.
2
Experiments
Table 2 summarizes t.he VCS experiments performed so far. All of them have detected the scattered electron and out,going proton in high-resolution magnetic spectromet,ers, selecting the exclusive phot,on channel by the missingmass bechnique. Also, being unpolarized experiments, they all measure t,he same two struct.ure functions, at different,values of q. An accurate determination of the absolute fivefold cross secbions is necessary, due to t.he relat,ively small polarizability effect.
273 ....................................................... .. ~ 8 0 ; p . C 4 ~ .....~ ................. d ........... ~
~
0 .c
eg.
0.5 0.4
-1
QQPh.45.degi.. ............
............
0.3
........... ~ . . ............,. ...........................
0.2
......
...............
. . . . . . . . . . . . :. . . . . . .
0.1 0 -0.1
1 0-
-0.2 -0.3 in-plane angle (deg)
in-plane angle (deg)
-
.- 0.5 0
2 0.4 0.3 0.2
-1
0.1 0 -0.1
-2
1 0-
-0.2 -100
0
100
in-plane angle (deg)
-0.3
-100
0
100
in-plane angle (deg)
Figure 3. (ep + epy) cross section components for: q = 1.08 GeV/c, q’ = 105 MeV/c, and E = 0.95 . The abscissa is the azimuthal angle of the outgoing photon when the polar axis is chosen perpendicular to the leptonic plane. “OOP” is the polar angle using this convention. Left plots: BH+Born (solid), BH (dashed), and Born (dotted) contributions. Right plots: the ratio ( d a c p - d a g H + g o r n ) j d a g H + g o r n for two calculations of d a c p : i) a first order GP effect, taking PLL - $PTT = 2.3 GeV-’ and PLT = -0.5 GeV-* (solid), ii) a DR calculation for parameter values A, = 0.92 GeV, A0 = 0.66 GeV (dash-dotted).
2.1
The MAMI experiment
’
The Mainz experiment measured photon electroproduction cross sections in the leptonic plane, at Q2 = 0.33 GeV2. The two structure funct,ions PLL- PTT/E and PLT were determined using the LET method as described in section 1.3, at q = 0.6 GeV/c and 6 = 0.62. Results are plotted in Fig. 4; they show good agreement with the calculation of Heavy Baryon Chiral Perturbation Theory ’. Several models predict an extremum of PLT at low Q 2 ,a feature which will be interesting to confirm experimentally. This turnover can be related to the behavior of the para- and diamagnetic contri-
274
100
PLL--PV/t(GeV')
0
90
c
80
-2
70
v
hP T
-1
60
50
-6
40 30 20
a
h PT i$.r10
10 0 0
0.4
0.2
Q' (GeV')
0
0.2
0.4 Q' (GeV')
Figure 4. VCS unpolarized structure functions measured at M i n z and their value a t the real photon point '. The curves represent two model predictions (CHPT and ELM lo), including (in dark grey) or not including (in light gray) the spin GI's (effect indicated by a n arrow).
but.ions to t.he p polarizability. In CHPT it originabes from the pion cloud, which yields a diamagnetic contribut,ion of posit,ive sign, visible at low Q2. For a review of model predictions see ref.9.
2.2
The BATES experiments
The Bates experiment 97-03 l1 has been performed at Q2 = 0.05 GeV2, i.e. in the region of the expected t,urnover of PLT. Measuremenk have been done in-plane and at 90" out-of-plane, using the OOPS spectrometers. The experiment covers a limited range in polar angle 6,, around 90°1 so t,he st,ruct.ure functions will be extract,ed mostly from the &dependence of t,he cross section. Dat,a analysis is in progress, presently concentrating on Montecarlo studies and absolute normalization. This experiment represents a Lab achievement, having made the first use of the high duty factor beam in the South Hall Ring and of the full OOPS system. The Bates experiment 97-05 l2 has been performed at Q2 = 0.12 GeV2 to study t,he N -+ A transit.ion, and data analysis is also in progress.
2.3 The JLab experiment Experiment E93-050 l3 was performed in Hall A of the Thomas Jefferson National Accelerator Facility (JLab) at Q2 = 1.0 and 1.9 GeV2. Data covers the region below pion threshold, and the resonance region up t.0 fi = 2 GeV at. Q2 = 1.0 GeV2.
275
The sbrong L0rent.z boost, from ~p cent,er-of-masst,o lab focuses the out,going prot,on in a narrow cone (see Table 2) allowing the hadron arm accept'ance t.0 cover t,he full phase space of t,he out,going phot,on in c.m. The key poi& t,o obtain accurat,e cross sections are a det,ailed Mont,e-carlo simulat,ion (including radiative correct,ions) and a det,ailed st,udy of cut,s in order to eliminat,e background, mainly due t.0 puncht,hrough prot,ons. Absolut,e nornializat,ion is checked in t,woways: i) by comput,ing t.he ( e p e p ) cross secbion from elast,ic dat,a t,aken during t.he experiment; ii) using t,he VCS dat,a, namely bhe import,ant' property that, bhe (epy) cross sect.ion should t,end t,o t,he known (BH Born) cross sect,ion when t,he final photon moment,um q' bends t,ozero ',Both t,est.sshow t,hat.the absolut,e normalization is correct, wit,hin 1-2 percent,, when using t.he most recent determinat,ion of proton form fact'ors: the JLab measurement, of t,he rat.io p G ~ / G n i and t,he Gbf fit. of ref.15. 0 Analysis below pion threshold: photon elect,roproduction cross sect,ions have been obt,ained at, fixed q = 1.08(1.60) GeV/c and fixed E = 0.95(0.88), corresponding t.0 the dat,a set, a t Q2 = 1.0 (1.9) GeV2. As an example, Fig. 5 shows some of t.he out,-of-plane cross sections measured for bot,h data set,s. These data illust,rat.ehow t,he (small) G P effect, increases with q' and how ibs shape agrees wit.h t,he LET prediction. More debails can be found in ref.17. of eq. 1 does not show any The quant,ity (doezp- duBH+BoVn)/(P.S.) not,iceable 9'-dependence, so it is averaged over q' and then fitted according lo the first method of section 1.3. The fit is performed on (in-plane out,-ofplane) cross sections and gives a reasonably good x2,confirming the validity of the low-energy expansion at these rat,her high Q2. Numerical results are report,ed in Table 3. A second analysis of t,his dat,a below pion threshold is presently underway, based on t.he DR model. A preliminary result at Q2 = 1.9 GeV2 is included in Table 3. 0 Analysis in the resonance region: these are the first VCS measurements ever performed in this kinematic domain. The initial goal was bo st,udy how resonances couple t,o the doubly EM channel, and search for possible missing resonances. Doing an excitation scan in W = 4 from M N to 1.9 GeV, cross sect,ions have been det,ermined at a fixed Q2 = 1.0 GeV2, backward angle Ocm = 167.2' and beam energy 4.032 GeV 16. They are presented in Fig. 6 as a funct,ion of W for various azimut.ha1angles 4. The DR model reproduces well t,he Delta region. Using these data, bhe second method of section 1.3 --f
+
''
+
=indeed, in eq. 1 the bracketed term is of order ( q ' ) O and the phase space factor (P.S.) is of order ( q' ) l .
276 Q2=
1.0GeV2
Q 2 = 1.9 GeV2
q=1080 MeWc &=0.95 €Y=(4@,14@)
q= 1600MeV/c, & = 0.88
t
I
., .
lo
. . . . . . . ........................................................................................................
l
~
-50
i
~
0
I
,
50
l
,
...................... . i I
-250
-200
.
..
.
I
I
.
I
I
. . .
. . .......................... , i
, h ,I
-150
0
50
~
.......
, 100
l
100
Q% fdd
-250
-200
.
.
.
.
.
-150
-100
-50
o
50
100
Figure 5. ( e p --t e m ) cross sections measured at JLab versus in-plane angle, for OOP= 50' (left) and 25' (right). Error bars are statistical only. The angle in abscissa is the same as in Fig. 3. The curves correspond to: BH+Born calculation (solid) and a first order G P effect (dotted).
has been applied for the first time. The free parameters of the DR model are adjusted by a x2 minimization, yielding the values of the two structure functions a t Q2= 1.0 GeV2 and E =0.95. Results are reported in Table 3. 2.4
Results summa?
Table 3 summarizes our present knowledge of the two structure functions measured in unpolarized VCS: the MAMI result, and the preliminary JLab results obtained so far, both below and above pion threshold. One first notices the fast decrease of the observables with Q 2 ,similarly to form factors. Second,
277 n
g
L
u!
-7
0
10
Lo
7
II
i lo-’
-s
0
$10-9 0
Lo
d-
-8
II
‘c10
%
2 S
0
Lo
Y
< b
b
II
lo-8
%
% 1o
0
-~
Lo 0 7
102
II 8
10-’
0
1o - ~
Lo
m 7
1o-8
II
%
1 0-’
0
-
Lo
lo-’
(D
o-8
II
1
8 I
I
I
I
I
W (GeV)
Figure 6. Photon electroproduction cross sections in the resonance region. The curve spanning the whole range in W is the BH+Born calculation. The curve limited to W < 1.25 GeV is the DR prediction for parameter values Aa = 1.0 and Ap = 0.45 GeV.
for the JLab data there is a nice agreement between the results obtained by the two methods, LET and DR. These new measurements should stimulate theoretical calculations of GPs at high Q2. Indeed most model predictions are presently limited to Q2 << 1 GeV2.
278 Table 3. Present results on VCS structure functions. (fo) indicate that syst.ernatic errors arc not fully determined. DR results at Q 2= 1.0 GeV2 arc from rcsonance region analysis.
f 0.22
(stet)
f 0.35
(syst)
f*
1.0
PLT structure function (GeV- )
1133 1600 1600
3
0.62 0.95 0.95 0.88 0.88
LET: - 5.0 LET: - 0.42 DR : - 0.53 LET: +0.009 DR : in [-0.05.+0.02]
*
0.8 ( s t a t ) =t0.11 ( s t a t ) f 0.12 ( s t a t ) f 0.041 ( s t a t )
f 1.8 ( s y s t ) f 0.02 ( s y s t ) f*
-:::;
(syst)
f 0.005 ( s y s t ) f*
Future prospects
Polarizabilities and Generalized Polarizabilities are inhinsic charact,erist,ics of composibe parbicles. As such it. is int,erest,ing to measure t,hem for every hadron, including e.g. the neut.ron, pion, etc, although t,his may seem a task for bhe far future. Undoubtedly, investigat,ions of the VCS process on the prot,on have been fruit,fiil, and will cont,inue to bring exciting new result,s in t,he coming years. Future developments are foreseen in various c.m. energy domains: 0 a t low energy, the mapping of the unpolarized structure funct.ions (PLL:PTT) and PLT versus Q2 can be completed, and PLL and PTT can be disentangled by an c-separat.ion. By studying Zp + e& with a polarized beam and recoil proton polarirnehy, one can in principle disentangle the six independent GPs entering t,he first order t,erm of the LET, giving access t.0 the spin GPs. Such experiments are planned a t Mainz and Bates. 0 In the resonance region, t,he VCS process was investigat'ed for the first hime by the JLab E93-050 experiment. It demonsbrat,ed the feasibility of G P extraction above pion threshold, owing to an enhanced sensitivity of the VCS cross section to GPs in the Delta resonance region. Future experiments along bhese lines at high Q2 are foreseeable, either with or without polarization degrees of freedom. 0 VCS at higher energies is certainly a very active field, with growing interest in Deep VCS and the GPDs. Using a longit,udinally polarized elect.ron beam,
279
t'he HERMES and JLab-CLAS collaborat,ions have det,erinined a Single Spin Asyminet,ry in e'p 4 epy 18, giving t,he first, input, t,o GPD models, and more such experimenh are planned at, JLah, HERMES and COMPASS in t'he near fut,ure. As energies increase, experiment.al resolut,ion 1imit.at'ionsmake it' more and more difficult. t.0 isolat,e t,he one-phot,onelect'roproduct.ion channel, and all present, and fut,ure experimenh plan to detect, all t,hree part,icles in t'he final st'at'e in order t,o reach exclusivit,y. Acknowledgments This work was support,ed by DOE, NSF, by cont,ract DE-AC05-84ER40150 under which t.he Sout,heast,ernUniversit,ies R.esearch Association (SURA) o p erat,es t.he Thomas Jefferson Nat,ional Accelerat,or Faci1it.y for DOE, by t,he French CEA, t.he UBP-C1ermont.-Fd and CNRS-IN2P3 (France), t'he FWOFlanders and t,he BOF-Gent, University (Belgium) and by t,he European Commission ER.B FhIRX-CT96-0008. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
M. Diehl, t,hese Proceedings. M. Vanderhaeghen et al., Nucl. Phys. A622 (1997) 144c. V. Olmos de Leon et al., Eur. Phys. J. A10 (2001) 207. P. Guichon et al., NudPhys. A591 (1995) 606. P. Guichon et al., Prog. Part. Nucl. Phys. 41 (1998) 125. B. Pasquini et al., Eur. Phys. J. A l l (2001) 185, and these Proceedings. J. Roche et al., Phys. Rev. Lett. 85 (2000) 708. T. Hernmert. et al., Phys. Rev. D55 (1997) 2630. See ref. [8], [lo], [6], and also: A. Metz et al., Z. Phys. A356 (1996); G. Liu et al., Aust. J. Phys. 49 (1996); B. Pasquini et al., nucl-t.h/0l05074. hl. Vanderhaeghen, Phys. Lett,. B368 (1996) 13. J. Shaw, R. Miskimen et al., Bates Proposal E97-03 (1997). N. Kaloskamis, C. Papanicolas et al., Bates Proposal E97-05 (1997). P. Bertin et al., JLab proposal E93-050 (1993). 0. Gayou et al., Phys. Rev. Let,t,. 88 (2002) 092301. E. Brash et al., Phys. Rev. C65 (2002) 051001. G. Laveissihre, Thesis DU 1309, UBP Clermont-Fd (2001), and also L. Todor, these Proceedings. L. Van Hoorebeke, these Proceedings. S. Stepanyan et al., Phys. Rev. Lett. 87 (2001) 182002; A. Airapetian et al., Phys. Rev. Lett. 87 (2001) 182001.
GENERALIZED PARTON DISTRIBUTIONS M. DIEHL Institut fiir Theoretische Physik E, RWTH Aachen, 52056 Aachen, Germany I review some basic facts about generalized parton distributions, and then report on selected issues where progress has been made recently: the description and physical interpretation of GPDs, and the theory of processes where they can be measured.
1
Introduction
In this talk I will attempt a status report on studies of generalized parton distributions ( G P D S ) . ~I >will ~ ~first ~ recall their basic properties and connections to other quantities describing hadron structure. Then I shall discuss in more detail two particular aspects which are the subject of most recent investigations in the field: the understanding of how information on hadron structure is encoded in GPDs and how they can be interpreted physically, and the understanding of the reaction mechanisms in the processes that can provide access to GPDs. I will unfortunately not be able to report on progress made on other aspects, in particular on processes at very high energy?v5 on GPDs for nuclear targets,6 and on GPDs involving gluon helicity flip.7 2
Some basics of GPDs
Generalized parton distributions are defined as Fourier transforms of matrix elements between different hadron states, such as
The quark and antiquark operators are separated by a light-like distance An (i.e., n2 = 0). These matrix elements are represented in fig. 1, in the regimes where they either describe the emission and reabsorption of a parton, or the emission of a parton-pair. Different GPDs are introduced to describe the various combinations of parton and hadron spin in the matrix elements, the most common ones are H , E , H , and E.2 They depend on the kinematical variables x and [, which describe longitudinal momentum fractions as shown in fig. 1, and on the invariant momentum transfer t = (p’ - P ) ~ . As in the case of usual parton distributions, the operators appearing in the definition of GPDs need to be renormalized. This induces a dependence on
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28 1
P’
P
Figure 1. A generalized parton distribution in the kinematical region where it represents the emission and reabsorption of a parton (a), and the emission of a parton pair (b). The fractions x and refer to the longitudinal component of the average hadron momentum
+(P +PI).
a factorization scale p2, which in a physical process provides the “borderline” between the hard subprocess explicitly calculated in perturbation theory and the long-distance physics described by the parton distribution. This dependence is perturbatively calculable, and the corresponding evolution kernels are known up to t w d o o p accuracy. From their definition (1) we can readily obtain the most important connections between GPDs and quantities which are familiar in the description of hadron structure: 1. In the limit where the two states Ip(p, s)) and Ip(p’, s f ) ) become equal, one recovers the usual parton densities, which thus provide boundary values of GPDs.
2. Taking moments of these distributions in the momentum fraction x gives the matrix elements of local currents, for instance of the vector current in (1). The moments of GPDs are thus given by elastic form factors. The well-known electromagnetic Dirac and Pauli form factors, FI ( t ) and Fz(t),are respectively obtained as lowest 2-moments of the GPDs H and E.
3. Crossing symmetry relates GPDs with matrix elements of the form
J
dx e i x z ( P + P ’ ) . n @(P, S)P(P‘, S ’ > l 4 ( - W 7 .n+(Xn) 1%
(2)
which describe the hadronization of a parton pair into a pair of hadrons.‘l8 They can be seen as the distribution amplitude for a hadron pair, and are analogs of the distribution amplitude for a single meson, say, a pion.
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Figure 2. Example F'eynman diagrams for DVCS (a) and the production of a meson (b). The large blobs represent GPDs, and the small blob in (b) represents the distribution amplitude of the meson M .
Factorization theorems describe how GPDs appear in the amplitude for exclusive scattering processes in a well-defined kinematical regime.g The foremost example is deeply virtual Compton scattering (DVCS), shown in fig. 2a. It is the process whose theory is most advanced, and the one which is probably the cleanest for extracting information on the unknown distributions. A variation of this process is timelike Compton scattering,1° which I will discuss in section 6 . A large class of other reactions is provided by meson production, fig. 2b. It provides a wealth of different channels (and thus a handle to disentangle GPDs for different quark flavors and for gluons), and contains nonperturbative information on both the target and the produced meson. On the other hand, their complexity makes these processes more difficult to analyze, and there is reason to believe that the values of Q2where the simple factorized description of fig. 2b is adequate, are larger than for DVCS, maybe 10 GeV2 and more. Apart from electroproduction ep + e p M of a meson M , other channels have recently been considered, such as up + p p D, at neutrino beam facilities," and the production of a heavy photon in 7rp + y'p + p+p- p.12
3
A three-dimensional image of hadrons
The fact that GPDs depend on two longitudinal momentum fractions 2 and
(, and in addition on t , which encodes that there can be a nonzero transverse , us immediately that we are in a position momentum transfer (p' - p ) ~tells to probe the transverse and the longitudinal structure of a fast moving proton in a correlated manner. Setting ( and t to zero one recovers the usual parton distributions, which have the intuitive interpretation of a density in longitudinal parton momen-
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tum. BurkardtI3 has shown that for [ = 0 we retain a density interpretation if we perform a Fourier transformation from (p' - p ) to~ impact parameter, which measures the transverse distance of the struck quark from the proton's center. Generalized parton distributions at f = 0 thus describe the transverse distribution of partons with a given longitudinal momentum fraction x. Going to nonzero [ we no longer have this density interpretation. I see this as a blessing rather than a curse: after all QCD is a quantum theory, and it may well be that to understand its bound states we will have to go beyond classical probabilities. In any case, generalized parton distributions probe the transverse and longitudinal structure of the proton in a way that has recently been described in the language of photography.14 The meaning of generalized parton distributions at nonzero [ can be elucidated in terms of light-cone wave f u n ~ t i o n s . ' ~ 'One ' ~ can write the usual parton densities as squared wave functions, summed over all configurations containing a parton with given momentum fraction x. Going t o [ # 0 we get the product of wave functions corresponding to different momentum fractions of the specified parton, as shown in Fig. 1. We thus go from classical probabilities to quantum mechanical correlations, or interference terms. Nonzero f further opens up the kinematical regime where the distributions describe the emission of two partons (Fig. lb). One then probes qq or gluon pairs in the target wave function. The sum rules mentioned in section 2 tell us that the two regimes are intimately connected: both contribute to the integral of the distributions over x at given f and t , which gives the elastic proton form factors. The same sum rules remind us that quantities like the Dirac form factor Fl(t) also contain information about the proton size. From the above discussion it follows that they give the transverse distribution of quarks, now averaged over all longitudinal momenta. This is the opposite reduction of information than the one we encountered in the usual parton densities. Generalized densities combine and interrelate these two partial descriptions. Note also that there are not many pointlike probes providing local currents for a direct measurement of form factors in the nucleon. In particular there is none for gluons to tell us about their transverse location compared to quarks. Such information may be gained in suitable diffractive processes where generalized gluon distributions are enhanced over the quark ones. Unless the transverse momentum transfer (p' - p ) is~ exactly zero, the polarizations of the initial and final proton in a GPD need not be the same, because transfer of orbital angular momentum can ensure angular momentum conservation in the longitudinal direction. This is another example of what we have just seen: by going away from the strictly collinear kinematics of the
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usual parton model quantities we get access to physics in the transverse direction, and a particular aspect of this is the orbital angular momentum along the longitudinal axis. The wave function representation tells us in particular that the generalized parton distribution E (and thus also its first moment, the Pauli form factor Fz(t)) would vanish if the proton only had configurations where the helicities of the partons add up to the helicity of the proton. This reflects the statement of Ji’s sum rule2 which connects E with the orbital angular momentum of quarks in the proton. 4
How might GPDs look like?
The wealth of information contained in GPDs comes with the challenge to handle functions of three kinematical variables 2, <, and t. A good understanding of what this functional dependence may look like is important to formulate realistic models of these functions. It is also needed in order to devise physically motivated parameterizations for them, which will probably be the starting point in trying to extract information from data, just as is the case for the ordinary parton densities. Efforts to model GPDs are proceeding along different lines. Most current parameterizations are based on the concept of double distribution^,'*^ which may be seen as “generating functions” for the GPDs. They incorporate the nontrivial requirements on the x and dependence imposed by Lorentz invariance, and present a convenient way to use the known parton densities as an input to the model. One can however not expect to obtain the physics of the qq or gg region by “extrapolating” information from the usual parton densities, so that such approaches are typically supplemented with terms that only have support in the region depicted in Fig. lb. Examples are the Polyakov-Weiss D-term and contributions describing pion exchange in the t-channel.” Other approaches include models based on the representation of generalized distributions in terms of light-cone wave functions.’* The possible structure of GPDs can also be explored in field theories such as QED15 or twodimensional QCD,lg which are simpler than full QCD. Finally, there have been attempts to calculate GPDs in models or approximations of QCD such as the MIT bag20, constituent quark models2’, or the chiral quark soliton Let us remark that several of these approaches do not support a simple factorizing ansatz of the type f(z,<,t ) = g(z, < ) F ( t )for the GPDs. In the light of our discussion above, this reflects that the correlation between transverse and longitudinal structure in the proton in indeed nontrivial. Recently, another study has considered parton-hadron duality in the connection with G P D s . ~ ~
<
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5
How precisely can one access GPDs?
For a reliable extraction of GPDs from exclusive processes, a quantitative understanding of the reaction mechanisms is necessary. This includes sufficient control over radiative corrections to the hard sub-processes, and of the corrections to the Bjorken limit, which are suppressed by inverse powers of the large scale Q. The evolution equations for GPDs are known to NLO accuracy,24 as are the hard scattering coefficients for Compton ~cattering.~' We will need to gain experience and understanding of when and why such corrections can be numerically important; a recent study for the Compton process has been performed by Freund and McDermott,26 and by Belitsky et ~ 2 . ~ ~ A large amount of work has recently been devoted to the first power corrections to the Bjorken limit in the Compton process, i.e., the terms going like l / Q in the a m p l i t ~ d e . ' ~Their l ~ ~ analysis can be done in close analogy to the spin dependent structure function g2 of inclusive DIS. Notably, the 1/Q contributions can be grouped into two classes. The first involves the handbag diagram of Fig. 2a, taking into account the finite transverse momentum ICT of the quark in the hard scattering, and is related to the twist-two distributions H, E , H , E through Wandzura-Wilczek type relations. The second kind of terms goes with twist-three non-forward proton matrix elements, diagrammatically represented by blobs with three parton legs instead of two. The relative size of these contributions is unknown, so that it remains to be seen whether the 1/Q power corrections can be used as additional handles on the twist-two distributions, or will provide a glimpse beyond g2 on the size of higher parton correlations in the proton. In this context it is important that, up to corrections, the l / Q terms in the Compton amplitude contribute only to transitions where the initial virtual photon is longitudinal, whereas the leading terms only involve transverse initial photons. Using angular distributions in the final state of the electroproduction process ep + em, one can separate the two types of contributions. This is twice good news: it means that on one hand the leading terms in suitable observables do not suffer potentially large 1/Q corrections, and on the other hand, that the l / Q terms can be studied for themselves, without a large background from leading scaling terms. What observables are suitable for such a separation has been studied in considerable detail for DVCS.27i29 One important finding is that beyond a certain accuracy it is easier to analyze cross sections instead of cross section ratios, where the different helicity transitions of DVCS enter in a more involved way. The existing data on DVCS from the HERMES32 and CLAS33 Collaborations provide first information on the dynamics of Compton scattering at
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a3 0.6 0.4 0.2 0 -0.2
-0.4 -0.6
...............................
.....,.......
Figure 3. The single spin asymmetry of the lepton beam in e p --t e py as measured by HERMES3' (upper panel) and CLAS33 (lower panel). The HERMES data is for an average (Q2) = 2.6 GeV', and the CLAS measurement for Q' between 1 GeV' and 1.75 GeV'.
moderate values of Q2.Up to corrections which are beyond the accuracy of the present data, the angular dependence of the lepton beam spin asymmetry should be like sin 4 for transverse y* and like sin 24 for longitudinal y*.The
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data shown in fig. 3 does not exhibit a significant sin 24 component, so that at this point there is no indication for large power suppressed terms in this process. For meson production processes the situation is much less well understood. The NLO corrections in a, to meson production via quark exchange (Fig. 2b) are known,30 and the size of some power corrections have been estimated,31 but we are far from a systematic treatment or understanding. It seems however that both radiative and power corrections can be of considerable size, so that more progress will be needed for quantitative analysis of these reactions. 6
Timelike Compton scattering
In the processes discussed so far the hard scale Q is provided by a virtual spacelike photon, radiated off a lepton scattered at large momentum transfer. Recently it has been proposed to consider reactions where a timelike photon of large invariant mass is produced in the final state.1° The simplest of these is the “inverse” process to DVCS and has been dubbed timelike Compton scattering (TCS): yp + y*p at small t and large virtuality Q of the final state photon. Theoretically, it is almost as clean as DVCS, with the sole complications arising from the timelike nature of the photon. Although analogies between TCS and other processes involving timelike photons have to be taken with care, it was estimated from the data of hadron production in e f e - collisions that ranges of Q where the leading twist description of TCS can work may be between about 2 GeV and the J / @ mass, and beyond the masses of the charmonium resonances. The physical process where to observe TCS is photoproduction of a heavy lepton pair, yp + C+C- p with C = e , p. Despite the close analogy to real p h e ton production Cp + Cyp, where DVCS can be accessed, there are important differences in the phenomenology of these reactions. In both cases, a BetheHeitler mechanism contributes at the amplitude level. Contrary to the case of DVCS, this contribution always dominates over the one from TCS in the kinematical regime where we want t o study it. On the other hand, the interference between the TCS and Bethe-Heitler processes can readily be accessed through the angular distribution of the produced lepton pair, whereas the corresponding observable for DVCS is the lepton charge asymmetry and requires beams of both positive and negative charge. To leading order in 1/Q and in a, the photon-proton amplitudes for DVCS and TCS, y*p + yp and yp + y*p, are exactly the same. If this correspondence were observed in data, it would constitute strong evidence for the dominance of the leading order handbag diagrams. At the level of
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a, corrections, the amplitudes for the two processes will differ, and their combined analysis has the potential to provide additional constraints on the GPDs one aims to measure.
7 Summary Generalized parton distributions connect and describe a wide range of aspects in the study of hadron structure. They provide unique glimpses at the interplay between longitudinal and transverse degrees of freedom in a fast moving hadron, and in particular at the role of orbital angular momentum carried by partons. An ongoing effort is required for learning to handle the complexity of information associated with these quantities. Two major lines of research here are the quantitative control of the processes where GPDs can be measured, and the understanding of how GPDs look like. Progress in the latter should eventually lead us to better understand the structure of hadrons itself. References
D. Muller et al., Fortsch. Phys. 42, 101 (1994) [hep-ph/9812448]. X. Ji, Phys. Rev. Lett. 78, 610 (1997) [hep-ph/9603249]. A. V. Radyushkin, Phys. Rev. D 56, 5524 (1997) [hep-ph/9704207]. A. D. Martin and M. G. Ryskin, Phys. Rev. D 64, 094017 (2001) [hep ph/OlO7149]. 5. J. Blumlein and D. Robaschik, Phys. Lett. B 517, 222 (2001) [hep ph/0106037]; Phys. Rev. D 65, 096002 (2002) [hep-ph/0202077]. 6. E. R. Berger et al., Phys. Rev. Lett. 87, 142302 (2001) [hep-ph/0106192]; A. Kirchner and D. Muller, hep-ph/0202279. 7. M. Diehl, Eur. Phys. J. C 19, 485 (2001) [hep-ph/0101335]; A. V. Belitsky and D. Muller, Phys. Lett. B 486, 369 (2000) [hep ph/0005028]. 8. M. Diehl et al., Phys. Rev. Lett. 81, 1782 (1998) [hepph/9805380]. 9. J. C. Collins et al., Phys. Rev. D 56, 2982 (1997) [hep-ph/9611433]; J. C. Collins and A. F’reund, Phys. Rev. D 59, 074009 (1999) [hep ph/9801262]. 10. E. R. Berger et al., t o appear in Eur. Phys. J. C, hepph/0110062. 11. B. Lehmann-Dronke and A. Schzer, Phys. Lett. B 521, 55 (2001) [hep ph/Ol07312]. 12. E. R. Berger et al., Phys. Lett. B 523, 265 (2001) [hep-ph/Ol10080]. 13. M. Burkardt, Phys. Rev. D 62, 071503 (2000) [hep-ph/0005108]. 14. J. P. Ralston and B. Pire, hepph/0110075. 1. 2. 3. 4.
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15. S. J. Brodsky et al., Nucl. Phys. B 596, 99 (2001) [hep-ph/0009254]. 16. M. Diehl et ad., Nucl. Phys. B 596, 33 (2001) [hepph/0009255]. 17. K. Goeke et al., Prog. Part. Nucl. Phys. 47,401 (2001) [hep-ph/0106012], and references therein. 18. M. Diehl et al., Eur. Phys. J. C 8, 409 (1999) [hep-ph/9811253]; H. Choi et al., Phys. Rev. D 64, 093006 (2001) [hep-ph/0104117]; B. C. Tiburzi and G. A. Miller, Phys. Rev. C 64, 065204 (2001) [hepph/0104198]; Phys. Rev. D 65, 074009 (2002) [hep-ph/0109174]. 19. M. Burkardt, Phys. Rev. D 62, 094003 (2000) [hep-ph/0005209]. 20. X. Ji et al., Phys. Rev. D 56, 5511 (1997) [hep-ph/9702379]; I. V. Anikin et al., hep-ph/0109139. 21. S. Scopetta and V. Vento, hepph/0201265. 22. V. Y. Petrov et al., Phys. Rev. D 57, 4325 (1998) [hepph/9710270]; M. Penttinen et al., Phys. Rev. D 62, 014024 (2000) [hep-ph/9909489]. 23. F. E. Close and Q. Zhao, hepph/0202181. 24. A. V. Belitsky et al., Nucl. Phys. B 574 (2000) 347 [hepph/9912379]. 25. L. Mankiewicz et al., Phys. Lett. B 425, 186 (1998) [hep-ph/9712251]; X. D. Ji and J. Osborne, Phys. Rev. D 58, 094018 (1998) [hepph/9801260]; A. V. Belitsky et al., Phys. Lett. B 474, 163 (2000) [hep-ph/9908337]. 26. A. F’reund and M. McDermott, hepph/0111472. 27. A. V. Belitsky et al., hepph/0112108. 28. I. V. Anikin et al., Phys. Rev. D 62, 071501 (2000) [hep-ph/0003203]. 29. M. Diehl et al., Phys. Lett. B 411, 193 (1997) [hep-ph/9706344]. 30. A. V. Belitsky and D. Muller, hepph/0105046. 31. M. Vanderhaeghen et al., Phys. Rev. D 60, 094017 (1999) [hepph/9905372]. 32. A. Airapetian et al. [HERMES Collaboration], Phys. Rev. Lett. 87, 182001 (2001) [hep-ex/0 106068]. 33. S. Stepanyan et al. [CLAS Collaboration], Phys. Rev. Lett. 87, 182002 (2001) [hepex/0107043].
BARYONS 2002: OUTLOOK WOLFRAM WEISE E C T , Villa Tambosa, I-38050 Villazzano (Tmnto), Italy and PhysiBDepartment, Technische Universitct Munchen, 0-85747Garching, Germany
1
Preamble
This is a sad moment: the outlook concluding this conference should have been presented by Nathan Isgur. It will be difficult to meet his standards. In his introductory talk at BARYONS '98 in Bonn, Nathan drew a picture of his vision for "Strong QCD". The zeroth order starting point, he hypothesized, for building hadrons should be relativistic constituent quarks tied together by flux-tube gluon dynamics. In a book-keeping strategy organized in terms of inverse powers of N,, the number of colors, one should then add the quark-antiquark sea and other l/Nc effects as perturbations. We were also reminded of the potentially important role played by the qQ vacuum condensate in connecting valence quarks and potentials on one hand with the current quarks and gluons of QCD on the other. All of these key notions have been very visible again at the present conference. So, have we advanced substantially in our understanding of constituent quarks, gluonic flux tubes, confinement, spontaneous chiral symmetry breaking and the QCD vacuum since our last BARYONS meeting? I believe the answer is a forceful "yes", in view of the significant progress achieved by the joint efforts of experiments and theory, but many issues still remain to be resolved. 2
Lattice QCD
With steadily increasing computational power, "solving" QCD on large Euclidean lattices has now become an important part of hadron physics. Lattice QCD was addressed by no less than four plenary speakers (C. Davies, R. Edwards, G. Schierholz, A.W. Thomas) who gave impressive surveys of the progress made in recent years. The gluonic flux tube and its translation into a static confining potential between (infinitely heavy) color sources has become "reality" on the lattice. The Y-shaped potential characteristic of static three-quark systems is predicted by lattice QCD, as well as hybrid
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29 1
baryons with three heavy quarks coupled to gluonic excitations (reviewed by Ph. Page). But so far, the dynamics of light quarks is not under control, at least not in the context of the confinement problem. New developments have been reported on baryon observables (masses, electromagnetic and axial form factors, moments of structure functions) extracted from lattice QCD. Improved actions are designed to reduce discretization errors. Effects of the finite lattice volume are seriously addressed. Procedures leading beyond the ”quenched” (no-fermion-loops) approximation are well on their way. Still, these results are limited to relatively large quark masses. The typical ”light” quark masses manageable on the lattice up to now, are 10-20 times larger than the u- and d-quark masses determined at renormalization scales around 1 GeV. The corresponding pion masses are well above 0.5 GeV, far away from physical reality, so that important aspects of chiral pion dynamics are presumably suppressed. While lattice calculations using small quark masses close to the chiral limit are out of reach in the foreseeable future, such huge efforts may not even be necessary. Low-energy QCD in the light-quark sector is realized in the form of an effective field theory based on chiral symmetry, and this theory can be used efficiently to extrapolate between lattice results obtained at higher u- and d-quark masses and the ”real world’’ of small quark masses. The feasibility of such extrapolations employing suitable Pad6 approximants (Leinweber, Melnitchouk, et al.) or extended versions of chiral perturbation theory (Hemmed et al.) has been discussed at this conference, with promising results. Once the lattice calculations will approach pion masses around 300 MeV in the near future, reliable extrapolations using effective field theory methods have a good chance of closing the remaining gap between lattice QCD and actual observables.
3
Constituent Quarks
What is a constituent quark? Over several decades we have learned to live with this phenomenological concept without really understanding what it means in detail. Constituent quarks have been remarkably successful in describing ratios of baryon magnetic moments and organizing the symmetry breaking patterns seen in the hadron spectrum. One can think of constituent quarks as quasi-particles in a way analogous to those introduced in many-body problems. For example, a good approximation for an interacting electron gas at moderate densities is in terms of weakly interacting quasi-electrons, i. e. electrons with their Coulomb interactions screened by a cloud of electron-
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hole excitations. Similarly, constituent quarks might be viewed as quarks dressed by clouds of quark-antiquark pairs and gluons. In distinction from the behaviour commonly associated with quasi-particles, however, constituent quarks do not interact weakly: they experience color confinement, and their residual interactions must be strong enough to generate the observed large hyperfine splittings in the baryon spectrum. One can address the constituent quark question from another perspective, by asking: how many quarks are there in a baryon? The answer from spectroscopy would simply be: N = 3. This is, of course, the basis of the time-honoured Isgur-Karl model, and we have heard an updated review on its further developments, successes and limitations by S. Capstick. From a different viewpoint, E. Klempt reminded us of the important role played by the color degree of freedom beyond just antisymmetrizing the baryon wave functions. When looking at deep-inelastic lepton-nucleon scattering the answer to the same question would rather be: N -+ 00. This is the picture projected by the HERA data and reviewed by R. Yoshida. Counting quarks means, in this context, taking the integral of F*(z)/zover the Bjorken scaling variable z,or equivalently, J d l n z F z ( z ) + 00, given the observed behaviour of the structure function Fz(z)at small 2. (Of course one must recall that smallz physics, when viewed in the laboratory frame, involves quark-antiquark and gluon fluctuations of the high-energy virtual photon which extend over distances large compared to the proton size. The fact that N + 00 is therefore a statement about the interacting photon-nucleon system at high energies, not about the isolated nucleon.) Constituent quarks somehow interpolate between "three" and "infinity". It is likely that their properties are l i k e d to the rich, highly non-trivial structure of the QCD vacuum. Y. Simonov pointed out that constituent quark masses and magnetic moments might have a direct relationship to the gluonic string tension. D. Diakonov emphasized the importance of instantons, large fluctuations of the gluon field. In this approach, the constituent quark mass at zero momentum is proportional to the average instanton size and inversely proportional to the squared average instanton separation in the QCD vacuum. With an instanton radius of about 1/3 fm and a separation of 1 fm, compatible with instanton simulations in lattice QCD, the zeremomentum constituent quark mass emerges at about 350 MeV, a remarkable result. The "running" quark m a s decreases rapidly at momentum scales larger than 1 GeV, just as it should. Lattice QCD studies of the Euclidean quark propagator performed by the Adelaide group (D. Leinweber et al.) find a similar behaviour of the momentum dependent quark mass in the Landau gauge (with the caveat to
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be added that a constituent quark mass is not a gauge invariant quantity in QCD) * Confinement still persists as the primary challenge in all efforts trying to understand the physical meaning of constituent quarks. Confinement is missing, for example, in the instanton approach despite its apparent successes. The nature of residual interactions between constituent quarks has been a much debated theme. Spin-flavour correlations characteristic of Goldstone boson exchange (as discussed e. g. by L. Glozman et al.) have been held against traditional one-gluon exchange descriptions. There is good reason to expect that both kinds of forces act (amongst others) peacefully side by side. One should not forget, after all, that a local interaction between two color-currents generates, via Fierz transformation, all sorts of exchange terms including color-singlet spin-flavour exchanges with meson quantum numbers. 4
Baryon Resonances
The research on baryon resonances has progressed enormously during the time span between this and the last BARYONS conference. These new developments, primarily driven by the experimental programmes of the CLAS detector at JLab, at Mainz and Bonn and at the GRAAL and LEGS facilities, define a new level of high-precision measurements. Out of the many highlights, only a few can be discussed here, with no attempt to achieve even partial completeness. An impressive example is the multipole analysis of neutral pion electroproduction data, reported by V. Burkert, which sets new standards for the separation of magnetic dipole and electric quadrupole transition formfactors in the delta resonance region at momentum transfers as high as 1 GeV. The search for missing resonances in the baryon spectrum is entering a new era as well. CLAS data on two-pion electroproduction indicate signals in the spectrum around center-of-mass energies of 1.7 GeV, which are not covered by commonly used isobar models. Virtual Compton scattering (ep + em) with its minimal final state interaction also proves to be a valuable source of information for systematic baryon resonance studies. At JLab’s Hall A the first measurement covering the entire region up to W = 2 GeV has been performed (reported by H. Fonvieille) and displays strong resonance excitations. Very impressive results have also been presented for resonance searches in electroproduction on the proton leadiig to kaon-hyperon final states, again by a CLAS collaboration. To round off the picture, T. Nakano showed promising developments in kaon photoproduction at SPRING-8 with focus on the A(1405) and A(1520), the detailed nature of which is still a matter of debate between standard quark models and coupled channels approaches.
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New high quality data from GRAAL were reported by A. D’Angelo. Following previous pioneering measurements at Mainz and Bonn, eta meson p h e toproduction now covers the region from near-threshold to 1.1 GeV in a single experiment, with stunning accuracy and the quest for further explorations into a possible structure around a photon energy of 1.05 GeV. Another very interesting case is the photon beam asymmetry measured in omega meson production on the proton at photon energies above 1 GeV. Purely diffractive t-channel exchange mechanisms would not produce any asymmetry at all. Non-zero asymmetry signals measured with high precision are therefore a distinct testing ground for N * resonance studies. Polarisation observables are a. key to the detailed analysis and understanding of resonances in multipole amplitudes. Experiments with polarized photon beams on polarized protons performed at Mainz and Bonn, and also recently at LEGS (as summarized by A. D’Angelo), are paving the way for an accurate examination of the Gerasimov-Drell-Hearn sum rule. The relevant GDH integral when taken up to about 1.8 GeV seems to pass beyond the canonical sum rule value by about 5-10 %. A further extension of the double polarization measurements to higher energies is therefore mandatory. The theoretical state of the art on baryon resonance physics was reviewed by T. Sato. Various models exist to deal with the multipole amplitudes for photo- and electroproduction, mostly based on effective Lagrangians with inclusion of dominant baryon resonances. The situation can be summarized as follows. The physics of the delta resonance is quite well under control. An exception is the N + A quadrupole transition amplitudes for which the d e tailed understanding still needs to be improved. While models including pion cloud effects are in good agreement with JLab data for Q2 above 0.4 GeV2, A. Bernstein pointed out in discussions that such calculations fail to reproduce the accurate Bates data at Q2 N 0.1 GeV2 where the theoretical treatment of pion cloud effects should actually be more reliable. In the second resonance region it is important to improve on descriptions of channels with two pions in the continuum. The theory of such nxN threebody channels has not yet reached a quantitatively satisfactory level. In the third and higher resonance region there is still much work to do on the theoretical side, even conceptually, concerning detailed resonance versus background analysis. Problems of this sort, with quasi-bound states embedded in a multiparticle continuum, exist also in nuclear physics, atomic physics and quantum optics, and it may be useful to borrow from the reaction theory expertise developed in those fields. Last not least, with the high productivity of several electron and photon facilities now in operation and further upgrades in sight, one should not forget
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the important information provided by experiments with hadron beams, as pointed out by M. Sadler. The picture will not be complete unless electromagnetic and hadronic probes are systematically used in a complementary way. 5
Spin Structure
Investigations of the nucleon’s spin structure are entering a new phase. It is now well established that quarks carry only a fraction, less than one third, of the proton spin. The next challenges are: to extract the flavour decomposition of those spin fractions, to isolate the gluon contribution to the total spin, and to analyse transverse spin degrees of freedom which provide additional independent pieces of information. G. van der Steenhoven gave an impressive status report and an exciting outlook into coming years. The HERMES experiment continues improving the data quality for the polarized structure functions g1 of the proton, the deuteron, and of the neutron as deduced from 3 H e . The accuracy of the flavour decomposition of quark spin fractions from the analysis of semiinclusive deep-inelastic scattering is expected to improve as well. The gluon contribution to the proton spin will be explored with COMPASS, HERMES and RHIC, by photon-gluon fusion and reconstruction of the produced charmed quark-antiquark pairs, and by measuring tracks of high transverse momentum, with an expected accuracy at the 10 % level. A novel quantity of considerable current interest is the density of transversely polarized quarks inside a transversely polarized proton, the ”transversity” distribution hl . By its very nature, hl emphasizes more prominently the valence quark aspects of spin structure, so it yields important complementary information to the longitudinal quark spin distributions. A further new dimension opens through Deep Virtual Compton Scattering (DVCS) measurements and the extraction of Generalized Parton Distributions (summarized by M. Diehl). According to Ji’s sum rule, DVCS has access to the total quark angular momentum (its spin plus orbital angular momentum). The feasibility of DVCS experiments has recently been demonstrated, in parallel, both by HERMES and by the CLAS collaboration at JLab. Another important issue is the Q2evolution of spin structure functions and the influence of baryon resonances at smaller Q2. JLab has taken a leadership role in these projects, as reviewed by R. de Vita. The preliminary data on the first moment of g1 for the proton begin to provide the systematics that is necessary to interpolate between the deep inelastic scattering region and the non-perturbative spin physics at lower Q2,down to the GDH sum
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rule at Q2 = 0. A very interesting new result is the CLAS measurement of g1(z) for the proton at Q N 1 GeV. It demonstrates the importance of the delta resonance (and possibly higher resonances) in the nucleon spin structure problem, even at reasonably large Q. This behaviour was predicted several years ago (Edelmann et al.) and the theory has been further developed in the meantime (Simula et al.). To those who confidently expected perturbative QCD to start already at Q 1 GeV, this came unexpected. It is an interesting question now whether the basic idea of quark-hadron duality (reviewed by S. Jeschonnek at the conference), namely that properly averaged hadronic observables can be described in terms of perturbative QCD, is at work also for spin structure functions.
-
6
Nucleon Form Factors and Polarizabilities
A bright highlight in the exploration of nucleon electromagnetic form factors (reviewed by E. Brash) is the recent observation by a polarization transfer measurement at JLab’s Hall A that charge and magnetization distributions in the proton are not proportional as was long thought. The ratio ~ G E / G drops continuously down to almost one half at Q2 N 4 GeV2, whereas it was previously assumed to be equal to one on the basis of simple universal dipole parametrizations for those form factors. The JLab data have triggered a reexamination of the Rosenbluth extraction of form factors from earlier cross section measurements. Some relativistic constituent quark models and the cloudy bag model describe the new situation properly, at least at a qualitai tive level. Further thinking about the dynamics which governs the proton’s constituents and their wave functions will obviously be stimulated by these new developments. Parity violation in elastic electron scattering as a tool to investigate admixtures of strange quark-antiquark pairs in the nucleon has been reviewed by F. Maas. Earlier predictions of large ground state matrix elements for strange quark currents in the nucleon are not confirmed. The SAMPLE experiment at Bates, the HAPPEX measurements at JLab and recent advances at Mainz all set quite low limits for the strange vector current in the proton, considerably lower than the 10 % level expected from previous estimates. This does not imply, of course, that strangeness is equally unimportant in other types of currents. For example, the scalar density of strange quarks in the nucleon might be considerably more pronounced. Renewed interest in this question is triggered by recent claims that the sigma term of the nucleon is substantially larger than its previously deduced value of (45 f 8) MeV.
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Electromagnetic and spin polarizabilities have always played an important part in our understanding of nucleon structure. Virtual Compton Scattering (VCS, reviewed by H. Fonvieille) and the generalized polarizabilities deduced from such experiments will be a rich source of new insights into the low-energy dynamics of the nucleon’s internal degrees of freedom. The accuracy reached in the pioneering VCS measurements at Mainz is a major step forward, and together with the VCS programmes at JLab and Bates, the progress in the field will be significant. On the theoretical side, the analysis of VCS data is greatly helped by sophisticated dispersion relation methods (B. Pasquini et al.) and by effective field theory approaches (H. Grieohammer et al.). 7
C h i d Dynamics
Low-energy QCD with light u- and &quarks is realized in the form of an effective field theory of pions, the Goldstone bosom of spontaneously broken chiral symmetry, coupled to ”heavy” sources such as baryons. The low-energy expansion of this theory in small momenta or small quark masses is called chiral perturbation theory (ChPT). Both its predictive capacity and its inherent limitations were lucidly summarized by T. Becher. Based on the pioneering work by Gasser and Leutwyler and by Weinberg, ChPT has been a remarkably successful theoretical tool, not only in its traditional domain, threshold pion-pion scattering, but also in understanding the role of the nucleon’s pion cloud in pion-nucleon scattering and photoproduction processes. One of those traditionally successful examples has been neutral pion photoproduction on the proton close to threshold. A further challenging test for ChPT is 7ro production induced by virtual photons and its systematic Q2dependence. H. Merkel reported on the very accurate Mainz measurements at Q2 = 0.05 and 0.1 GeV2, close to threshold, a region where the chiral lowenergy expansion is expected to work well. But apparently it doesn’t! The ChPT predictions of V. Bernard et al. systematically fail as one moves away from the real-photon point to Q2 > 0. (Admittedly, the MAID multipole amplitudes have similar difficulties when confronted with these high-precision data.) The issue raised by these findings is twofold: the data systematics should be enlarged by measurements at several additional values of Q2;and the ChPT calculations will have to meet this challenge by moving to the next higher order. Rigorous ChPT is limited in its applicability t o sometimes very small convergence regimes when resonances axe produced nearby. A prominent example is the delta resonance. In the ”official” power counting philosophy, its effects are relegated to higher orders. But the prominent role of the A(1232) in the strong M1 transition that governs the paramagnetic response of the
298
nucleon, an evident empirical fact, calls for a different kind of book-keeping. In the large NC limit, the nucleon and the A are degenerate: there is no particular reason to treat the baryon octet and the decuplet on a different basis in heavy-baryon ChPT. Extended versions of chiral effective field theory do in fact promote the delta to leading order in combined chiral and large-Nc expansions, a useful strategy. Such a scheme has been successfully employed, for example, in analysing the strong energy dependence of the generalized magnetic dipole polarizability of the nucleon (as reported by H. GrieBhammer). It is also a key element in chiral extrapolations of nucleon properties deduced from lattice QCD (T. Hemmert et al., W. Melnitchouk et al.). With inclusion of strangeness, non-perturbative features of meson-baryon dynamics can be handled efficiently by combining the chiral SU(3) chiral effective Lagrangian with coupled channels techniques familiar from nuclear reaction theory. While sacrificing some of the puristic ChPT power counting rules, the physics benefit from iterating important subclasses of driving amplitudes to all orders is certainly rewarding. Most recent developments (E. Kolomeitsev, M. Lutz), reported at this conference, now include the full baryon decuplet in addition to the octet. The number of free parameters is constrained by large-Nc bookkeeping. The quantitative agreement of such calculations with a large number of observables in a variety of meson-baryon channels is quite remarkable. Is the restoration of chiral symmetry (from its spontaneously broken Nambu-Goldstone realization to the unbroken Wigner-Weyl mode) visible in the high-mass sector of the baryon spectrum? This interesting question (raised by L. Glozman and T. Cohen) alludes to possible parity dublets in the spectrum, i. e. degeneracies between positive and negative parity baryon resonances of the same spin. Several such cases can be located in the mass region around 2 GeV, but there are several other examples which seem not to follow this rule. The parity dublet criterion in its strict sense would apply to narrow states, whereas most of the excited baryon states in question have large widths. On the other hand, in the asymptotic continuum region, identical spectral distributions of parity partners are a familiar phenomenon, as seen for example in the large s behaviour of vector and axial vector spectral functions in the p and a1 channels. In any case, such discussions emphasize again the need for more systematic explorations of high lying excitations in the N and A spectrum.
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8
Looking forward
This conference has given us once again a very lively and convincing demonstration that baryons (and their prototype, the nucleon) represent a most fascinating QCD many-body problem. It exhibits all of the phenomena ass* ciated with QCD, notably confinement, spontaneous chiral symmetry breaking and asymptotic freedom. While the perturbative high-energy sector of QCD is quite well understood, its non-perturbative features, the complexity of the QCD vacuum and its relationship to confinement and sponta.neous symmetry breaking continue to be outstanding challenges. Last but not least, nuclear physics needs ultima.tely to be understood in these terms, and the issue (alluded to in G. A. Miller's talk) of how a nucleon changes its properties in a nuclear environment (a QCD many-body problem intertwined with the nuclear many-body problem) is as burning as ever. One can say without exaggeration that the field is in a promising and forward-looking situation. It is driven by three basic elements which are now operating in a healthy balance: it is "data driven", with emphasis on high precision and full utilization of polarization observables; it is "brain driven", with advanced theoretical approaches constrained by symmetries of QCD; and it is "computer driven", with future computational capacity and speed progressing into the multi Teraflop regime. Given the variety of running facilities at our disposal and upgrades in sight (JLab, Bates, MAMI C, HERMES, COMPASS, RHIC-Spin, SPFUNG8, ..., amongst others), the perspectives for deepening our understanding of QCD phenomena are certainly good. But one should also re-emphasize the importance of systematic investigations using hadron beams. In particular, our knowledge about systems with strange and charmed quarks is still underdeveloped.
I close with an expression of deep gratitude to Bernhard Mecking, John Doming0 and all members of the JLab team who have made this conference an exciting and memorable event.
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Session on Structure Functions and
Form Factors Convenors E. Beise A. Bruell X. Ji M . Vanderhaeghen
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THE Q2 DEPENDENCE OF POLARIZED STRUCTURE FUNCTIONS T. A. FOREST Louisiana Tech University,P. 0. Box 10348, Ruston, LA 7127.2-0046, USA E-mail:
[email protected] A comprehensive program to measure polarized structure functions in the resonance region and beyond using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab has completed taking data. One of the experimental goals is to measure the first moment(r1) of the polarized structure function, g l , as a function of Q2 by scattering polarized electrons from polarized proton (NH3) and deuteron (ND3) targets. Deep inelastic scattering measurements obtain positive values for the first moment at large Q2. The first moment is constrained by the Gerasimov-Drell-Hearn sum rule to have a negative slope at the photon point. The CLAS measurements encompass the transition from the low Q2 region dominated by resonances and other non-perturbative effects to the high Q 2 region where quasi-free partons dominate the interaction. Inclusive results for the double spin asymmetry A1 and the first moment of gl are reported which span a range in Q2 from 0.2 to 1.5 (GeV/c)' and up to W=2.5 GeV, thus probing a range in Bjorken-x from 0.04 to 0.8.
1
Introduction
A wealth of polarized structure function data has been collected over the past quarter century by scattering polarized leptons from polarized nuclear targets at very high energies 2 . Qualitatively, these scattering experiments probed the nucleon in an asymptotic free region where its constituents, quarks and gluons, dominate the interaction as quasi-free partons. These deep inelastic measurements have revealed that the constituent quark spins are not the dominant contribution to the spin of a nucleon, at least in the region of asymptotic freedom. As the squared four momentum ( Q 2 )transfered to the nucleon decreases] the virtual photon interaction becomes more sensitive to a region of prominent resonances indicative of coherent scattering. Finally at the photon point, the interaction is predominantly sensitive to the macroscopic properties of the nucleon such as its magnetic moment. To get a more complete and consistent picture, the EG1 run group has measured polarized structure functions over a range in Q2 which encompasses a large portion of this transition region. This was done by using the nearly 47r coverage of the CLAS to detect the reactants which emerged when polarized electrons interact with polarized NH3 and ND3 nuclear targets.
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304 0.4 < Q2< 0.6 GeV2/c2
0.8
*
0.4 h
k +
g
o
h
2 -0.4 !
-0.8
i+
H(e,e )X
1 1.2 1.4 1.6 1.8 2 2.2
W (GeV)
1.2 1.4 1.6 1.8 2 2.2
W (GeV)
Figure 1. The measured asymmetry in the bin 0.4 < Q” < 0.6. The squares represent measurements made at SLAC. The solid circles are the results from the EG1 experiment. The dashed line indicates the impact of the kinematicaly weighted asymmetry A2. The solid line is a parametrization of the world data set which was used for radiative corrections. Systematic errors are shown on the horizontal axis.
2
Results
The transition region is probed, quantitatively, in terms of the first moment (rl)of the polarized structure function 91. The structure function g1 is expressed in terms of the nucleon momentum fraction carried by the struck constituent, Bjorken-x = Q 2 / 2 M v , the unpolarized structure function Fl and a linear combination of the transverse asymmetry A1 and the transverselongitudinal asymmetry A2 such that
where A1 is the transverse asymmetry determined by taking the difference in the spin 112 transverse cross-section with the spin 312 and dividing by their sum. A2 is the transverse-longitudinal interference cross-section divided by
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0.1
0.05 0 -0.05
0
0.5
1
1.5
Q’( GeVIc)’
0.5 1 1.5 Q2 (GeV/cf
2
Figure 2. The first moment as a function of Q’. The solid squares are from SLAC. The open circles represent measurements from EG1 which only include contributions from the resonance region (W<2 GeV). The open squares combine measurements from EG1 with a parametrization of the world data set for the kinematic regions not measured. Systematic errors are given along the horizontal axis. The dash-dot line represents the slope of the GDH sum rule. The solid line is a pQCD calculation by Larin. The dashed and dotted lines are models based on parameterizations by Burkert and Soffer, respectively.
the total cross-section used to determine Al. Figure 1 shows the asymmetry measured for one Q2 bin which includes measurements taken at SLAC at the same kinematics. The lines represent fits to the world data set. The dashed line identifies the limited impact of the kinematicaly weighted asymmetry A2 on the total asymmetry and has been absorbed by the reported systematic error. The first moment is determined by integrating the polarized structure function measurements with respect to Bjorken-x and within a particular Q2 bin
At the photon point, the GDH sum rule requires that the first moment approach with a negative slope as illustrated by the dash-dot lines in Figure 2. At large Q2, deep inelastic scattering measurements indicate that the moment has values greater than zero. The line in Figure 2b represents the next
306
to leading order QCD approximation to the first moment which agrees with the EMC measurements at Q2 M 11 GeV2 to within 2%. Until recently the experimental data in the intermediate Q2 region below 2 GeV2 was limited to measurements from SLAC and HERMES ’. While these experiments were among the first to explore this region, it was not clear where in Q2 the transition would pass through zero, or more importantly if this moment would follow the expectations derived from the GDH sum rule. The first installment of data from the EG1 group using CLAS clearly indicate the Q2 region in which the moment becomes negative. The data currently under analysis will be used t o evaluate the slope prediction at the photon point based on the GDH sum rule. 3
Conclusions
A data set is now available which constrains theoretical descriptions of the polarized structure function first moment from the DIS region down to Q2 values of 0.2 for the proton and 0.5 for the Deuteron (GeV/c)2. The proton data disagree with the pQCD calculation and the prediction by Soffer for Q2 around 1 (GeV/c)2 while the parametrization by Burkert and Ioffe appears t o describe the data well. The data also show a transition of the first moment t o values less than zero occurring near Q2 values of 0.25 (GeV/c)2 for the proton and 0.75 (GeV/c)2 for the Deuteron. Resonances contribute to the proton first moment at the 40% level for values of Q2 above 0.5 (GeV/c)2. After analyzing the recently accumulated data, the kinematic range will be extended down t o Q2 of 0.05 (GeV/c)2 and up to 4.5 (GeV/c)2.
*
References 1. S. Gerasimov, Sov. J. Nucl. Phys. 2, 430 (1966):S.D. Drell and A. C. Hearn, Phys. Rev. Lett. 16, 908 (1966). 2. SMC et. al.,Phys. Rev. D 60, 072004 (1999), P.L. Anthony et. aZ.,Phys. Lett. B 493, 19 (2000), A. Airapetian et. aE.,Phys. Lett. B 494, 1 (2000). ,CERN,HERA. 3. CLAS collaboration, Nucl. Inst. Meth. A 460, 460 (2001), Nucl. Inst. Meth. A 449, 81 (2000), Nucl. Inst. Meth. A 465, 414 (2001). 4. K. Abe et. al., Phys. Rev. D 5 8 , 112003 (1998). 5. K. Ackerstaff et. al., Phys. Lett B 404, 383 (1997). 6. S.A. Larin, Phys. Lett B 334, 192 (1994). 7. V.D. Burkert and B.L. Ioffe, Phys. Lett B 296, 223 (1992). 8. J. Soffer and O.V. Teryaev, Phys. Rev D 51, 25 (1995).
MEASUREMENT OF R = CL/UT IN THE NUCLEON RESONANCE REGION M. ERIC CHRISTY Hampton University, Hampton VA 23668, USA E-mail:
[email protected] We report on new measurements in Hall C at JLAB of longitudinal and transverse separated proton structure functions in the resonance region (1 < W 2< 4 GeV2) and spanning the four-momentum transfer range 0.2 < Q 2 < 4.0 (GeV/c)2.
1
Motivation
In the one photon exchange approximation, the cross section for unpolarized inclusive electron-proton scattering can be expressed in terms of the helicity coupling between the photon and proton as du
[ C T ( Z , Q 2 ) + E ~ L ( ZQ, 2 ) ] , d0dE' where QT and (TL are the photo-absorption cross sections for pure transversely and longitudinally polarized photons, respectively, I' is the flux of transverse virtual photons and E is the photon relative longitudinal polarization. In terms of the structure functions Fl(x,Q 2 ) and F L ( ~Q 2, ) , the double differential cross section can be written as
=
Direct correspondence between equations 1 and 2 shows that F l ( x , Q 2 ) is purely transverse, while the combination
is purely longitudinal. The separation of the unpolarized structure functions into longitudinal and transverse parts from cross section measurements can be accomplished via the Rosenbluth technique ', where measurements are made over a range in E at fixed x, Q2 and dull? is fit linearly with E . The intercept of such a fit gives OT (and therefore Fl (x,Q 2 ) ) ,while the slope gives the structure function ratio R(x,Q 2 )= O L / O . T = F t ( z , Q2))/2zF1(x, Q2). High precision measurements of the structure function ratio R have been available for over a decade in the deep inelastic scattering region. However,
307
308
Figure 1. A single Rosenbluth separation, with the W 2 , Q2 and extracted value for R ( W 2 , Q 2 listed ) on the plot.
the current world’s data on R (and therefore, the longitudinal and transverse structure functions, FL and Fl in the resonance region is both sparse and of low quality, with typical errors on the order of 100% or more In the Bjorken limit, R vanishes as a consequence of scattering from asymptotically free spin-1/2 quarks, but becomes finite at smaller Q2 due to contributions from both hard gluon exchange and transverse momentum components of the struck quark. At the other extreme, the real photon point at Q2= 0 has R(z,0) = 0, due to the purely transverse nature of the real photon. In the resonance region, one might expect that R could become quite large due t o higher-twist effects. However, it has been suggested that the quark-hadron duality exhibited in F2 should be manifest in both longitudinal and transverse structure functions. 23314t5.
778
2
Experiment
Experiment E94-110 was performed in HallC at JLAB to address the lack of precision data on R for the proton in the resonance region. The experiment covered the kinematic range of 0.3 < Q2 < 4.0 (GeV/c)2and W 2from elastics to 4.0 GeV2. Rosenbluth separations were performed to extract longitudinaltransverse (L-T) separated structure functions at all Q2,W 2 ,where enough range in E existed to allow a good linear fit. A sample Rosenbluth fit and
309
Figure 2. Rosenbluth extracted values of R(z,Q 2 ) from E94-110 (blue circles) as a function of Q2 for various z bins. Also shown are extractions from SLAC DIS (green triangles) and a global parameterization of all the SLAC DIS data (red curve) is seen to describe the average resonance region well. The arrow indicates the position defined by W 2= 3 GeV2
the extracted value of R,from the current analysis, is shown in figure 1. In addition to the Rosenbluth extactions, a global fitting procedure was employed to separate the longitudinal and transverse strength. Provided that enough of the kinematic space is measured, there should be one unique way of doing this separation, and checks were performed to test the uniqueness of the final fit. 3
Results and Conclusions
In figure 2 is plotted the Rosenbluth extracted values of R(z,Q2)as a function of Q2for various z bins. Also plotted is the fit to DIS data from SLAC g . The agreement on average of the resonant values and the DIS fit, extended beyond its region of validity, is remarkable. This agreement could be interpreted as the first observation of quark-hadron duality in separated longitudinal and transverse channels. The Rosenbluth extracted values for F1 and FL are shown in figure 3, for a large sample of the data. Plotted for comparison is the result of the global fitting. Excellent agreement is observed between the different procedures. Both longitudinal and transverse channels exhibit resonant behavior, with the A resonance less pronounced in the transverse channel for Q2 > 1 (GeV/c)2. The data represent the first high precision measurement of unpolarized
310
" 5
,
"..-.'., ,,,
, ,-;*--1,, , , , , , , , , , ~
, . 1
..
.
: , j,
Figure 3. Extracted F1 (Left), and FL (Right), as a function of bjorken z for various ranges in Q 2 . The Rosenbluth separated data (open blue circles) are plotted with the full uncertainties (statistical + systematic). The structure function model (red curve) determined from an iterative procedure is seen to describe the data well. The position of the A P~s(1232)resonance is indicated by the red arrow.
L-T separated structure functions for the proton in the resonance region. The large kinematic range measured allows for a determination of the Q2 dependence of individual resonance regions. Among the futher investigations planned is the extraction of the QCD moments for all the unpolarized structure functions, as well as quantitative tests of quark-hadron duality.
References
1. M. N. Rosenbluth, Phys. Rev. 79, 615 (1956) 2. F.W. Brasse e t al., Nucl. Phys. B110, 413 (1976) 3. L. W. Whitlow et al., Phys. Lett B250, 193 (1990) 4. L.H. Tao, Ph.D. Thesis, The American University (1994) 5. C.E. Keppel, Ph.D. Thesis, The American University (1994) 6. I. Niculescu, R. Ent, C.E. Keppel, Phys. Rev. Lett. 85, 1186 (2000) 7. C.E. Carlson and N.C. Mukhopadhyay, Phys. Rev. D41, 2343 (1990) 8. C.E. Carlson and N.C. Mukhopadhyay, Phys. Rev. D47, 1737 (1993) 9. K. Abe et al., Phys. Lett. B250, 193 (1999)
THE COLLINS FRAGMENTATION FUNCTION IN HARD SCATTERING PROCESSES A. BACCHETTAl, R. KUNDU', A. METZ', P.J. MULDERS' Division of Physics and Astronomy, Faculty of Science, F'ree University De Boelelaan 1081, NL-1081 HV Amsterdam, the Netherlands Department of Physics, RKMVC College Rahara, North 24 Paraganas, India The Collins function belongs to the so-called time-reversal odd fragmentation functions. In spite of this property, we explicitly generate a non-zero Collins function in the framework of a simple field theoretical model by calculating the fragmentation of a quack into a pion at the one-loop level. We also estimate the Collins function at a low energy scale using the chiral invariant model of Manohar and Georgi. Different spin and/or azimuthal asymmetries measurable in semi-inclusive DIS and e+e- annihilation, which contain the Collins function, are briefly discussed as well. In particular, the measurement of a purely azimuthal asymmetry in e+e- annihilation can allow the extraction of the Collins function from data.
1
Introduction
The Collins function H:, describing the fragmentation of a transversely polarized quark into an unpolarized hadron l , plays an important role in studies of the nucleon spin structure. Although H k is time-reversal odd, it can be non-zero due to final state interactions. We show for the first time in a field theoretical approach that a non-vanishing Collins function can be obtained through a consistent one-loop calculation of the fragmentation process, where massive quarks and pions are the only effective degrees of freedom and interact via a simple pseudoscalar coupling '. To obtain a reasonable estimate of H k we calculate the Collins function in a chiral invariant approach at a low energy scale 3. We use the model of Manohar and Georgi 4 , which incorporates chiral symmetry and its spontaneous breaking] two important aspects of QCD at low energies. The Collins function enters several spin and azimuthal asymmetries in oneparticle inclusive DIS. Of particular interest is the transverse single spin asymmetry, where Hf appears in connection with the transversity distribution, for which we predict effects of the order of 10%. In principle in semi-inclusive DIS only the shape of the Collins function can be studied, while a purely azimuthal asymmetry in e+e- annihilation allows one to measure also its magnitude. For this asymmetry we obtain effects of the order of 5%.
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Figure 1. One-loop corrections to the fragmentation of a quark into a pion contributing to the Collins function. The Hermitian conjugate diagrams are not shown.
2
Model calculation of the Collins function
Considering the fragmentation process q * ( k ) + 7r(p)X we define the Collins function, which depends on the longitudinal momentum fraction z of the pion and the transverse momentum k, of the quark, as
with the correlation function
To describe the matrix elements in Eq. (2) at a low energy scale, we assume that massive (constituent) quarks and Goldstone bosons are the relevant effective degrees of freedom. For simplicity, we use in a first step a pseudoscalar interaction between quarks and pions as given by the lagrangian M z ) = isB(z)-Y542)7+).
(3)
While at tree level the Collins function is zero, the situation changes if rescattering corrections are included in A(k,p ) . In a consistent one-loop calculation the diagrams in Fig. 1 contribute to Hf and give rise to the result ~;l-lOo*
# 0.
(4)
The reason for the non-vanishing Hf is the non-vanishing imaginary part in the fragmentation process q* 4 7rq at the one-loop level. Our calculation suggests that the Collins function, being non-zero in such a simple model, is very unlikely to vanish in reality. To get an estimate of the Collins function at a low energy scale we make use of the chiral invariant model of Manohar and Georgi 4 , which describes the normal unpolarized fragmentation function D1 fairly well 3. The z behaviour
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Figure 2. Model result for the ratio H~‘’’’)/DI
as a function of z.
of asymmetries containing H b is typically governed by the ratio
Independent of the parameter choice in our approach increasing with increasing z , as shown in Fig. 2.
3
3,
this ratio is clearly
Observables
In semi-inclusive DIS, three important single spin and azimuthal asymmetries containing the Collins function exist. Neglecting quark mass terms one has 1 (sinq5h)uL 0: -
Q
[ (CI h L ( z )+ cz h 1 ( ~ ) ) H ~ ( ~ ’+~ other ) ( z ) terms , (6) 1
where only the asymmetry numerators are written down. Cp), (4s) is the azimuthal angle of the produced hadron (target spin), and the subscript UL, e.g., indicates an unpolarized beam and a longitudinally polarized target. Also the transversity ( h l ) and two twist-3 distributions (hL,e)enter, c1 and c2 are kinematical factors. HERMES data on (sin ~ ] I ) U L and preliminary data on (sinq5h)LU from Jlab allow us to draw two conclusions about H f , both of which agree with our model calculation (Eq. (4) and Fig. 2): (i) The Collins function is non-zero. (ii) The Collins effect is rising with increasing z. Note that the other terms in (6), athough supposed to be small, somewhat hamper the analysis of (sin&)UL. For the transverse spin asymmetry in Eq. (8), being one of the most promising observables to measure h l , we obtain values
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Figure 3. Left panel: spin asymmetry (sinq5)UT of Eq. (8) as a function of z , assuming hi = gi (solid line), and assuming hi = (fi g1)/2 (dashed line). Right panel: azimuthal asymmetry (Pi1 cos 24),+,- of Eq. (9), integrated over the angular range 0 5 0 5 x , and over the z2 ranges 0.2 5 zz 5 0.8 (solid line) and 0.5 5 z2 5 0.8 (dashed line).
+
up to about 10% (left panel of Fig. 3), which should at any rate be observable. At present, data on semi-inclusive DIS allow us t o extract in an assumptionfree way only the shape of Hi'-. The azimuthal asymmetry * z 3
accessible in e+e- annihilation into two hadrons, can provide information on the magnitude of Hi'-as well. As shown in the right panel of Fig. 3, our result for this asymmetry is of the order of 5%. Possible accurate measurements of this observable at BABAR or BELLE would be very useful to better pin down the Collins function from the experimental side. References
1. J. Collins, Nucl. Phys. B 396, 161 (1993). 2. A. Bacchetta, R. Kundu, A. Metz and P. J. Mulders, Phys. Lett. B 506, 155 (2001). 3. A. Bacchetta, R. Kundu, A. Metz and P. J. Mulders, hep-ph/0201091, to appear in Phys. Rev. D. 4. A. Manohar and H. Georgi, Nucl. Phys. B 234, 189 (1984). 5. P. J. Mulders and R. D. Tangermann, NucE. Phys. B 461, 197 (1996); Nucl. Phys. B 484, 538 (1997) (Erratum). 6. A. Airapetian et aE. [HERMES Collaboration], Phys. Rev. Lett. 84, 4047 (2000); Phys. Rev. D 64, 097101 (2001). 7. H. Avakian, contribution t o this conference. 8. D. Boer, R. Jakob and P. J. Mulders, Phys. Lett. B 424, 143 (1998).
LEADING AND HIGHER TWISTS IN THE PROTON POLARIZED STRUCTURE FUNCTION GP AT LARGE BJORKEN X S. SIMULA INFN, Sezione Roma III, Via della Vasca Navale 84, I-00146 Roma, Italy M. OSIPENKO Physics Department, Moscow State University, 119899 Moscow, Russia G. RICCO, M.TAIUT1 Uniu. of Genova and INFN - Genova, Via Dodecanneso 33 I-1 614 6, Genova, Italy Power corrections to the Q2 behavior of the Nachtmann moments of the proton polarized structure function gy are investigated at large Bjorken 2 by developing a phenomenological fit of both the resonance (including the photon point) and deep inelastic data up to Q2 50 (GeVIc)’. The leading twist is treated at N L O in the strong coupling constant and the effects of higher orders of the perturbative series are estimated using soft-gluon resummation techniques. In case of the first moment higher-twist effects are found to be quite small for Q2 >, 1 (GeV/c)2, and the singlet axial charge is determined to be ao[lO ( G e v / ~ )= ~ 0.16f0.09. ] In case of higher order moments, which are sensitive to the large2 region, higher-twist effects are significantly reduced by the introduction of soft gluon contributions, but they are still relevant at Q2 few (GeV/c)2 at variance with the case of the unpolarized transverse structure function of the proton. This finding suggests that spin-dependent correlations among partons may have more impact than spinindependent ones. It is also shown that the parton-hadron local duality is violated in the region of polarized electroproduction of the A(1232) resonance. N
N
1
Introduction
The experimental investigation of lepton deepinelastic scattering ( D I S ) off proton and deuteron targets has provided a wealth of information on parton distributions in the nucleon. In the past few years some selected issues in the kinematical regions corresponding to large values of the Bjorken variable z have attracted a lot of theoretical and phenomenological interest; among them one should mention the occurrence of power corrections associated t o dynamical higher-twist operators measuring the correlations among partons. The extraction of the latter is of particular relevance since the comparison with theoretical predictions either based on lattice QCD simulations or obtained from models of the nucleon structure represents an important test of QCD in its non-perturbative regime.
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In Refs. and the world data on the unpolarized nucleon structure functions FF and FE have been used to carry out power correction analyses. In this contribution we summarize the main results of the extension of such a twist analysis to the case of the polarized proton structure function gy, performed in terms of Nachtmann moments. The latter however require the knowledge of the polarized structure function gy in the whole x-range for fixed values of Q2, and therefore a new parameterization of gy, which describes the D I S proton data up to Q 2 50 (GeV/c)2and includes a phenomenological Breit-Wigner ansatz able to reproduce the existing electroproduction data in the proton-resonance regions, has been developed '. The interpolation formula for gf has been successfully extended down to the photon point, showing that it nicely reproduces the very recent data on the energy dependence of the asymmetry of the transverse photoproduction cross section as well as the experimental value of the proton Drell-Hearn-Gerasimov ( D H G ) sum rule. According to our parameterization of gf the generalized DHG sum rule is predicted to have a zero-crossing point at Q2 = 0.16 3~0.04 (GeV/c)2. Finally, the Q2 behavior of low-order polarized Nachtmann moments has been obtained in the Q2-range between 0.5 and 50 (GeV/c)2. N
2
Parton-hadron local duality in gy
-
An important feature of the results obtained in Ref. is that the resonant contribution to the polarized Nachtmann moments is negative for Q2 few (GeV/c)2. This is mainly due to the well established fact that the proton transverse asymmetry A: in the A(l232)-resonance regions is negative up to Q2 3 + 4 (GeV/c)2.Thus, for Q2 few (GeV/c)2the resonant contribution to the polarized proton structure function is opposite in sign with respect to the unpolarized case (see Ref. '). It is therefore legitimate t o ask ourselves whether the parton-hadron local duality, observed empirically in the unpolarized transverse structure function of the proton, holds as well in the polarized case. To this end we have generated pseudo-data in the resonance regions and in the D I S regime via our interpolation formula for gy. Our results clearly shows that: i) at values of Q2 as low as 0.5 (GeV/c)2there is no evidence at all of an occurrence of the local duality, as in the case of the unpolarized transverse structure function of the proton 7,and ii) in the kinematical regions where the A(1232) resonance is prominently produced, the local duality breaks down at least for Q2 up to few (GeV/c)2,while in the higher resonance regions for Q2 >, 1 (GeV/c)2it is not excluded by our parameterization. Note that in the unpolarized case the
-
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onset of the local duality occurs 6,7 at Q2 N 1 t 2 (GeV/c)2,including also the A(1232) resonance regions. It should be mentioned that the usefulness of the concept of parton-hadron local duality relies mainly on the possibility to address the D I S curve at large x through measurements at low Q2 in the resonance regions. I t is therefore clear that the breakdown of the local duality in the region of the A(1232) resonance forbid us to get information from duality on the behavior of the scaling curve at the highest values of x. 3
Twist analysis of the polarized Nachtmann moments
In this Section we present the power correction analysis of the polarized Nachtmann moments, MA1’(Q2), obtained in Ref. The leading twist, pL1’(Q2), is treated both at next-to-leading ( N L O ) order and beyond any fixed order by adopting available soft gluon resummation ( S G R ) techniques. As for the power corrections, a phenomenological ansatz is considered, viz.
’.
where the logarithmic pQCD evolution of the twist-4 (twist-6) contribution is accounted for by an effective anomalous dimension (7i6’)and the parameter a4 :) (a:?) represents the overall strength of the twist-4 (twist-6) term at the renormalization scale p 2 , chosen to be equal t o p2 = 1 (GeV/c)2.In order to fix the running of the coupling constant a,(Q2), the updated PDG value cxs(h’$) = 0.118 is adopted. In case of the first Nachtmann moment ( n = 1) the corresponding leading twist term, 6pP)(Q2),does not receive any correction from SGR and therefore at N L O it reads as
7i4)
The non-singlet moment AqNSis taken fixed at the value AqNS= 1.095, deduced from the experimental values of the triplet and octet axial coupling constants, with the latter obtained under the assumption of SU(3)-flavor symmetry. The values of the singlet axial charge ao(p2) and of the four higher-twist quantities a?), 7i4),a r ) and yi6) are determined by fitting our pseudo-data, adopting the least-X2 procedure in the Q2-range between 0.5 and 50 (GeV/c)2.It turns out that the total contribution of the higher twists is tiny for Q2 >, 1 (GeV/c)’, but it is comparable with the leading twist already at Q 2 0.5 (GeV/c)2. Since the first moment basically corresponds to the
318
area under the structure function g: (as it is the case of the second moment of the unpolarized structure function F;), the dominance of the leading twist in M I(1) (Q2 ), occurring for Q2 >, 1 (GeV/c)2,reflects only the concept of global duality and not that of local duality (cf. Ref. 7). In our analysis, where the leading and the higher twists are simultaneously extracted, the singlet axial charge (in the AB scheme) is determined to be ao(l0 G e V 2 ) = 0.16 Z!C 0.09, which nicely agrees with many recent estimates appeared in the literature. Our value of a0 is therefore significantly below the naive quark-model expectation (i.e. compatible with the well known ”proton spin crisis”), but it does not exclude completely a singlet axial charge as large as E 0.25. In case of higher-order moments (n 2 3) both the N L O approximation and the S G R approach have been considered for the leading twist. The comparison of the corresponding twist analyses shows that, except for the third moment, the contribution of the twist-2 is enhanced by soft gluon effects, while the total higher-twist term decreases significantly after the resummation of soft gluons. Thus, as already observed in the unpolarized case, also in the polarized one it is mandatory to go beyond the N L O approximation and to include soft gluon effects in order to achieve a safer extraction of higher twists at large 5,particularly for Q2 N few (GeV/c)2. Finally, the twist decomposition of the polarized Nachtmann moments has been compared with the corresponding one of the unpolarized (transverse) Nachtmann moments obtained in Ref. adopting the same S G R technique. It turns out that the extracted higher-twist contribution appears to be a larger fraction of the leading twist in case of the polarized moments. This findings suggests that spin-dependent multiparton correlations may have more impact than spin-independent ones. References 1. G. Ricco et al.: Nucl. Phys. B 555, 306 (1999). 2. S. Simula: Phys. Lett. B 493, 325 (2000). 3. S. Simula et al.: Phys. Rev. D 65, 034017 (2002). 4. J. Ahrens et al.: Phys. Rev. Lett. 87, 022003 (2001). 5. V. Burkert: Czech. J. Phys. 46, 628 (1996). 6. E. Bloom and F. Gilman: Phys. Rev. Lett. 25, 1140 (1970); Phys. Rev. D 4, 2901 (1971). 7. G. Ricco et al.: Phys. Rev. C 57, 356 (1998); Few-Body Syst. Suppl. 10, 423 (1999). S. Simula: Phys. Lett. B 481, 14 (2000); Phys. Rev. D 64, 038301 (2001).
SINGLE-SPIN ASYMMETRIES AT CLAS H .AVAKIA N Jefferson Lab, 12000 Jefferson Ave, Newport News, VA 23606, USA E-mail:
[email protected] We report the first measurement of the beam-spin asymmetry in the electroproduction of positive pions above the baryon resonance region at CLAS at beam energy of 4.25 GeV. At large fractions of virtual photon momentum carried by the pion the amplitude of measured sin@modulation is 0.037 f 0.006.
Single-spin asymmetries (SSA) in azimuthal distributions of final state particles in deep inelastic scattering (DIS) give access to subtle distribution and fragmentation functions, which cannot easily be accessed in other ways. The total cross section for single pion production by longitudinally polarized leptons scattering off unpolarized protons is defined by a set of structure functions and contains two main contributions. The beam-spin independent part of the cross section (ouu)arises from the symmetric part of hadronic tensor and the helicity (A,) dependent part ( c T L ~ )arises , from the anti-symmetric part of the hadronic tensor 47r a2 s dULU = A, Q4 dX,dy d z d 2 P i ~
xB
y
f
i sin 4 X k T ,
The 4 is the azimuthal angle between scattering plane formed by the initial kl and final k2 momenta of the electron and the production plane formed by the transverse momentum P_Lof the observed hadron and the virtual photon. The relevant kinematical (scale) variables are defined as: x B = Q 2 / 2 ( p l q ) , y = ( P l q ) / ( P 1 h ) , z= ( S p ) / ( p l q ) , where Q2 = -q2, q = k1 - k2 is the momentum of the virtual photon, PI and P are the target and observed final-state hadron momenta. Assuming that the quark scattering process and the fragmentation process factorize and that the fragmentation functions scale and only depend on the fractional energy z , the structure functions could be presented as a convolution of a distribution function (DF) and a fragmentation function (FF). Both assumptions have yet to be experimentally confirmed at CEBAF energies. The DF and FF responsible for non zero 'HLT in semi-inclusive deep inelastic scattering (SIDIS) were first identified by Levelt and Mulders l . They include the twist-3 unpolarized distribution function introduced by Jaffe and Ji and the polarized fragmentation function first discussed by Collins 3 .
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Though large SSA have been observed in hadronic reactions for decades and recently in SIDIS with polarized targets 5,6 the only existing measurement of the beam-spin asymmetry in semi-inclusive lepto-production of pions in DIS, so far is the measurement of asymmetry consistent with 0 at relatively low z ( z < 0.7) ,within large statistical errors, reported recently by the HERMES collaboration 5 . Results of our analysis of data from Jefferson Lab’s CLAS detector reveal very significant single-beam spin asymmetries in pion azimuthal distributions in electroproduction in DIS range (Q2 > 1, W 2 > 4) at large z.
The Experiment In this analysis, we used CLAS electroproduction data taken in March 1999. Scattering of 4.25 GeV longitudinally polarized electrons from a liquid hydrogen target was studied in a wide range of kinematics. The average electron polarization was measured with a M ~ l l epolarimeter r and was 70 % with fractional uncertainty of 3%. Scattered electron and proton were measured using the CLAS detector. Electrons were selected by a hardware trigger using a coincidence of the gas Cerenkov counters and the lead-scintillator electromagnetic calorimeters. Pions were identified using momentum reconstruction in the tracking system and time of flight from the target to the scintillators. The total number of 7r+ events after all quality, vertex, acceptance, fiducial and kinematic cuts was 400k. The CLAS data was compared with LUND (PEPSI-tLEPTO-tJETSET) based Monte-Carlo. Very good agreement in different kinematic distributions of data and LUND predictions was found. The cuts used to extract the asymmetry for semi-inclusive sample were defined from the comparison of CLAS data and LUND MC. At CEBAF energies (4-6GeV) the data exhibit behavior consistent with scattering in the current dominated regime at relatively large z . A cut ZF > 0.15 (ZF = P ~ / 1 4 was ) used for a minimum longitudinal momentum fraction of the pion in the CM frame. A second cut z > 0.5 was applied to the fraction of virtual photon energy carried by the pion to restrict the kinematics to region where the predictions based on the semi-inclusive approach are consistent with the data. In this region the major part of 7r+ are in fact produced directly from string fragmentation according to the LUND model. The upper limit z < 0.8 was chosen to exclude the kinematic region, where the higher-twist effects and diffractive effects could be dominant. In addition in this intermediate range of z (0.5 < z < 0.8) the z-distribution of final state pions at CLAS are in good agreement with N
32 1
LUND-MC and high energy experiments like SLAC and HERMES, showing no dependence on x,, which suggests a "precocious" onset of scaling already at energies as low as 4.25GeV. A cut on the missing mass of e'r+ system M X > 1.1 is used to eliminate pure exclusive events. To minimize the radiative corrections a cut on the fraction of the energy of incoming electron carried by the virtual photon y = u / E < 0.85 is imposed, limiting corrections to unpolarized cross section to a few percent '. The +dependent spin asymmetries are isolated by extracting moments of the cross section for two helicity states weighted by the corresponding dependent functions (W(4)= sin 4, sin24...). These moments are given by
+
.
Nf
where N* and P* are the number of events and luminosity weighted polarizations for positive/negative helicities of the electron, respectively. Beam SSA A::' for opposite helicities and their sum extracted from the CLAS data as azimuthal moments compared to the same quantity extracted as a spin asymmetry are in good agreement indicating acceptance corrections are not significant within statistical uncertainties. Main contributions to systematic error coming from the beam polarization error and sin 4, cos 4, cos 24 modulations of the CLAS acceptance are estimated to be less that 20% of the value of statistical errors. The A::' averaged over 2 spin states as a function of z and x, is plotted in Fig. 1. The' :A : is positive for the positive electron helicity in the range of 0.15 < X B ~< 0.4. Within statistical errors no significant dependence on x B was observed in single-spin asymmetry z-dependence for different ranges of x, . This behavior is consistent with factorization in the kinematic range 0.5 < z < 0.8. The target SSA measured by HERMES 5 , analyzed in terms of the fragmentation effect, in addition to a contribution from the Collins function contain other contributions which in certain kinematic range might be significant ',lo. This makes the beam-spin SSA a cleaner observable for extraction of the Collins fragmentation function at large 2, where the analyzing power is large. The preliminary analysis of target S S A ( A ~ Lwith ) the CLAS polarized target is in agreement with HERMES result confirming the striking difference in the z-dependence of beam and target SSA. In conclusion,we have presented the first measurement of the beam-spin asymmetry in semi-inclusive pion electroproduction above the baryon resonance region. The z-dependence of beam SSA in SIDE analyzed in terms of the fragmentation effect probes the polarized FF The study of transversity
'.
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Figure 1. The beam-spin azimuthal asymmetry (sin4 moment in the cross section) extracted from hydrogen data at 4.25GeV as a function of z (left plot) and Bjorken Z B in the range 0.5 < z < 0.8 (right plot). Error bars show the statistical uncertainty and the band represents the systematic uncertainties.
in semi-inclusive DIS is one of the aims of the upgraded HERMES experiment at HERAll and of the COMPASS experiment at the CERN SPS12 and the knowledge of Collins fragmentation function is its important missing part. References
1. J . Levelt and P. J. Mulders, Phys. Lett. B 338,357 (1994) 2. R.L.Jaffe and X.Ji Nucl. Phys. B 375,527 (1992) 3. J. Collins, Nucl. Phys. B 396, 161 (1993) 4. K.Heller et al. ’Proceedings of Spin 96’,Arnsterdam,Sep.1996,~23 5. HERMES collaboration, Phys. Rev. Lett. 84,4047 (2000) 6. A. Bravar, Nucl. Phys. (Proc. Suppl.) B79 (1999) 521. 7. L. Mankiewicz et al. Comput. Phys. Commun. 71,305 (1992) 8. A.Akushevich et. a1 Eur. Phys. J.C. 10,681 (1999). 9. P.J. Mulders, R. M.Boglione, Phys.Lett B 478 (2000) 114; 10. H. Avakian, Proceedings of DIS-2000, Liverpool University 2000. 11. HERMES Collaboration, HERMES 00-003. 12. COMPASS Collaboration, CERN/SPSLC 96-14.
STUDY OF THE A(1232) USING DOUBLE-POLARIZATION ASYMMETRIES J. KUHN AND A. BISELLI FOR THE CLAS COLLABORATION
Rensselaer Polytechnic Institute , Department of Physics 110 8th Street, R o y N Y 12180, USA E-mail: kuhnjQrpi. edu , biselliOangel.phys.rpi. edu An extensive experimental program to measure the spin structure of the nucleons is underway in Hall B at Jefferson Lab using a polarized electron beam incident on polarized hydrogen and deuterium targets, consisting of frozen N H 3 and N D 3 material. Spin degrees of freedom offer the possibility to test, in an independent way, existing models of resonance electroproduction. The most accessible resonance is the A(1232) since it does not overlap with other states and decays strongly via 7r emission. The present analysis select the A+(1232) in the exclusive channel p7Z, e'p)?rO from data of the EG1 run period, taken in the Fall of 1998, to extract single and double spin asymmetries in a Q2 range from 0.5 to 1.5 GeV2/c2. Results of the asymmetries are presented as a function of the center of mass decay angles of the 7ro and compared with the unitary isobar model and two dynamic models.
1
Introduction
The cross-section for electroproduction of nucleon resonances can be written in the following form
where r is the virtual photon flux, a0 z is the unpolarized cross section a n d ce = and net 5 are the contributions from having a - d pk l o t ~ & polarized beam, a polarized target and both beam and target polarized. P, and Pt are the polarization of beam and target, respectively. (T is a function of six complex helicity amplitudes, which in turn can be expanded into multipoles. For the A(1232) the only terms contributing are the El+, MI+ and S1+ multipoles and the interference of these terms with the background. It is clear that by measuring only from unpolarized experiments only partial information on the cross-section can be obtained. Therefore experiments that use polarized beams and targets are needed to gather new information on the resonant and non-resonant contributions to the cross-section. At the intermediate energies used in this analysis (Eaeam= 2.565 GeV) pQCD is not valid and effective field theories were developed. These models
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use previous unpolarized photo- and electroproduction data to fix the various free parameters that arise in the calculation. The polarized cross-sections can then be predicted, and by performing experiments with polarized beams and polarized targets it is possible to verify or constrain the models. For this work three models were considered: The Mainz unitary isobar model MAID1 in two versions (MAID98 and MAID2000), the effective Lagrangian model by N. Mukhopadhyay and R. Davidson2 and the dynamical model by T. Sat0 and H. Lee3. 2
Experimental Setup
The data for this analysis was taken in the Fall of 1998with the CLAS detector system4 in Hall B at Jefferson Laboratory in Newport News, VA. Since the CLAS detector uses a toroidal magnetic field, which is zero along the beam axis, it is possible to insert a polarized target into the detector. The target, consisting of solid “ N H 3 , was polarized using dynamic nuclear polarization and was immersed in a T = 1 K 4He cooling bath. The holding field of B = 5 T had a very high uniformity of = With this setup target polarizations of P, = +38% and P, = -54% were achieved. In addition to the 15NH3target a solid 12C target and an empty target cell were used for background studies.
9
3
Analysis
Figure 1. Missing mass squared for the reaction C$+ cut used t o identify the missing 7ro.
e‘pX. The vertical lines indicate the
Events were selected in the Q2 range from 0.5 GeV2/c2 to 0.9 GeV2/c2 and from 0.9 GeV2/c2 to 1.5 GeV2/c2. Only the region of the A(1232) was considered by choosing 1.1 < W < 1.3 GeV/c2. The 7ro was identified by a
325
cut on the square of the missing mass from the detected final state particles (see figure 1). The cut was chosen so that the spectrum, after subtraction of the nuclear background from scattering of electrons off of the protons in the 15N nucleus, was well imide the accepted region. The asymmetries are defined as different combinations of the events collected with different target and beam polarizations
where for example N t l indicates the number of events with the beam polarization up (?) and the proton polarization down ($). The extracted asymmetries can be seen in figure 2. The results are compared to the four models mentioned before. A x2 comparison of the data with the different models prefers the model by T. Sat0 and H. Lee. The two MAID results are close to each other and are a slightly worse description, whereas the Effective Lagrangian model agrees poorly with the data. 4
Conclusions
An experiment with polarized beam and polarized target was performed with the CLAS detector at Jefferson Laboratory in the Fall of 1998. The extracted asymmetries A , , At and A,t from the reaction elp‘+ e’p7ro follow the predictions from different electroproduction models. A X2-test preferred the dynamic model by T. Sat0 and H. Lee. The unitary isobar model MAID describes the data also rather well, but an Effective Lagrangian model by R. Davidson and N. Mukhopadhyay is in poor agreement. A run that collected an additional 25 x lo9 events was concluded in early 2001 with beam energies from p = 1.6 to 5.7 GeV/c and an extended Q2 range from 0.05 to 3.0 GeV2/c2. This data set is expected to reduce the error bars on the asymmetries by a factor of approximately three. Acknowledgments
This work was supported by the National Science Foundation under grant number PHY-0098602.
326
y
-
:
, ,
:
. ....... . . . ., . .. ... .
m
...
' >
od-
I
Figure 2. Asymmetries A,, At and A,t as a function of the center of mass angles of the pion, cos(O*) and 4*.
References [l] D. Drechsel, 0. Hanstein, S.S. Kamalov and L. Tiator A unitary isobar
model for pion photo- and electroproduction o n the proton up t o I GeV Nucl Phys A645,145 (1999) [2] R.M. Davidson, N.C. Mukhopadhyay and R.S. Wittman Efective Lagrangian approach t o the theory of pion photoproduction an the A(1232) region Phys Rev D43,71 (1991) [3] T. Sat0 and T.S. Lee Meson exchange model f o r 7rN scattering and y N + nN reaction Phys Rev C54, 2660 (1996) [4] CEBAF conceptual design report for experimental equipment (1990)
CLAS MEASUREMENT OF no ELECTROPRODUCTION STRUCTURE FUNCTIONS L. C. SMITH, FOR THE CLAS COLLABORATION Physics Department, 382 McCormick Road, Universaty of Virginia Charlottesville, VA 22904, USA E-mail:
[email protected] Electroproduction of the A(1232) is well suited for the study of mechanisms responsible for resonance formation and decay. The Q 2 dependence of the quadrupole A -i NT transition is electric ( E l + ) and scalar ( S l + ) multipoles in the 7- N -i especially sensitive t o details of the quark wave functions and the evolution from pion to quark degrees of freedom. New no electroproduction data taken with CLAS at Jefferson Lab are compared to recent models which incorporate the dynamical effects of the pion cloud. The ratios El+/Ml+ and S1+/M1+ are extracted using a partial wave analysis over the interval Q2=0.41.8 GeV2.
1
Introduction
Understanding nucleon resonances has been of fundamental interest since the discovery of the A(1232) by Fermi 50 years ago. While QCD prescribes quarks and gluons as the elementary constituents of hadrons in the hard scattering limit, there is still no clear picture of how these degrees of freedom contribute to low energy phenomena like resonance formation and decay. The SU(6) classification of the A(1232) as a simple quark spin-flip excitation neatly explains the observed dominant magnetic dipole ( M I )electromagnetic coupling. However, the A can also be excited using hadronic probes and a unified description of these transition processes is needed. Because of the absence of overlapping resonances which can complicate the analysis, the low-lying A(1232) provides a simple and unique system in which t o explore QCD in the non-perturbative regime. The status of the A(1232) as a benchmark for testing nucleon models has inspired a number of experimental programs worldwide t o improve the database of differential cross sections and polarization observables using photon and electron beams and polarized targets. The N* program at JLAB is providing new data on t h e transition form-factors of nucleon resonances by utilizing the CLAS spectrometer to map out the single pion electroproduction structure functions. These measurements plan t o cover a range in Q2 from about 0.1 to 6.0 GeV2 and span the resonance region up t o W=2 GeV. Fkcently the CLAS collaboration published the first set of results for the quadrupole strength of the 7 * N -+ A(1232) 3 mo transition For this
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measurement, the electric and Coulomb quadrupole/magnetic dipole ratios REM= El+/Ml+ and RSM= Sl+/Ml+ were extracted using a partial wave analysis of the p ( e , e’p)7r’ reaction over the four-momentum transfer range Q2=0.4-1.8 GeV2. The new results (Fig. 1) show a substantial improvement in accuracy over previous measurements in this Q2 interval. Although generally considered t o be evidence of non-spherical components in either the nucleon or A wave function, the physical interpretation of a non-zero longitudinal and transverse quadrupole transition depends strongly on the degrees of freedom assumed to be active within the hadron. At sufficiently low Q2,the dynamical effects of the pion cloud (which through chiral symmetry breaking lead to the constituent quark mass) may dominate the electromagnetic coupling. Models which incorporate pion couplings, such as the Skyrmion and describe the data better than a purely effective Lagrangian approaches quark/gluon framework. 314
M0
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Figure 1. CLAS measurements (a) of the Q2 dependence of multipole ratios REM and RSM averaged over the W range 1.20-1.24 GeV compared to previous and recent measurements.
On the other hand, as Q2+ 03 the dominance of hadron helicity conservation as demanded by pQCD would result in a reshuffling of strength within the multipoles, such that REM+ +1 and RSM-+ constant. Such trends are clearly not present in the current data up to Q2= 4 GeV2, as confirmed by a recent dispersion relation analysis of the JLAB data by Aznauryan 5 . The model-independent multipole analysis in the A region still depends on the assumption of MI+ dominance. This assumption may not hold for data taken at larger Q2,and a more direct analysis of the structure functions could be more revealing. Fig.2 shows typical W dependence of the structure
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functions in the A(1232) region for Q2 = 0.9 GeV2. The longitudinal and transverse interference terms are separated in a model-independent fitting of the q5: dependence of the cross section. Resonant behavior is clearly evident in both LTTT and U L T , in particular the change of sign in LTLT due to the interference of Re(Ml+) with non-resonant amplitudes. COSZP'=-Q.~
<
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Figure 2. Structure functions extracted from CLAS p ( e , e ' p ) r o data at Q2= 0.9GeV2. The form a bcos(2q5:) c c o s ( C ) was fitted t o 12 @' bins t o extract the three structure functions plotted in each W and ws 0: bin. Curves show predictions of various unitarized phenomenological reaction models.
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Further information can be obtained from the Legendre moments of the structure functions, (here expanded up to L=l): UT
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OLT
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The W and Q2 dependence of the Legendre moments are shown in Fig. 3 compared to the reaction models (MAID ', Sat0 and Lee and Dubna-MainzTaipei 4). Generally the models only agree at the resonance pole, while off-
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resonance the sensitivity to backgrounds is large and differences between models more dramatic. Our data are clearly able to resolve between the different predictions. Since the resonant amplitudes are usually calculated from quark models, the coupling between resonant and non-resonant processes may play a crucial role in the interpretation of measured multipoles. -
0'=0.525
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Figure 3. W dependence (left) and Q2 dependence (right) of Legendre moments Ao, A1, A2, CO,Do, D1 for the p(e, e'p)?ro reaction extracted from fits to CLAS measurements of structure functions using Eq. 1. Prediction of various pion cloud models are shown.
0.5
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Figure 4. Ratio of ~ T tTo the total cross section utot for three W bins below the A(1232) (left), at the top of the A(1232) (middle) and in the 2nd resonance region (right).
Finally, the structure function UTT can also serve as a direct measure of the approach to pQCD, since UTT represents the interference between helic-
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ity non-conserving and helicity conserving amplitudes. The ratio oTT/otot should therefore approach zero as helicity conservation begins to dominate, independent of any assumptions 13. Fig. 4 shows this is clearly not happening at the A(1232) peak, although below resonance and in the second resonance region UTT appears to be vanishing as Q2-+ 2 GeV’. References 1. K. Joo et al., Phys. Rev. Lett, 88,122001 (2002). 2. H. Walliser and G. HoIzwarth, Z. Phys. A 357, 317 (1997). 3. T. Sat0 and T.-S.H. Lee, Phys. Rev., C63,055201 (2001). 4. S.S. Kamalov et al, Phys. Rev. C , 64,032201R, (2001). 5. I. Aznauryan, nucl-th/0207087 (2002). 6. D. Drechsel, 0. Hanstein, S.S. Kamalov, L. Tiator, Nucl. Phys., A645, 145 (1999). 7. R. Beck et all Phys. Rev. Lett., 78,606 (1997). 8. G. Blanpied et all Phys. Rev. Lett. 79,4337 (1997). 9. C. Mertz et al, Phys. Rev. Lett. 86,2963 (2001). 10. T. Pospischil et all Phys. Rev. Lett. 86,2959 (2001). 11. F. Kalleicher et all Z.Phys. A359,201 (1997). 12. V.V. Frolov et al, Phys. Rev. Lett., 82,45 (1999). 13. G.A. Warren and C.E. Carlson, Phys. Rev. D, 42,3020 (1990).
KAON ELECTROPRODUCTION AT LARGE MOMENTUM TRANSFER PETE E.C. MARKOWITZ For the Jegerson Lab Hall A and E98-108 Collaborations Physics Department Florida International University Miami, F L USA E-mail:
[email protected] Exclusive H(e,e’K)Y data were taken in January, March and April of 2001 at the Jefferson Lab Hall A. The electrons and kaons were detected in coincidence in the hall’s two High Resolution Spectrometers JHRS). The kaon arm of the pair had been specially outfitted with two aerogel Cerenkov threshold detectors, designed to separately provide pion and proton particle identification thus allowing kaon identification. The data show the cross section’s dependence on the invariant mass, W , and 4-momentum transfer, Q 2 ,along with results of systematic studies. Ultimately the data will be used to perform a Rosenbluth Separation as well, separating. the longitudinal from the transverse response functions. Preliminary data on this L / T ratio are presented.
1
Introduction
Exploring the electromagnetic structure of the hadronic spectrum is part of Jefferson Lab’s primary mission of basic research into the nuclear building blocks. The kinematical region accessible with beam energies upto 6 GeV allows investigation of both nucleon and light meson structure. The electromagnetic production of kaons allows measurement of the structure of mesons containing a strange quark. Jefferson Lab operates in an ideal kinematical range for such studies; Jefferson Lab is able to measure strange quark electroproduction from threshold through the deep-inelastic scattering (DIS) region. Experiment E98-108’ was approved to measure kaon electroproduction over a broad kinematical range. The experiment separates the longitudinal, transverse, and longitudinal-transverse interference responses to the unpolarized cross section. One goal is to obtain a data set allowing the extrapolation (in the Mandelstam variable t) of the isolated longitudinal response to the kaon mass pole. The reaction at the kaon mass pole would correspond to scattering an electron off of a free kaon and is correspondingly sensitive t o the internal elecromagnetic structure of the kaon. By extrapolating the data taken to the mass pole, the goal is to constrain that kaon electromagnetic form factor.
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A second goal is to examine the behavior of transverse response in this kinematical region, which overlaps with both the resonance region and extends DIS region. The kaon production reaction been calculated in terms of the hard scattering model of Brodsky and Lepage with three different baryon Distribution Amplitudes'. A quark calculation to leading twist using the Born approximation is also available3. Both calculations are for photoproduction; similar electroproduction calculations for the transverse response are not available. A third goal is to use the longitudinal-transverse interference response function to constrain which reaction models contribute to the measurement. Once these reaction models are understood, the longitudinal response will provide sensitivity to the kaon electromagnetic form factor. 2
Present Status
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Measurements of the y p + K+ Y and e p + e' K+ Y (Y = A, Co) reactions are limited by short lifetimes (c . t~ = 370 cm, c . t~ = 8 cm), small production rates (an order of magnitude smaller than for pions) and high thresholds [Eth(KA)= 911 MeV, Eth(KCo)= 1.05 GeV]. The unseparated cross sections are known with an accuracy of about 10%11,9,12 and provide an empirical fit to the unseparated cross section based on phase space, a simple monopole Q2-form factor, and an exponential drop with t. The past ten years have seen the first new data on electromagnetic kaon p r o d ~ c t i o n . ~ * ~ Recent data on kaon photoproduction shows a more complicated relation between the coupling of resonances and the kaon-hyperon final state system. The single polarization asymmetries are available for A production with errors of 25% to 50%. The photon energy range in the published data is limited to 0.9 5 E-, 5 1.4 GeV (a few additional points were measured6y4 at a fixed momentum transfer t = -0.147 GeV' in the energy range E7= 1.05 - 2.2 GeV). On the theoretical side, new calculations based on Regge models now provide fits comparable to the hadrodynamic models which include higher spin resonances to fit the photoproduction data However the current situation for kaon electroproduction remains less satisfactory, both from the experimental and theoretical point of view. Jefferson Lab experiment E93-1085 was the first actual Rosenbluth separation, and demonstrated that the longitudinal response is large (approximately threequarters the size of the transverse response) at t = tmin or 8,, = 0. That experiment also demonstrated that Jefferson Lab is well suited for such precision separations, with the small emittance of the beam, the excellent particle
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identification of the detectors, and the accuracy of the spectrometers for cross section measurements. In kaon electroproduction, the mass pole is in the unphysical region where t > 0. Instead, the electroproduction process attempts to isolate the t-channel by extrapolating the longitudinal response in t to the unphysical kaon mass pole. Such an extrapolation is model dependent meaning that it is desirable to check the extrapolation against available data on the kaon form factor at lower Q2. The only unambigous data on the kaon form factor is from high-energy scattering of kaon beams from atomic e1ectr0ns.l~Due to the inverse kinematics, the measurements were limited to low 4-momentum transfers (.02 < Q2 < .12 (Gev/c)2). The measurements were able to determine the kaon charge radius by looking at the slope of the cross section with respect to Q 2 . [Interestingly, within the next year the addition of the septum magnets to Hall A would let Hall A do a comparison of electroproduction with actual meson-electron elastic scattering in about 3 days for the kaon, plus about the same for the pion.] 3
Experimental Setup
The experiment took place in Hall A at the Thomas Jefferson National Accelerator Facility’s CEBAF accelerator. The standard equipment in Hall A has been described e1~ewhere.l~ Electron beams of energies upto 5.7 GeV were incident on liquid hydrogen targets of nominal 4 cm and 15 cm lengths. Electrons and kaons were detected in coincidence in the two magnetically symmetric high resolution spectrometers (HRS). The HRS spectrometers were outfitted with special particle identification: on the electron side there were a gas Cerenkov counter and a lead glass calorimeter to veto 7r- mesons, while on the hadron side two different aerogel Cerenkov counters were used t o separately veto pions and protons. The pions were vetoed in the A1 aerogel which has a refractive index of 1.015 by requiring that the detector A1 not fire. Protons were vetoed in the A2 aerogel which has a refractive index of 1.055 by requiring that the detector did fire.
4
Preliminary Results
Figure 1 shows the reconstructed mass of the unobserved baryon in the H(e,e’ K) reaction, in this case either a A or C hyperon. The ratio of these two production cross sections is observed to drop rapidly with Q 2 ,however because
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Q'=r.9 (GeV/c)'
Online Missing Mass (MeV)
Figure 1. The A-hyperon reconstructed from the (H(e,e' K)Y missing mass.
the phase space acceptance for the two reactions also changes rapidly, final results are dependent on the ongoing acceptance studies. The quality of the particle identification can be judged by the lack of background in the plot. The range in W covered by the experiment does not show any striking behavior; the unseparated cross sections smoothly follows the nearly flat reaction phase space as shown by the photoproduction data. Similarly, the unseparated cross sections drop off approximately as 1/(Q2 2.67)2 as given by the E93-108 data. Here minor discrepancies to the global fit should be expected since the data were all taken at different &-values(the virtual photon polarization). Figure 2 shows the very preliminary separations for the data at Q 2 = 2.4 (GeV/c)2 and W = 1.8,l.g GeV plotted versus E , the polarization of the virtual photon. A straight line fit to those data will provide the separated longitudinal and transverse contributions. The inner errror bars are the statistical errors while the outer error bars reflect a conservative estimate of what the systematic uncertainties are at this point in the analysis. The ultimate
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Figure 2. The cross sections at Q2 = 2.4 (GeV/c)2 and W = 1.8,l.g GeV plotted versus E .
error bars will be dominated by the statistics. As can be seen from the plot, at the larger momentum transfers of this experiment (as compared to E93-018), the longitudinal cross section is decreasing relative to the transverse but is still appreciable. 5
Outlook
The data analysis is continuing. The preliminary results indicate that the quality of the data is excellent and show that the longitudinal response decreases faster than the transverse with increasing Q 2 . Additonal results are expected in the coming months. The collaboration is finishing construction of two septum magnets which will be used with nuclear targets for hypernuclear production experiments. The resolution is critical for hypernuclear measurements making the Hall A HRS a good match. The backgrounds are also expected to rise in these exper-
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iments, and the collaboration, led by the Roma’/INFN group is constructing a RICH to provide additional particle identification. We expect to run the hypernuclear experiment in the fall of 2002. At higher energies there is the possiblity of looking at semi-inclusive production off polarized targets to measure the sea quark distributions as well; such data would be complementary to the existing Drell-Yan and Hermes data. References
1. Jeflerson Lab Experiment E98-108,P. Markowitz, M. Iodice, S. Frullani, C. C. Chang, 0. K. Baker spokespersons (1998). 2. P. Kroll, M. Schurmann, K. Passek, W. Schweiger, Phys. Rev. D 55 4315 (1997). 3. G. R. Farrar, K. Huleihel, H. Zhang, Nucl. Phys. H,655 (1991). 4. M. Bockhurst etal., Z. Phys. C @ 37 (1994). 5. G. Niculescu, etal., Phys. Rev. Lett. 8l,1805 (1998). 6. P. Feller, et.aZ., Nucl. Phys. B39 413 (1979). 7. J.C. David, C. Fayard, G.H. Lamot, B. Saghai, Phys. Rev. C 53 2613 (1996). 8. R. A. Adelseck, B. Saghai, Phys. Rev. C 42 108 (1990). 9. C. J. Bebek et al., Phys. Rev. D l5,47 (1977). 10. T. Azemoon et al., Advance in Nucl. Phys. l7,47 (1987). 11. P. Brauel et al., Z. Physik, 3, 101 (1979). 12. A. Bodek et al., Phys. Lett. 417 (1974). 13. S. R. Amendolia et.aZ., Phys. Lett. B 178,435 (1986). 14. The Jefferson Lab Hall A Collaboration, Paper in progress, to be submitted to Nuclear Methods and Instrumentation.
u,
ARE RECOIL POLARTZATION MEASUREMENTS OF Gg/G& CONSISTENT WITH ROSENBLUTH SEPARATION DATA? J. ARRINGTON Argonne National Laboratory, Argonne, IL, USA Recent recoil polarization measurements in Hall A at Jefferson Lab show that the ratio of the electric to magnetic form factors for the proton decreases significantly with increasing Q 2 . This contradicts previous Rosenbluth measurements which indicate approximate scaling of the form factors ( p p G ; ( Q 2 ) / G & ( Q 2 )x 1). The cross section measurements were reanalyzed to try and understand the source of this discrepancy. We find that the various Rosenbluth measurements are consistent with each other when normalization uncertainties are taken into account and that the discrepancy cannot simply be the result of errors in one or two data sets. If there is a problem in the Rosenbluth data, it must be a systematic, r-dependent uncertainty affecting several experiments.
The structure of the proton is a matter of universal interest in nuclear and particle physics. The electromagnetic structure of the proton can be parameterized in terms of the electric and magnetic form factors, G E ( Q ~ ) and Gw (Q2), which can be measured in elastic electron-proton scattering. The electric and magnetic form factors can be separated using the Rosenbluth technique1, or by measurements of the recoil polarization of the struck nucleon2. Figure 1 shows the ratio of ppGE/GM as a function of Q2 for the Jefferson Lab recoil polarization measurements3 and from a global Rosenbluth analysis of the cross section measurements4. Clearly we must understand this discrepancy if we want to be confident in our knowledge of the proton form factors. While it is possible that there is a fundamental problem with one of these techniques, we first want to understand if we can explain the difference in terms of less fundamental problems (e.g. experimental errors or analysis procedures). The Rosenbluth measurements are more sensitive to experimental uncertainties as Q2 increases, and extractions that involve combining multiple data sets are sensitive to their relative normalization factors. Thus, we wish to examine both the individual cross section measurements and the analysis procedures to see if there could be problems that would explain the discrepancy between the two techniques. In the global analysis shown in fig. 1, many data sets are combined, and a global fit is performed to extract the relative normalization of the experiments as well as the value of GE and G M at several Q2 values. Errors in one or more of the experiments or improper normalization procedures for experi-
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k
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Figure 1. Ratio of electric to magnetic form factor from a global analysis of cross section data (circles) and from the JLab measurements of recoil polarization (diamonds).
ments which combine multiple measurements could cause such a global fit to give an incorrect result. In addition, because relative normalization factors are being fit, it is possible that one could vary the normalization factors for one or more experiments by an amount that is within the experimental uncertainty in such a way that the ratio of GE/GM changes significantly, while the overall x2 of the fit is not significantly increased (2. e. the global minimum might give the results shown in fig. 1, but a local minimum may give a global fit that is almost as good in which the ratio of GE/ G M falls with Q 2 ) . A new global fit was performed in order to investigate possible problems in the previous data or analyses. Experiments where multiple detectors were used to take portions of the data were broken up, so that there were 16 data sets (and 16 normalization parameters) for the 13 experiments included. As this analysis was focussed on the discrepancy at larger Q 2 , data below Q2 = 0.3 GeV2 were excluded. The small angle data (0 < 15") from the Walker measurement were also excluded, because a later SLAC experiment found corrections that had been neglected in the analysis5. The new fit gives results that were similar to the global analysis by Walker, and no data set had an anomalously large contribution to the x2. Additional fits were performed with individual data sets left out, to see if the result might be driven by a single (potentially bad) data set. No single experiment had a large impact on the overall fit, and even removing the three data sets that had the largest effect only decreased the ratio of G EJGM by -5-10% at high Q 2 . While improvement to the global analysis and removal of data sets did not allow for agreement between the two techniques, there is still the question as
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to whether a different solution for the relative normalizations could be found which brings the experiments into agreement without significantly decreasing the quality of the fit. This was tested in two different ways. First, GM was fit to the data, with the ratio of GEIGMdetermined from a parameterization of the recoil polarization data (p,,GE/GM = 1- 0.13Q2). This increased the total x2 by 69 for the fit to 301 cross section data points. Even though the normalization parameters are allowed to vary in this procedure, the overall quality if fit is much lower when the the fit to the cross section data is forced to match the recoil polarization results. Fixing the ratio of GE/GM to match the recoil polarization measurements gives these data more impact on the fitting then they should have and ignores their uncertainties, so this test likely overestimates the inconsistency. A global analysis including both the cross section data and the GEIGM polarization measurements from fig. 1 (including their statistical and systematic errors) also gives a significantly worse overall fit, though not as bad as when the ratio is fixed in the fit (16 data points are added to the fit and the total x2 increases by 49). Finally, it has been noted3 that individual extractions of GEIGM from different cross section measurements are inconsistent. However, these extractions often involve combining two or three data sets that cover different E ranges, which requires determining the cross-normalization between experiments. While various procedures have been used to determine these normalization factors, the uncertainty in the normalization is often not taken into account in extracting GE and G M , even though a normalization error can yield a correlated change in the ratio at all Q2 values. Thus, it is difficult to verify the consistency of the underlying cross section data based on these extractions. If one examines only experiments where a single detector covered m adequate range of E to perform a Rosenbluth separation, these experiments are consistent with each other and give results similar to the previous global fits (although with significantly reduced precision). One can increase the amount of data available by including experiments where multiple detectors were used, but where direct cross-calibrations were possible within the experiment. Again, this set of experiments give consistent results, and are in good agreement with the cross section global analysis. The inconsistency of the Rosenbluth extractions appears to come from the assumptions made when combining data sets at different E values, and does not indicate a fundamental inconsistency between the different measurements. Even if the recoil polarization result is correct and the problem lies with the cross section data, we must still understand the problem with the Rosenbluth measurements. If the recoil polarization data is correct, this implies that there is a problem in the cross section measurements that introduces
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a systematic €-dependence in multiple data sets. Even with perfect knowledge of G E I G M ,we need these cross sections to extract the absolute values of GE and G M , and we cannot extract precise and accurate values for the form factors if we do not know what the problem is with the cross section measurements. In conclusion, the disagreement between the recoil polarization and Rosenbluth measurements cannot be explained by assuming that there is a problem with one or two data sets, nor can they be made to agree by simply adjusting the relative normalization factors in a global analysis (without significantly worsening the quality of the fit). There is no evidence of problems within any of the data sets (with the exception of the low angle Walker data), and the existing Rosenbluth measurements are completely consistent. The extractions of GE from these data are only inconsistent when one includes analyses that combine different data sets without properly taking into account the uncertainties in the relative normalizations. Thus, there is no experimental evidence to tell us which of these techniques is failing. It is important to determine which is correct not only because we want to know the form factors of the proton, but also because these techniques are used in other measurements, and a fundamental problem with either technique could affect other measurements. Future measurements at JLab including a high precision Rosenbluth6 separation and a new recoil polarization measurement' (using a different experimental setup) will help us understand the discrepancy and determine if it is a fundamental problem with one of the techniques or a problem with the existing data. This work is supported (in part) by the U.S. DOE, Nuclear Physics Division, under contract W-31-109-ENG-38. References
1. M. N. Rosenbluth et al., Phys. Rev. 79, 615 (1950). 2. R. G. Arnold, C. E. Carlson, and F. Gross, Phys. Rev. C23, 363 (1981). 3. M. K. Jones et al., Phys. Rev. Lett, 84, 1398 (2000) ; 0. Gayou e t al., Phys. Rev. C64 038292 (2001). 0. Gayou et al., Phys. Rev. Lett, 88 092301 (2002). 4. R. C. Walker et al., Phys. Rev. D49, 5671 (1994). 5. R. C. Walker, C. E. Keppel, and A. F. Lung, private communications. 6 . JLab E01-001, J. Arrington and R. E. Segel spokespersons. 7. JLab E01-109, E. J. Brash, C. Perdrisat and V. Punjabi Spokespersons.
Effect of recent % and R, measurements on extended Gari-Krumpelmann model fits to nucleon electromagnetic form factors Earle L. Lonion Center for Theoretical Physics Laboratory for Nuclear Science and Departrnen,t of Physics Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 The Gari-Kriimpelmann (GK) models of nucleon electroniagnet.ic form factors. in which the p , w,and r$ vector meson pole contribut.ions evolve at, high monientum transfer to conform to the predict,ions of perturbative QCD (pQCD), was recent,ly extended to include t,he width of t,he p meson by subst,it,utingt,he result of dispersion relat,ions for t,he pole and the addition of p’ (1450) isovect,or vector meson pole. This exte.nded model was shown t o produce a good owrall fit to all the available nucleon electromagnetic form factor (emff) data. Since then new polarization data shows t,hat the electric to magnet,ic rat,ios Rp and R, obtained are not. consistent. wit,h t,he ~ GE, data in their range of momentum transfer. The model is further older G E and extended to include t,he w’ (1419) isoscalar vector meson pole. It, is found that while this GKex cannot simultaneously fit the new Rp and the old GE, data, it can fit. the new Rp and R, well simultaneously. An excellent fit to all the remaining data is obtained when the inconsistent G E and ~ GE, is omitted. The model predictions are shown up to momentum transfer squared, Q 2 , of 8 GeV2/c2
In a variety of related models of the nucleon [l] eniff were fitted to the complete set of data available before September 2001. One group of models included variants of the basic GK model of p, w,and 4 vector meson pole terms with hadronic form factors and a teriii with pQCD behavior which dominates at high Q2 [2]. Four varieties of hadroiiic foriii factor parameterization (of which two are used in [2]) were compared. In addition to the GK type niodels we considered a group of models (generically designated DR-GK) that use the analytic approximation of [3] to the dispersion integral approximation for the p inesoii contribution (similar to that of [4]), modified by the four hadronic form factor choices used with the GK model, and the addition of the well established p‘ (1450) pole. Every model had an electric and a magnetic coupling paranieter for earh of the three pole terms: four ~ “cut-off’ inasses for the hadronic form-factors and the QCD scale mass scale, A Q for~ the logarithmic momentum transfer behavior in pQCD. In addition the effect of a normalization parameter was sometimes considered for the dispersion relation behavior of the p iiiesoii in the DR-GK models. When the set of parameters in each of the eight niodels was fitted to the full set of data available before publication, for G,, Gbtp, GE,, G*tn and the lower Q2 values of Rp = pPG~,/G,tp, three GK and all four DR-GK models attained reasonable x2 (when the inconsistency of some low Q2GE,, and GM,data was taken into account), but the extended DR-GK models had significantly lower x2. Furthermore AQCDwas reasonable for three of the DR-GK models but for only the one of the GK models that had an unreasouably large anomalous magnetic coupling nP. It was concluded that the three DR-CK models were the
342
343 best iiuclmii einff to use in prediction of nuclear electroniagiietic properties. All thee were found to be moderately coiisisteiit in their predictions up to Q2 of 8 GeV2/c2. However tlie part of tlie above data set froni receiit Rp ratio data [5] for 0.5 GeV2/c2 5 Q2 5 3.5 GeV/”/c2. swamped statistically by all t,lie other data. was systematically lower than the fitted iiiodels (Fig.5 of [l]) contributing disproportionately to x2. This ratio is determined by itii wyiiiiiietry iiieasurenieiit in the scattering of polarized electrons on protons. Multiplied by the well deteriiiiiied values of Gn, one obtains values for GE, which are not subject to the uiicertainty iiiliereiit in the Rosenbluth separation iiieasurenieiits in which GE, is obtained by subtracting tlie iiiucli larger contribution of Gn, from the unpolarized ~ froni tlie nieasured Rp are consistently below cross sectiou. As expected tlie G E derived those of tlie older Roseiibluth separation values. It is plausible t o expect that tlie old GE, data is responsible for restrictiiig tlie best fit of tlie niodels to be substantially above tlie experiiiieiital Rp values. With this in niiiid tlie particularly high data of [GI was oiiiitted from tlie fit to the inodel type DR-GK’(1) of [1] and the flexibility of a p iiiesoii dispersioii integral iioriiialization parameter N was included. In this article the original version is designated as GKex(O1) and when fitted to tlie smaller data set as GKex(O1-). As seen in Tables I aiid 11. there is only a small change in the fit to GE, a d Rp? although tlie parameters of the fit change substantially. After tlie publication of [l]new data [7] extended tlie iiieasurenieiits of Rp up to Q2 = 5.6 GeV2/cZ,exacerbating tlie discrepancy with tlie predictions of the best niodels in [l].Very recently R, E pnG~,/G~,f,has been obtained directly [8] by tlie scattering of polarized electroiis on deuterium and detecting tlie polarized recoil neutron at Q2 = 0.45. 1.15 a i d 1.47 GeV2/c2. The preliminary results are coiisisteiit with tlie Galster [9] paraiiieterization froni lower Q2 data
which, in parallel to tlie situation for Rp, iiiiplies much lower values of GE, in their Q 2 range when coupled.with GA~,values (either the precision data of [lo] or tlie iiiodel fits). In this paper. in additioii to the above coiiiparisoii of GKex(O1) and GKex(O1-). we fit the model of type DR-GK’(l), with the added isoscalar vector iiiesoii ~’(1419)pole. to the ~ iii direct following data sets, choseii to deteriiiine the effect of the old GE, aiid G E data coiiflict with the values of h!,,and Rp from nioderii polarization measurements: (a) The fit GKex(02L) froin the full data set of [1]with the addition of [7] and [8]. the oiiiissioii of [GI (as above for GKex(O1-)) and the GE, values for Q22 0.779 GeV2/c2 of [11].[13] aiid [12]. (b) The fit of GKex(O2S) t o tlie same data set as above except for tlie omission of tlie GE, values for Q2 2 1.75 GeV2/c2 of [14]. It is seeii in Tables I and I1 that the oinission of the conflicting G E data, ~ GKex(02L), has a iiiuch bigger influence thaii the oiiiissioii of [GI, GKex(O1-). eiiabling a much better fit to &, in addition to a very good fit t o R,, compared t o GKex(O1). With the reiiioval of tlie conflicting GE, data. GKex(OPS), the fit to all the reiiiaiiiiiig data, iiicludiiig Rp, is very satisfactory.
344 TABLE I: Model paraniet,ers. Common t,o all models are = 3.706. K~ = -0.12. mp = 0.776 GeV. m, = 0.784 GeV. m4 = 1.019 GeV. m g = 1.45 GeV and m,, = 1.419 GeV. Parameters1
Models
GKvx(O1) GKrx(0l-) GKcx(02L) GKt.x(O2S) 0.0636 0.0598 0.0608 0.0401 -0.4175 -15.9227 5.3038 6.8190 0.7918 0.6981 0.6896 0.6739 5.1109 1.9333 -2.8585 0.8762 -0.3011 -0.5270 -0.1852 -0.1676 13.4385 2.3241 13.0037 7.0172 1.1915 1.5113 0.6848 0.8544 0.2552 0.2346 18.2284 1.4916 0.9660 1.1276 0.9407 0.9441 1.3406 1.8598 1.2111 1.2350 2.1382 1.2255 2.7891 2.8268 0.1163 0.1315 0.150 (a) 0.150 (a) 0.8709 1.0 (a) 1.0 (a) 1.0 (a)
(a)
not, varied
TABLE I 1 Contributions to the standard deviation, x2, from each data type for each of the models. The number of data points contributing is in parentheses. For each data type the first row corresponds to the data set for which the model parameters were optimized, the second row to the full data set. Dati Data Models GKex(O1-) GKex(02L) GKex(O2S) tYPf set GKex(0l)
GW opt
full opt full opt full opt full opt full
R, opt
- full Totd opt full
43.3(68)
43.6(68) 48.1(68) 47.9(68) same as above 67.2(48) 48.2(44) 75.3(44) 30.5(36) 67.2(48) 74.8(48) 112.2(48) 136.8(48) 122.4(35) 120.2(35) 121.0(35) 122.7(35) same as above 64.8(23) 64.2(23) 24.1(15) 24.2(15) 65.3(24) 65.0(24) 68.2(24) 68.3(24) 22.6(17) 29.0(17) 23.1(21) 11.8(21)1 114.0(21) 106.5(21) 23.1(21) 11.8(21) O.O(O) O.O(O) 0.6(3) 0.6(3) 9.6(3) 17.7(3) 0.6(3) 0.6(3) 326.7(191) 298.9(187) 336.3(195) 237.7(178) 421.8(199) 427.8(199) 369.2(199) 388.1
345 [l] Earle L. Lomoii. Phys. Rev. (264, 035204 (2001).
[a] M.F. Gari and W. Krumpelmann, Phys. Let,t,.B274, 159 (1992); errat.um. Phys. Let,t,. B282, 483 (1992). [3] P. Mergell. Ulf-G. Meissner and D. Drechsel. Nucl. Phys. A596,367 (1996). [4] G. Hiihler et, al.. Nucl. Phys. B114, 505 (1976). [5] M.K. Jones et, al.,Phys. Rev. Lett. 84, 1398 (2000). [6] R..C. Walker et. al.. Phys. Rev. D49, 5671 (1994). 171 0 . Gayou et al. ArXivmucl-ex/OlIlOlO v l . 15 Nov 2001. [S] Richard Madey, private coniinunicat.ioi1;Bull. APS46, DB 10. p 34>Oct,. 2001. [9] S. Galst,er et al., Nucl. Phys. B32, 221 (1971). [lo] H. Anklin et al., Phys. Lett. B428, 248 (1998). [ll] K.M. Hanson et. al., Phys. Rev.D8, 753 (1973). [12] A. Lung et al.. Plys. Rev. Lett. 70, 718 (1993). 1131 W. Bark1 et, al., Phys. Lett~.B39,407 (1972). [14] L. Andivahis et al., Phys. Rev. D50, 5491 (1994).
MEASUREMENT OF THE ELECTRIC FORM FACTOR OF THE NEUTRON AT Q2 = 0.6 - 0.8 (GEV/C)2 M. SEIMETZ, FOR THE A1 COLLABORATION Institut fur Kernphysik, Beeherweg 45, 55099 Mainz, G e m a n y E-mail: seimetzQkph.uni-mainz.de The electric form factor of the neutron, G E , ~is, measured at Q2 = 0.6 0.8 (GeV/e)2 in a new D(Z,e'n')p experiment at Maina University. A neutron polarimeter, optimized to withstand high electromagnetic background rates, was built for the Three Spectrometer Hall of the A1 collaboration. We present the experimental setup and the status of the data analysis.
1
Physics Motivation
The elastic form factors parametrize the nucleon's ability as a whole to absorb momentum transfer in a scattering reaction. In a nonrelativistic framework they are related to the charge and magnetization distributions, and thereby give an idea of the inner structure of the nucleon. In fact, they allow a crucial test for every nucleon model. Therefore, measurements of GE and GM offer insight into the basic constituents of matter. Among the four Sachs form factors, GE,,, is the least precisely known, due to various experimental difficulties. First of all, no free neutron target is available. Therefore light nuclei (D, 3He) are commonly used, which in general implies model dependencies of the GE,,, results on nuclear binding effects. Secondly, in the Rosenbluth cross section G E , is~ dominated by the much greater magnetic form factor, GM,,. Thirdly, absolute neutron cross sections are hard to measure because they require a calibration of the neutron detection efficiency. These obstacles can to a great extent be circumvented with double polarization measurements, which provide results with small systematic and model errors for the ratio GE,,,/GM,~. The first experiments mostly in the Q2 < 0.5 (GeV/c)2 regime, proved G E ,to ~ be almost a factor 2 larger than obtained from elastic ( e , d ) scattering '. The new A1 experiment brings two data points at higher four-momentum transfers in order to extend the known Q2 range. 2
Measurement of GE,,,in D(Z,e'n')p
The A1 experiment is based on the spin transfer in the elastic scattering of polarized electrons on unpolarized nucleons 3 . The outgoing nucleon has non-
346
347
Figure 1. Sketch of the A1 neutron polarimeter (side view).
vanishing polarization components, P, and P,, proportional to the form factor products GEGM and G K , respectively, 2 being the direction of momentum transfer and 2 lying in the electron scattering plane. The polarization ratio R p = P,/P, is thus proportional to G E I G M ,multiplied with kinematical factors. Together with the known value of G M , ~R,, gives the desired value of GE,,. The neutron polarimeter, needed to measure R,, and the other components of the experimental setup are described in the following. The A1 measurement is performed in the Three Spectrometer hall at Mainz. A beam of polarized electrons, provided by the MAMI accelerator with P, 21 84%, hits a 5cm long liquid deuterium target cell. A magnetic spectrometer analyzes the momentum of the scattered electrons with high resolution, allowing for a precise reconstruction of the reaction kinematics. The outgoing neutrons are detected in the neutron polarimeter (Fig. 1) at forward angles around 30". Their scattering angles and time of flight are measured in a highly segmented wall of plastic scintillators. A t the same time, the neutron polarization is determined in the following way: A transverse polarization, Pt, of the outgoing neutron is analyzed by the strong n p and nC scattering reactions in the first scintillator wall, leading to an asymmetry in the azimuthal angle @,,
A = P,A,tfPt sin(@,)
,
(1)
348
corresponding to an up-down asymmetry in the neutron distribution on a second scintillator wall. Although the experiment is sensitive only to the transverse polarization component, both P, and P, can be disentangled by precessing the neutron spin in a magnetic dipole field perpendicular to the (2,z ) plane. The tangent of the angle xo where Pt vanishes gives the desired ratio P,/P,. The effective analyzing power and the absolute electron beam polarization cancel out. Thereby systematic uncertainties are minimized. The polarimeter is surrounded by massive concrete shielding in order to protect the large-area scintillators from electromagnetic background. Furthermore, a 5cm thick lead shielding is placed inside the magnet gap in front of the 1st wall. The 2nd wall is divided into two parts above and below the beam without direct target view, but in a way that neutrons scattered in the 1st wall can be detected in the 2nd wall with angles corresponding to high analyzing powers. Data were taken at the central four-momentum transfers Q2 = 0.6 and 0.8 (GeV/c)2. The energy of the electron beam was 855 and 883 MeV, respectively, at beam currents of up to 10pA. A Moller polarimeter was used to monitor the electron beam polarization. In part of the beam time a LH2 target was used for calibration purposes and the investigation of systematic errors due to charge exchange effects.
3
Data Analysis
A central aspect of the data analysis is the identification of quasielastically scattered neutrons and their separation from charged and uncharged background. This can be achieved by various means. The high resolution of the magnetic spectrometer already allows a suppression of pion production events on the electron arm. Veto paddles, partly implemented in the hardware trigger, filter out charged particles. Further veto conditions between each neutron detector and its neighbours refine this separation in the offline analysis. Protons lose part of their kinetic energy in the lead shielding, and even if they are not stopped, their time of flight is significantly greater than for the neutrons. In addition, the energy deposition of the neutrons is related to the scattering angles in the 1st wall, which allows the definition of cuts. Four histograms of an distributions axe obtained, distinguishing between positive and negative beam helicities, and the neutrons being scattered above or below the electron scattering plane. They are combined to a helicity asymmetry distribution with the sine-like dependence on an given in Eq. 1. An example is given in Fig. 2, with the current of the spin precessing magnet
349
K \
d
30
20 10
0 -10
-20
- 30
0
20 40 60 80 100120140160180
Figure 2. Asymmetry for maximum positive and negative magnet currents I M .
being at its positive and negative maxima, respectively, corresponding to big transverse neutron polarizations. Data were taken for seven different values of Inn, which permits a neat determination of the angle x o of vanishing Pt. The analysis is still in progress, but first results seem to confirm that G E ,is~ significantly bigger than assumed from former unpolarized experiments. The G E ,data ~ taking will be completed in May and June 2002. Our goal is to achieve an overall error of AGE,n/GE,n = 10%.
Acknowledgments This work has been supported by SFB 443 of the Deutsche Forschungsgemeinschaft (DFG) and the Federal State of Fthineland-Palatinate.
References 1. H. Schmieden, Form Factors of the Neutron, in Proc. Baryons, World Scientific, Bonn, 1998, and the references therein. 2. S. Platchkov et al., Nucl. Phys. A 510, 740 (1990). 3. R.G. Arnold, C.E. Carlson, F. Gross, Phys. Rev. C 23, 363 (1981). 4. K.I. Blomqvist et al., Nucl. Instrum. Methods A 403, 263 (1998).
NEUTRON ELECTRIC FORM FACTOR VIA RECOIL POLARIMETRY R. MADEY',', A.YU. SEMENOV', S. TAYLOR3, A. AGHALARYAN4, E. CROUSE5, G. MACLACHLAN', B. PLASTER3, S. TAJIMA7, W . TIREMAN', CHENYU YAN', A. AHMIDOUCH', B.D. ANDERSON1, R. ASATURYAN4, 0. BAKER', A.R. BALDWIN', H. BREUER", R. CARLINI', E. CHRISTY', S. CHURCHWELL7, L. COLE', S. DANAGOULIAN2,8, D. DAY", M. ELAASARl', R. ENT', M. FARKHONDEH3, H. FENKER', J.M. FINN5, L. GAN', K. GARROW', P. GUEYE', C. HOWELL7, B. HU', M.K. JONES', J.J. KELLY", C. KEPPEL', M. KHANDAKER13, W.-Y. KIM14, S. KOWALSK13, A. LUNG3, D. MACK', D.M. MANLEY', P. MARKOWITZ", J. MITCHELL', H. MKRTCHYAN4, A.K. OPPER', C. PERDRISAT5, V. PUNJABI13, B. RAUE15, T. REICHELT", J. REINHOLDI5, J. ROCHE', Y. SATO', W. SEOi4, N. SIMICEVIC17, G. SMITH', S. STEPANYAN4, V. TADEVOSYAN4, L. TANG', P. ULMER", W . VULCAN', J.W. WATSON', S. WELLS17, F. WESSELMANNl', S. WOOD2, CHEN YAN', S. YANG14, L. YUAN', W.-M. ZHANG', H. ZHU'', AND X. ZHU' (The Jefferson Laboratory E93-038 Collaboration) ' K e n t State University, Kent, Ohio 4&?42, USA Thomas Jefferson National Accelerator Facility, Nevvport News, Virginia 23606, USA 3Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Yerevan Physics Institute, Yerevan 375036, Armenia 5 T h e College of William and Mary, Williamsburg, Virginia 23187, USA Ohio University, Athens, Ohio 45701, USA 'Duke University, Durham, North Carolina 27708, USA 'North Carolina A & T State University, Greensboro, North Carolina 27411, USA Hampton University, Hampton, Virginia 23668, USA loUniversity of Maryland, College Park, Maryland 20742, USA '' University of Virginia, Charlottesville, Virginia 22904, USA "Southern University at New Orleans, New Orleans, Louisiana 70126, USA l3Norfolk State University, Norfolk, Virginia 23504, U S A l4Kyungpook National University, Taegu 702-701, Korea l5Florida International University, Miami, Florida 33199, USA l6Rheinische Friedrich- Wilhelms- Universitat Bonn, 0-53115 Bonn, Germany "Louisiana Tech University, Ruston, Louisiana 71272, USA l8Old Dominion University, Norfolk , Virginia, USA 23508
'
'
350
351 The ratio of the electric to the magnetic form factor of the neutron, GE,/GM,, was measured via recoil polarimetry from the quasielastic d(e‘,e’n’)p reaction at ~ ]Hall C of the Thomas three values of Q2 [ viz., 0.45, 1.15, and 1.47 ( G ~ V / C )in Jefferson National Accelerator Facility. Preliminary data indicate that G E , follows the Galster parameterization up to Q2 = 1.15 (GeV/c)2 and appears to rise above the Galster parameterization at Q2 = 1.47 (GeV/c)2.
1
Introduction
The electric form factor of the neutron, GEn,is a fundamental quantity needed for understanding both nucleon and nuclear structure. The Jefferson Laboratory E93-038 Collaboration conducted quasielastic scattering measurements on a liquid deuterium target at three values of Q2 [viz., 0.45, 1.15, and 1.47 (G~V/C)~ the ] , squared four-momentum transfer. 2
Description of the Experiment
Top Rear Array /
Bottom Rear Arr Front Vetornagger
Lead Curtain /charyLis/’ Target LD2, LH2 Figure 1. Experimental Arrangement.
The experimental arrangement is shown in Fig. 1. A beam of longitudinally polarized electrons scattered quasielastically from a neutron in the deuteron in a 15-cm long liquid deuterium target. The scattered electron was detected in the High Momentum Spectrometer (HMS) in coincidence with the recoil neutron. The polarization vector of the neutron lies in the scattering plane. A neutron polarimeter (NPOL) measured the up-down scattering
352
asymmetry from the component of the neutron polarization vector projected on the axis that is perpendicular to the momentum vector of the neutron. The dipole magnet (Charybdis) ahead of NPOL precessed the neutron’s polarization vector through an angle x. We extracted g s G E/GMn ~ via two different sets of precession angles. For sequential measurements with x = 0, 590 deg., =-KR
(&’/(L’)
(1)
where K R is a kinematic function of the electron scattering angle 6 and Q2, and &/ (EL<) is the scattering asymmetry from the sideways (longitudinal) component of the neutron polarization vector. For sequential measurements with the polarization vector precessed through an angle 4zx
<-
where ([+) is the scattering asymmetry from the projection of the neutron polarization vector on the transverse axis when the precession angle is -x (+x). We chose x = k 40 deg. A significant advantage of the ratio technique is that the scale and systematic uncertainties are small; in particular, the analyzing power of the polarimeter cancels in the ratio of the scattering asymmetries, and the beam polarization cancels also because it varied little during sequential measurements. The polarimeter consisted of twenty detectors in the front array and twelve detectors in each of the two (upper and lower) rear arrays for a total of 44 plastic scintillation detectors. The 100 cm x 10 cm x 10 cm dimensions of each scintillator in the front array were small enough to permit high luminosity. A double layer of “vetoftagger” detectors directly ahead of and behind the front array identified charged particles. Each layer of the rear array consisted of two central scintillators, each 25.4 cm x 10.16 cm x 101.6 cm, with a 50.8 cm x 10.16 cm x 101.6 cm scintillator on each side. The detectors in each rear array were shielded from the direct path of neutrons from the target. A 10-cm thick P b curtain attenuated the flux of electromagnetic radiation and charged particles incident on the polarimeter; the singles rate in a front veto detector was nearly five times higher with a 5-cm thick P b curtain. The flight path from the target to the center of the front array was 7.0 m.
3
Extraction of Scattering Asymmetries
Each event is a triple coincidence event between an electron in the HMS, a neutral particle in the polarimeter fiont array, and either a neutral or charged
353
particle in the polarimeter rear array. To suppress accidentals, we generated a coincidence time-of- flight (&OF) spectrum with the timing from the polarimeter established by a neutron event in the front array. Also, we generated four additional time-of flight spectra, termed AT O F , between a neutron event in the front array and an event in the rear array for scattering either to the upper (U) or lower (D) rear array for each (+ or -) helicity state of the beam. From the yields in the AT O F peak for each of these four spectra, we calculated the cross ratio r , which is defined as the ratio of two geometric means, (N:. NO)'/2 and (NC . NA)l12 , where NU' (NO) is the yield in the A TOF peak for nucleons scattered up (down) when the beam helicity was positive (negative). The physical scattering asymmetry is then given by ( r - l)/(r+l), 4
Preliminary Results
o NIKHEF ii6,e.n) 0 Mainz 'I3ag.e.n) A3 0 ~ a i n z'I3&(g,epn)AI Mainz d(&e'n) A3 JLAB x('(Z.e'n) E93-026
*
0.0
0.5
1.0 QZ
1.5
2.0
2.5
[(Gev/c)q
Figure 2. World data on GE,, versus Q 2 as obtained from polarization measurements. The points on the abscissa [GE, = 01 are projections.
Preliminary results for GE,, are plotted vs Q2 in Fig. 2 together with the current world data on GE,, as obtained from polarization measurement^'-^. Data from E93-038 indicate that GE,, continues to follow the parameterization of Galster e t ~ 1 . ~up ' to Q2 = 1.15 (GeV/c)' and appears to rise above the Galster parameterization at Q2 = 1.47 (GeV/c)'. Schiavilla and Sickll extracted values of GE,, from nuclear physics data on the quadrupole form
3
-
factor of the deuteron, and obtained results up to Q2 1.65 (GeV/c)2 consistent with the Galster parameterization, which is a simple two-parameter fit to data below Q2 0.7 (GeV/c)2. Our preliminary data will serve to test predictions of various models A successful model must be able to predict both GE,, and G E ~These . preliminary data reduce the uncertainty in our knowledge of the interior charge density of the neutron, as seen from the radial distribution of the charge density in the paper of Kellylg.
-
Acknowledgments The support of the Jefferson Lab scientific and engineering staff in Hall C and the accelerator staff is gratefully acknowledged. This work was supported in part by the National Science Foundation, the Department of Energy, and the Deutsche Forschungsgemeinschaft. The Southeastern Universities Research Association (SURA) operates the Thomas Jefferson National Accelerator Facility under the US. Department of Energy contract DE-AC05-84ER40150. References
T. Eden et al., Phys. Rev. C 50, R1749 (1994). M. Meyerhoff et al., Phys. Lett. B 327, 201 (1994). J. Becker et al., Eur. Phys. J. A 6, 329 (1999). J. Golak et al., Phys. Rev. C 63, 034006 (2001). M. Ostrick et al., Phys. Rev. Lett. 83, 276 (1999). C. Herberg et al., Eur. Phys. J. A 5, 131 (1999). I. Passchier et al., Phys. Rev. Lett. 82, 4988 (1999). D. Rohe et al., Phys. Rev. Lett. 83, 4257 (1999). H. Zhu et al., Phys. Rev. Lett. 87, 081801 (2001). S. Galster et al., Nucl. Phys. B32, 221 (1971). R. Schiavilla and I. Sick, Phys. Rev. C 64, 041002(R) (2001). F. Cardarelli and A. Simula, Phys. Rev. C 62, 065201 (2000). M.F. Gari and W. Krumpelmann, 2.Phys. A 322, 689 (1985). M.F. Gari and W. Krumpelmann, Phys. Lett. B 274, 159 (1992). G. Holzwarth, 2. Phys. A 356, 339 (1996). S. Boffi et al., Eur. Phys. J. A 14,17 (2002). W. Plessas et al., Nucl. Phys. A699, 312c (2002). 17. R.F. Wagenbrunn et al., Phys. Lett. B 511, 33 (2001). 18. P. Mergell, U.G. Meissner, and D. Drechsel, Nucl. Phys. A596, 367 (1996). 19. J.J. Kelly, hep-ph/0204239 (2002).
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
THE G" EXPERIMENT : MEASUREMENTS O F THE STRANGE F O R M F A C T O R S OF THE P R O T O N J. ROCHE FOR THE Go COLLABORATION The College of William and Mary / Jefferson Laboratory. Wallinmsbury, VA, USA. In the Go experiment, parity violation asymmetries in elastic electron scattering from the nucleon will be measured. The primary purpose of the experiment is to separate the s quark contributions (Gg(Q2)) and (GL(Q2)) from the overall charge and magnetization densities of the proton. With this aim in view, a dedicated apparatus has been constructed and is currently being installed at JLab / Hall C.
Parity violation in elastic electron scattering arises through the interference of Zo and the y exchange. The relative asymmetry of the reaction for the two helicity states of the beam, can be expressed as' : ~ TG&G& - (1 - 4sin2 BW)&'G&G> A = - - GFQ2 E G & G+
4Jzm
+
E ( G & ) ~T ( G L ) ~
(1)
where : GL and G L are the proton electrc-magnetic form-factors, Gg and G$ are the proton weak form-factors and G> is the axial form-factor of the nucleon2. The measurements of Gg, G& and G> combined with the knowledge of the electro-magnetic form-factors of the proton and the neutron, allows one to extract the s quark contribution (GL and G>) to the overall nucleon structure. In this decomposition, one need only to assume charge symmetry between the proton and neutron' and SU(3). As a result, one can express the measured asymmetry directly in terms of strange form-factors :
where 77 is the asymmetry completly known if neutron and proton form factors are known. For the Go experiment, 17 ranges between -1 and -35 x ~ O - ~ . 1
The Go program relative to other p a r i t y violation experiments
Three asymmetry measurements are necessary to extract GZ, G& and G; without any other experimental assumptions. Table 1 shows, for experiments measuring the strange form-factors, the kinematics used to provide the necessary experimental data. Most measure asymmetries at a given angle from two
355
356 Experiment SAMPLE (MIT-Bates) HAPPEX4 (JLab) SAMPLE’Ol HAPPEXII PV-A4 (MAMI) GO (JLab)
Target P
d P d p
He4 P P P P
d
Be (deg.) 146 146 12.3
Q” (GeV”) 0.1 0.1 0.47
146 6
0.04 0.1 0.1 0.23 0.1 0.1 ... 1.0 0.3, 0.5, 0.8 0.3, 0.5, 0.8
6
35 35 7 110 110
Observables G L = 0.14 f 0.29 f 0.31 G> = 0.22 f 0.45 =t0.39 G& 0.392GL = 0.025 f 0.020 f0.014 GS, 3.8G: Gg O.1GL GS G k 0.2GL GS O.lGS,
+
+ + + +
G L , G&, G;
Table 1. Scope of the experiments measuring the strange form-factors.
different targets (like SAMPLE or HAPPEX 11), then they utilize kinematic suppression of one of the observables (resp. G& or G2). The Go program5 is the only one planned which will completely separate Gg, G& and G:. Asymmetries are measured with hydrogen target at forward (7”) and lydrogen and deuterium targets at backward (110”) electron angles. Moreover, the complete Go experiment will measure the evolution of those observables for three different momentum transfers Q 2 . Figure 1 shows the expected total errors of the Go measurements compared to the predictions of two different models : Chiral Perturbation Theory6 and Lattice QCD’. Note that though both models computations actually agreea with the zero-compatible results of the published SAMPLE and HAPPEX experiments, they predict non-zero individual values for G& and GL. Also, note that given the precision of the experiment, the Go data points will be sensitive to the Q 2 evolution such as the ones predicted by those models. The projected errors presented here include the statistical accuracy of the measurements (? = 5%), the systematic precision, as well as the knowledge of the electro-magnetic form-factors of the proton and the neutron. Though the Go collaboration has designed a specific apparatus of large solid angle (0.5-0.9 str), able to handle a large luminosity ( 2 ~ 1 cm-’ 0 ~ ~s-l), the Go overall errors are dominated by statistics .
aNote that the Chiral model actually uses the SAMPLE and the HAPPEX results t o fix two of its perturbative constants.
357 1.0
1.0
0.5
0.5
0.0
0.0
-0.5
-0.5
-1.0
-1.0
0.0 0.2
2
Figure 1. The projected errors of the Go measurements compared to two different models.
0.4
0.6
0 '
(GaV?
oa
1.0
1.2
0.0
0.2
0.4
0.6
0.0
1.0
1.2
9' (GoV')
The Go experimental technique
The Go experiment will use a 40pA beam with 70% polarization hitting a long cryogenic target (0.2 cm). A special purpose, super-conducting toroidal spectrometer, with azimuthally symmetric angular acceptance has been constructed. In the forward angle mode (see sketch in figure 2), individual particles will be counted in a set of 16 pairs of scintillators per octant placed in the focal plane. Each scintillator pair provides one bin in Q2. The bending angle is 35" and collimators protect the detectors from direct view of the beam. In the first part of the experiment, the protons recoiling from ep scattering at a fixed incident electron beam of 3 GeV will be detected at 0, = 70" f 10" for Q2 ranging from 0.1 to 1.0 GeV2. Time of flight measurement over a 32 ns window will be used to supplement momentum selection by the spectrometer and separate elastic from inelastic contributions. For this purpose, the beam will be pulsed at 31.25 MHz, although usually CEBAF operates at 499 MHz. Custom timeencoding electronics allow readout of high rates of the order of 2 MHz per scintillator pair. In a second part of experiment, the full detector will be rotated back-to-front in order to detect electrons at backward angles (0, = 111" f lo"), giving a comfortable lever arm for a Rosenbluth separation. In this configuration, each incident beam energy (0.4, 0.6 and 0.8 GeV) will correspond to a given Q2 (resp. 0.3, 0.5 and 0.8 GeV2). An additional scintillator hodoscope will allow kinematic separation of elastic and inelastic electrons. Inelastic asymmetries will measure the weak neutral transition current in the region of the A-resonance'. In order to separate the axial form-factor G,: data will be taken with proton and deuterium targets. For the deuterium measurements, aerogel Cerenkov counters will provide r / e separation.
358 Figure 2. Sketch of the Go apparatus in the forward configuration. The recoil particles are deflected by the magnet toward 8 focal plane detectors called octants. E k l m n Be
3
Conclusion
The Go experiment is currently undergoing installation in Hall C at JLab. All components (magnet, target, detectors and electronics) of the apparatus have been completed by an international (North American and French) collaboration of 80 physicists and are mounted on the beamline. Commissioning of the apparatus will take place between October and December 2002. The schedule for the different phases of the Go experiment, will be interleaved with other experiments using the standard Hall C apparatus. By performing a complete separation of Gg, GG and G;, the Go experiment will enlarge the extent of existing data on the strange quark content of the nucleon. Moreover, the complete Go experiment will measure the evolution of these form-factors for Q2 ranging from 0.3 to 0.8 GeV’.
References 1. F. Mass, Strunge form-factors of the ~iucleon,these proceedings. 2. S. Covrig, Status o,f the SAMPLE Deu.te.r.l:rint, experiment at 125 MeV, these proceedings. 3. R. Hasty et al., Science 290, 2117(2000). 4. K.A. Aniol et al., Phys. Lett. B 509, 211(2001). 5. JLab proposals E00-006 and E01-116, D. Beck spokesperson,
http://www.npl.uiuc.edu/exp/GO/GOMain.html 6. T. Hemmert, B. Kubis and U. Meissner, Phys. Rev. C60:045501, 1999. 7. S.J. Dong, K.F. Liu and A.G. Williams, Phys. Rev. D58:074504, 1998. 8. JLab proposal E01-115, S.P. Wells and N. Simicevic spokespersons.
THE NUCLEON FORM FACTORS IN THE CANONICALLY QUANTIZED SKYRME MODEL E. NORVAISAS, A. ACUS Institute of Theor. Phys. and Astronomy, Goitauto 12, Vilnius 2600, Lithuania E-mail:
[email protected];
[email protected] D.O. RISKA Helsinki Institute of Physics; Dept. of Phys., University of Helsinki, 0 0 0 1 ~Finland E-mail:
[email protected] The canonical quantization procedure in SU(2) Skyrme model ensures the existence of stable soliton solution with nucleons quancum numbers. An interesting consequence of the canonical ab initio quantization of the model is the natural appearance of a finite effective pion mass even for the chirally symmetric Lagrangian. The explicit expression for electric and magnetic form factors of nucleon have been derived. The calculated form factors are close to empirical ones.
1
Introduction
The chiral topological soliton model with topologically stable solutions, which represent baryons is that of T.H.R. Skyrme. The first comprehensive phenomenological application of the model to nucleon structure was the semiclassical calculation of the static properties of the nucleon in ref.2. That approach to the model did however have the more principal imperfection in that its lack of stable semiclassical solutions with good quantum numbers. In ref.3 was shown the existence of stable canonically quantized skyrmion solutions. In addition the Skyrme model was generalized to representations of arbitrary dimension of the SU(2) group. An interesting consequence of the canonical ab initio quantization of the Skyrme model is the natural appearance of a finite effective pion mass even for the chirally symmetric Lagrangian. This realizes Skyrme’s original conjecture that ”This (chiral) symmetry is, however, destroyed by the boundary condition (V(o0)= l), and we believe that the mass (of pion) may arise as a self consistent quanta1 effect ” To derive the explicit expressions for electric and magnetic form factors of the nucleon we employ the expressions €or the Noether currents derived in ref.3. Numerical results are plotted for the representations with j = 1/2; 1; 3/2 and also for the reducible representation j = 1@ 1/2 CB 1/2 @ 0. The different representations of the quantized Skyrme model may be interpreted as different phenomenological models.
’.
359
360
2
Quantum skyrmion
The chirally symmetric Lagrangian density that defines the Skyrme model may be written in the form 2: f: 1 L[u(r,t)]= - - ~ { R , R P } -%{ [R,, R ” ] ~ } , (1) 4 32e2 where RP is the ”right handed” chiral current R, = (8,U)Ut. The unitary field U(r, t ) in a general reducible representation of the SU(2) group, may be expressed as a direct sum of Wigner’s D matrices in terms of Euler angles. Quantization of the skyrmion field U is brought about by means of rotation by collective coordinates that separate the variables, which depend on time and spatial coordinates U(r, q(t)) = A (q(t))&(.)At (q(t)).Here the matrix Uo is the generalization of the classical hedgehog ansatz to a general reducible representation3. The collective coordinates q(t) are dynamical variables that satisfy the commutation relations [qa, qb] # 0. The energy of the canonically quantized skyrmion, which represents a baryon with spin-isospin e in an arbitrary reducible representation has the form:
+
Here M ( F ) is the classical skyrmion mass, a ( F ) is the moment of inertia of the skyrmion and A M j ( F ) is a (negative) mass term, which appears in the canonically quantized version of the model:
AMj(F)=
15e37::2(F) /dii2
sin2 F 15 + 4d2 sin2 F ( l - 2)I.
+ 2d39 + 2dl FI2
(3)
where di are constants and depends only on representation j (see ref.3). Dimensionless variable p is defined as f = ef,r. In the semiclassical case, the quantum mass correction A M j ( F ) drops out, and variation of the expression (2) yields no stable solution. The canonical quantization procedure leads to the expanded energy expression (2), variation of which yields a (selfconsistent) integro-differential equation with boundary conditions F ( 0 ) = T and F ( m ) = 0. In contrast to the semiclassical case, the asymptotic behaviour of F ( f ) at large f falls off exponentially as:
F(F) = k
(7+ r--) -T
exp(-rTz,F).
(4)
The stable quantum skyrmion exist if rTz: > 0. The positive quantity rn, = ef,rTz, admits an obvious interpretation as an effective pion mass.
361
I 0.5
1 Q ' (GeV I c)'
1.5
2
Figure 1. Proton electric form factor G c ( Q 2 )with relativistic corrections.
t
1 0.5
1 Q1
1.5
2
lGeV I c)
Figure 2. Proton magnetic form factor GP,(Q2) with relativistic corrections.
3
Form factors
The two parameters of the Lagrangian density, fn and e , have been determined here so that the empirical mass of the proton (938 MeV) and its electric mean square radius (0.735 fm') are reproduced for each value of j. The expressions for nucleon form factors we derived in ref.4. Here we present the numerical calculations of electric and magnetic nucleon form factors in the representations of the SU(2) group with j = 1/2,1,3/2 and in the reducible representation 1 @ 1/2 @ 1/2 @ 0. The effect of Lorentz boosts for these form factors is taken into account by means of the rescaling. The best agreement with experimental data on the form factors obtain with the reducible SU(2) representation, which in fact is the SU(3) group octet restricted to the SU(2). The electric and magnetic proton form factors and magnetic neutron form factor are close to experimental data. In Fig.3 we plotted electric form factors of neutron. The experimental data in this case have too wide uncertainty
362
0.5
1
1.5
Q'(GeV/c12
Figure 3. Neutron electric form factor Gg(Q2)with relativistic corrections.
-t
Figure 4. Neutron magnetic form factor G&(Q2) with relativistic corrections.
margins for model discrimination. The new experimental results indicates this form factor to much larger than what earlier data have suggested and thus closer to the present calculated values, even though these are still much larger than the empirical results. References 1. T.H.R. Skyrme, Nucl. Phys. 31, 556 (1962). 2. G.S. Adkins, C.R. Nappi, and E. Witten,NucZ. Phys. B 228, 552 (1983). 3. A. Acus, E. NorvaiBas and D.O. Riska, Phys. Rev. C 57, 2597 (1998). 4. A. ACUS,E. NorvaiBas and D.O. Riska, Physica Scripta 64, 113 (2001). 5. S. Platchkov et al., Nucl. Phys. A 510,740 (1990). 6. C. Herberg et al., Eur. Phys. J. A 5 , 131 (1999). 7. J. Becker et al., Eur. Phys. J. A 6, 329 (1999).
SOFT CONTRIBUTION TO THE NUCLEON ELECTROMAGNETIC FORM FACTORS
R.J. FRIES Physics Department, Duke University, P. O.%ox 90305, Durham, N C 27706 and Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
V. M. BRAUN, A. LENZ AND N. MAHNKE Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany E. STEIN Physics Department, Maharishi University of Management, NL-6063 NP Vlodrop, Netherlands and Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany We present a calculation of the nucleon form factors in the light cone sum rule approach' employing higher twist distribution amplitudes that were recently obtained using conformal symmetry of QCD.2 Comparing our predictions with the most recent measurements at Jefferson Lab we find that the experimental data are well described by soft contributions that include nonleading helicity structures in the nucleon distribution amplitudes.
The coupling of the nucleon to the electromagnetic field can be described by the Dirac and Pauli form factors F1(Q2)and F2(Q2),
or equivalently by the the electric and magnetic Sachs form factors G E ( Q ~ ) and G M ( Q ~defined ) as G M ( Q ~=)F1(Q2)++F2(Q2) and G E ( Q ~=)P I ( & ' ) + Q2/(4M2)F2(Q2).Here P is the nucleon momentum, M its mass and q the momentum of the photon that couples to the nucleon. At Q2 = 0 the Pauli and Dirac form factors are normalized to the electric charges FP(0) = 1, F;"(O) = 0 and magnetic moments E;(O) = 1.79, F,"(O) = -1.91 of the nucleon, respectively. In the range of intermediate momentum transfer, i.e. a few GeV2, we expect that the hard contribution corresponding to a minimal number of gluon
363
364
Figure 1. Tree level diagram for the parton side of the sum rule.
exchanges between the quarks has to be supplemented by soft, or end-point contributions that are due to the so-called Feynman mechanism to transfer the large momentum and can be thought of as originating &om the overlap of soft wave functions. In several model calculations it was shown that soft contributions alone are capable of producing the form factors comparable with the data. The motivation for this work is first, to demonstrate that wave function components with a different helicity structure compared to the leading twist are important for the soft contribution, and, second develop a quantitative and less model-dependent approach for their evaluation. We suggest to use light cone sum rules (LCSRS) for this purpose, develop the necessary formalism and report the results of the first, leading order calculation of the nucleon form factors in this approach. The calculation uses in an essential way the results of ref.2 where a complete description of the lowest Fock state of the nucleon in terms of distribution amplitudes with different helicity has been worked out in detail. The three-quark nonleading helicity structures correspond to contributions with orbital angular momentum and have higher twist; they give rise to helicity-violating contributions to exclusive amplitudes and proved to be crucial for the description of the form factors. The LCSR calculation starts with the evaluation of the correlator
z”T,(P, q) = i
1
d4x eiq.z@IT { m $ m ( ~IP) )l
(2)
where jEmis the electromagnetic current, z a light cone vector and ~ c z ( 0 )= eiik [u~(O)C#U’(O)] 7 5 $dk(0) is an interpolating field for the proton. Using Eq. (1) one can find the nucleon contribution as:
(3)
365
2
I
6
' Qz
1
2
'
Qz
Figure 2. LCSR prediction for the soft contribution to the magnetic form factor of the proton (left) and the neutron (right) vs SLAC data. G D = dipole fit. ASY = asymptotic distribution amplitudes, SR = P-waves included, dashed = asymptotic with smaller ratio -A1
/fN-
Figure 3. The same as above for the ratio of electric over magnetic and electric over dipole form factors, respectively. SLAC and Jefferson Lab data are shown.
Here P' = P - q . On the other hand we can calculate this correlator in perturbative QCD. The lowest order contribution is given by the diagram in Fig. 1. Here the nucleon distribution amplitudes enter the game. From symmetry we see that only the vector structures can contribute. To the leading conformal spin accuracy the calculation involves two nonperturbative parameters fN and XI corresponding to the normalization of twist-3 and twist-4 amplitudes that are chirality-conserving and chirality-violating, respectively. In the final results only the ratio XI/ fN enters. We also include an additional off-light cone correction which brings in no new parameters. A matching of structures between the partonic calculation for z"T, and the corresponding hadronic calculation in Eq. (4)finally gives expressions for F1(Q2)and F2(Q2).In Fig. 2 we show results for the magnetic form factors of the proton and the neutron in comparison with SLAC data.3*4In Fig. 3 we show the same for the electric form factors in comparison with SLAC4 and recent Jefferson Lab data.5*6We give the results for the asymptotic distri-
366 I
1
2
3
4
5
6
Q’ 1
Figure 4. The ratio QFz/Fl for the proton vs. recent Jefferson Lab data.
bution amplitudes as well as including P-waves in the conformal expansion.2 The asymptotic distribution amplitudes generally give much better results. We also show curves where we decreased the relative normalization of twist-4 to twist-3, -A1 f f N ,to about 30% below the standard value of 5.1. With this value, which is still consistent with the theoretical error bars, the magnetic form factors can be described quite nicely. In particular we can reproduce the correct Q2 dependence in this region. For the electric form factor the results, now including spin flip amplitudes, also look reasonable. We would like to stress that these first results have to be considered as a demonstration of viability of the approach. A quantitative description requires the calculation of a, corrections to the parton side of the sum rule. Recently new Jefferson Lab data7 for the ratio F 2 fF1 has been discussed intensively. The data indicates that this ratio behaves like 1f Q rather than the expected 1/Q2 for intermediate Q2. In Fig. 4 we show the LCSR result for QF2 f F l for the proton versus data from Jefferson We note that the LCSR prediction for the ratio QFAIF1 is indeed flat in a broad region. References 1. V. M. Braun, A. Lenz, N. Mahnke and E. Stein, Phys. Rev. D 65,074011
(2002). 2. V. Braun, R. J . Fries, N. Mahnke and E. Stein, N d . Phys. B 589, 382 (2000). 3. L. Andivahis et al., Phys. Rev. D 50, 5491 (1994). 4. A. Lung et al., Phys. Rev. Lett. 70, 718 (1993). 5. M. K. Jones et al., Phys. Rev. Lett. 84, 1398 (2000). 6. 0. Gayou et al., Phys. Rev. C 64, 038202 (2001). 7. 0. Gayou et al. Phys. Rev. Lett. 88, 092301 (2002).
ELECTROWEAK PROPERTIES OF THE NUCLEON IN A CHIRAL CONSTITUENT QUARK MODEL S. BOFFI AND M. RADICI Dipartimento di Fisica Nucleare e Teorica, Universitd d i Pavia, and INFN, Sezione d i Pavia, I-27100 Pavia, Italy L. GLOZMAN, W. PLESSAS AND R.F. WAGENBRUNN Institut fur Theoretische Physik, Universitat Graz, A-SO10 Graz, Austria W. KLINK Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242, USA Results for all elastic electroweak nucleon form factors are presented for the chiral constituent quark model based on Goldstone-boson-exchange dynamics. The calculations are performed in a covariant framework using the point-form approach to relativistic quantum mechanics. The direct predictions of the model yield a remarkably consistent picture of the electroweak nucleon structure.
We present results for the elastic electroweak nucleon observables as a progress report of a more comprehensive programme aiming at a consistent description of the electroweak properties of baryons at low energy. The theoretical context is represented by the chiral Constituent Quark Model (CQM) based on the Goldstone-boson exchange (GBE) quark-quark interaction, that is induced by the spontaneous chiral symmetry breaking in QCD and that accurately reproduces the baryon spectrum of light and strange flavors The dynamics of quarks inside the nucleon is essentially relativistic. Therefore, we have adopted the point-form realization of relativistic quantum mechanics, where the boost generators are interaction-free and make the theory manifestly covariant 2 . The electromagnetic photon-quark interaction is assumed point-like, but in point-form the momentum delivered to the nucleon is different from the one delivered to the struck quark; hence, we will name this approach the Point-form Spectator Approximation (PFSA) 3 . The quark wave functions deduced from fitting the baryon spectrum are used as input and no further parameter is introduced, since quarks are considered point-like and the point-form allows for an exact calculation of all boosts required by a covariant description. Results have recently been published for electromagnetic *, axial and pseudoscalar nucleon form factors. They are summarized here in Figs. 1-2, and in Tab. 1. The agreement with experimental data is remarkable and it indicates that by a proper choice of low-energy degrees of freedom a quark model is capable
'.
367
368 1.5
.,
/
1.25
1 0.75
0.5 ,
1.2
-I
1
Y
0.8 0.6 1.2 1
0.8 0.6 10 -2
10
-'
1 O'(GeV/c)'
Figure 1. Proton electric and magnetic form factors. Top and middle panels: ratios of electric ( G C ) and magnetic proton form factors to the standard dipole parametrization G D . Bottom panel: ratio of GC to G L . PFSA predictions of the GBE CQM (solid lines) are compared with nonrelativistic results (dashed lines) and experiment. In the top and middle panels the experimental data are from Ref. In the bottom panel recent data from TJNAF (filled triangles) are shown together with various older data points (see Ref. and references therein). All the ratios are normalized to 1 at Q2 = 0.
(GL)
'.
Table 1. Proton and neutron charge radii and magnetic moments as well as nucleon axial radius and axial charge. Predictions of the GBE CQM in PFSA (third column), in nonrelativistic approximation (NFUA, fourth column), and with the confinement interaction only (last column). Exp. 0.780(25) -0.113(7) 2.792847337(29) lo -1.91304270(5) lo 0.635(23) l 1 1.255f'O.006 lo
PFSA 0.81 -0.13
I NFUA I I
0.10 -0.01
I
Conf. 0.37 -0.01
;;lfig
369
0.1 0.08 0.06 0.04 0.02 0 -0.02 -0.04
2 1.75 1.5 1.25 1 0.75 0.5 0.25 0 0
1.2 1.1 1 0.9 0.8 0.7 0.6 -2 10
1
2
0
3 4 QZ( GeV/c)'
1
QZ( GeV/c)*
4 Q2(GeV/c)'
10 10 -l
2
""""
'
"-
'
10-1
""""
'
"
1
Q'(GeV/c)'
Figure 2. Left panel: neutron electric and magnetic form factors; in the top panel, G;; in the bottom panel, ratio of G& to the standard dipole parametrization G o , normalized to 1 at Q2 = 0; solid and dashed lines as in Fig. 1; the dot-dashed line represents the PFSA results for the case with confinement only; experimental data are from Ref. l 2 (top) and Ref. l3 (bottom). Right panel: nucleon axial and induced pseudoscalar form factors G A and G p , respectively; the PFSA predictions of the GBE CQM are always represented by solid lines; in the top panel, a comparison is given to the nonrelativistic results (dashed) and to the case with a relativistic current operator but no boosts included (dot-dashed); experimental data are shown assuming a dipole parameterization with the axial mass value M A deduced from pion electroproduction (world average: squares, Mainz experiment l 1: circles) and from neutrino scattering l4 (triangles); in the bottom panel, the dashed line refers to the calculation of G p without any pion-pole contribution; the experimental data are from Ref. 15.
of describing the spectroscopy and the low-energy dynamics of baryons at the same time. However, a more detailed comparison with data shows that there
370
is still room for quantitative improvements, e.g. by considering two-body electromagnetic current operators and constituent quark sizes. References
L.Ya. Glozman et al., Phys. Rev. D 58,094030 (1998). W.H. Klink, Pbys. Rev. C 58,3587 (1998). S. Boffi et al., hep-ph/0108271,Eur. Phys. J A, in press. R.F. Wagenbrunn et al., Phys. Lett. B 511,33 (2001). L.Ya. Glozman et a]., Phys. Lett. B 516,183 (2001). L. Andivahis et d.,Phys. Rev. D 50,5491 (1994); R.C. Walker et al., Phys. Rev. D 49, 5671 (1994); A.F. Sill et d.,Phys. Rev. D 48, 29 (1993); G. Hohler et al., Nucl. Phys. B 114,505 (1976); W. Bartel et al., Nucl. Phys. B 58,429 (1973). 7. M.K. Jones et al., Phys. Rev. Lett. 84,1398 (2000). 8. K. Melnikov and T. van Ritbergen, Phys. Rev. Lett. 84,1673 (2000). 9. S. Kopecky et al., Phys. Rev. Lett. 74,2427 (1995). 10. D.E. Groom et al., Eur. Phys. J. C15, 1 (2000). 11. A. Liesenfeld et al., Phys. Lett. B 468,20 (1999). 12. T. Eden et al., Pbys. Rev. C 50, R1749 (1994); M. Meyerhoff et al., Phys. Lett. B 327,201 (1994); A. Lung et al., Phys. Rev. Lett. 70,718 (1993); C. Herberg et al., Eur. Phys. J. A 5, 131 (1999); I. Passchier et al., Phys. Rev. Lett. 82,4988 (1999); D. Rohe et al., Phys. Rev. Lett. 83,4257 (1999); M. Ostrick et al., Phys. Rev. Lett. 83,276 (1999); J. Becker et d.,Eur. Phys. J. A 6,329 (1999). 13. P. Markowitz et al., Phys. Rev. C 48,R5 (1993); S. Rock et al., Phys. Rev. Lett. 49,1139 (1982); E.E.W. Bruins et al., Phys. Rev. Lett. 75, 21 (1995); H.G m et al., Pbys. Rev. C 50,R546 (1994); A. Lung et al., Phys. Rev. Lett. 70,718 (1993); H. Anklin et al., Phys. Lett. B 336, 313 (1994); H.Anklin et al., Phys. Lett. B 428,248 (1998). 14. T. Kitagaki et al., Phys. Rev. D 28,436 (1983). 15. G. Bardin et al., Phys. Lett. B 104,320 (1981); Seonho Choi et al., Phys. Rev. Lett. 71,3927 (1993). 1. 2. 3. 4. 5. 6.
NUCLEON HOLOGRAM WITH EXCLUSIVE LEPTOPRODUCTION
A.V. BELITSKY Department of Physics, University of Maryland, College Park, MD 20742-4111,
USA
D. MULLER Fachbereich Physik, Universitat Wuppertal, 0-42097 Wuppertal, Germany
Hard exclusive leptoproductions of real photons, lepton pairs and mesons are the most promising tools to unravel the three-dimensional picture of the nucleon, which cannot be deduced from conventional inclusive processes like deeply inelastic scattering.
1. From macro to micro Why do we see the world around us the way it is? Human eyes can detect electromagnetic waves in a very narrow range of wavelength, A, w 0.4 - 0.7pm, which we call visible light. The light from a source, say the sun, is reflected from the surface of macro-objects and is absorbed by the eye’s retina which transforms it into a neural signal going t o the brain which forms the picture. The same principle is used in radars which detect reflected electromagnetic waves of a meter wavelength. The only requirement t o “see” an object is that the length of resolving waves must be comparable t o or smaller than its size. The same conditions have to be obeyed in case one wants t o study the microworld, e.g., the structure of macromolecules (DNA, RNA) or assemblies (viruses, ribosomes). Obviously, when one puts a chunk of material in front of a source of visible light, see Fig. 1, the object merely leaves a shadow on a screen behind it and one does not see its elementary building blocks, i.e., atoms. Obviously, visible light is not capable t o resolve the internal lattice structure of a crystal since the size of an individual atom, say hydrogen, is of order ratom, ( a e m m e ) - ’ (10 KeV)-l and the light does not diffract from it. Therefore, to “see” atoms in crystals one has to have photons with the wavelength A, 5 ratom,or equivalently, of
-
371
372
Figure 1. Left: A beam of visible light does not resolve the crystal’s structure. Right: A n X-ray beam does and creates a diffraction pattern o n the photo-plate.
the energy E7 2 r,:,. To do this kind of “nano-photography” one needs a beam of X-rays which after passing through the crystal creates fringes on a photo-plate, see Fig. 1. Does one get a three-dimensional picture from such a measurement? Unfortunately, no. In order to reconstruct atomic positions in the crystal’s lattice one has to perform an inverse Fourier transform. This requires knowledge of both the magnitude and the phase of diffracted waves. However, what is measured experimentally is essentially a count of number of X-ray photons in each spot of the photo-plate. The number of photons gives the intensity, which is the square of the amplitude of diffracted waves. There is no practical way of measuring the relative phase angles for different diffracted spots experimentally. Therefore, one cannot unambiguously reconstruct the crystal’s lattice. This is termed as “The Phase Problem”. None of techniques called to tackle the problem provides a parameter-free answer. When we study hadronic matter at the fundamental level we attempt to perform the “femto-photography” of the interior constituents (quarks and gluons) of strongly interacting “elementary” particles such as the nucleon. Quantum ~ p w p adynamics, the theory of strong interaction, is not handy at present to solve the quark bound state problem. Therefore, phenomenological approaches, based on accurate analyses of high-energy scattering experimental data and making use of rigorous perturbative QCD predictions, are indispensable for a meticulous understanding of the nucleon’s structure. As we discuss below most of high-energy processes resolving the nucleon content, such as described in terms of form factors and inclusive parton densities, suffer from the same “Phase Problem” and therefore they lack the opportunity to visualize its three-dimensional structure. A panacea is found in newborn generalized parton distributions ’, which are measurable in exclusive leptoproduction experiments.
373
2. Form factors Nucleon form factors are measured in the elastic process CN 4 C’N’. Its amplitude is given by the lepton current L,(A) = Gt(k - A)y,ue(k) interacting via photon exchange with the nucleon matrix element of the quark electromagnetic current j,,(z) = C , e,q(z)y,q(z):
Here the matrix element of the quark current is decomposed in terms of Dirac and Pauli form factors (A = p2 - P I ) , accompanied by the Dirac bilinears h, = 21N(P2)ypUN(Pl)and el, = 2 1 ~ ( ~ 2 ) i a , ~ A ~ u ~ ( ~ 1In ) the Breit frame pi = -pi = A/2 there is no energy exchange El = E2 = E and thus relativistic effects are absent. The momentum transfer is threedimensional A2 = -A2, so that -#
(P2ljO(O)lPl) =
(PZ(I(O)IPI)
I
i = ---$;[A 2MN
x Z]@IGM(--A~) ,
(2)
+
are expressed in terms of Sachs electric G E ( A ~ ) = F1(A2) A2/(4M;)Fz(A2) and magnetic G M ( A ~ = ) F1(A2) F2(A2) form factors. Introducing the charge q = J d 3 Z j o ( Z ) and magnetic moment ii = 1d 3 Z [ Zx ;](z) operators, one finds the normalization
6
6
+
The interpretation of Sachs form factors as Fourier transforms of charge and magnetization densities in the nucleon requires to introduce localized nucleon states in the position space 1Z) as opposed to the plane-wave states used above Ip),
Here a very broad wave packet Q(p3 = const is assumed in the momentum space. Then the charge density p(Z) of the nucleon, localized at Z = 0, is
(2 = OIjo(Z)~Z= 0)
cT73
= @;@,lp(.’) = p;+1 J -e-ib’?GE( -&2)
1
(5)
and similar for the magnetic form factor. The famous Hofstadter’s experiments established that the proton is not a point-like particle ppoint(Z) =
374 * Generalized panan dishibution at 11-0
* Parton density
Formfdctor
Figure 2. Probabilistic interpretation of form factors, parton densities and generalized parton distributions at 1) = 0 in the infinite momentum frame p , + 00.
S3(?) which would have GFint = const, but rather G E ( - ~ ’ ) z (1 +
L . ” T & / with ~ ) -the ~ mean square radius T N x 0.7fm.
The Breit frame is not particularly instructive for an interpretation of high-energy scattering. Here an infinite momentum frame (IMF) is more useful, see discussion below. In this frame, obtained by a z-boost, the nucleon momentum is p , = (p1 p z ) , 00. In the IMF one builds a nucleon state localized in the transverse plane at b l = (2,y)
+
--f
Then one finds that the transverse charge distribution of the nucleon wave packet, see Fig. 2, is given by the two-dimensional Fourier transform of form factors ( P a b l = Olj,
Fi (-A:)+
(bl) I P Z , bl = 0) = h+
... .(7)
As previously one assumes a rather delocalized transverse momentum wave function CpL!D*(p, + A1/2)!D(pL- A l / 2 ) M 1. Thus, we can interpret form factors as describing the transverse localization of partons in a fast moving nucleon, irrespective of their longitudinal momenta and independent on the resolution scale. 3. Parton densities The deeply inelastic lepton-nucleon scattering LN amplitude 1 A N X = @Lp(q)(PXIjp(O)lP) 7
+
L’X probes, via the (8)
375
the nucleon with the resolution h/Q M (0.2fm)/(Q inGeV), set by the photon virtuality q2 = -Q2. Recalling that the nucleon’s size is r N 1fm, one concludes that for Q2 of order of a few GeV, the photon penetrates the nucleon interior and interacts with its constituents. The cross section of the deeply inelastic scattering is related, by the optical theorem, to the imaginary part of the forward Compton scattering amplitude N
The very intuitive parton interpretation has its clear-cut meaning in the IMF. A typical interaction time of partons is inversely proportional to the energy deficit of a given fluctuation of a particle with the energy EO and three-momentum po = ( p L o , z o p Z ) into two partons with energies E1,2 and three-momenta p 1 , 2= ( P ~ z1,2pZ). ~ , ~ It , scales, for p , -+00, as
A t - - =1 AE
1
P.2 4 0O. (10) P ~ o / x o- P ~ , / X I- ~ : 2 / ~ 2 Therefore, one can treat partons as almost free in the IMF due to the time dilation. The virtual photon “sees” nucleon’s constituents in a frozen state during the time of transiting the target which is, thus, describable by an instantaneous distribution of partons. Here again the analogy with X-ray crystallography is quite instructive: Recall that an X-ray, scattered off atoms, reveals crystal’s structure since rapid oscillations of atoms in the lattice sites can be neglected. Atoms can be considered being at rest during the time X-rays cross the crystal. The transverse distance probed by the virtual photon in a Lorentz contracted hadron, is of order h z l 1/Q, see Fig. 2. One can conclude therefore that simultaneous scattering off an nparton cascade is suppressed by an extra power of (l/Qz))”-’. The leading contribution to daDIs is thus given by a handbag diagram, i.e., the photonsingle-quark Compton amplitude. The character of relevant distances in the Compton amplitude (9) is a consequence of the Bjorken limit which implies large Q2 (small distances) and energies v = p . q (small times) at fixed ZB = Q2/(2v). By going to the target rest frame one immediately finds that at large Q2 the dominant contribution comes from the light-cone distances z 2 M 0 (l/Q2) between the points of absorption and emission of the virtual photon in (9) because zl/(Mzg), Z+ M ~ B / Q ~ . Since the hard quark-photon subprocess occupies a very small spacetime volume but the scales involved in the formation of the nucleon are
EO- El
N
- E2
N
N
-
376
much larger, hence, they are uncorrelated and will not interfere. The quantum mechanical incoherence of physics at different scales results into the factorization property of the cross section (9),
where fg is a parton distribution, - the density of probability to find partons of a given longitudinal momentum fraction x of the parent nucleon with transverse resolution 1/&,
1
1
(PlQ(Oh+q(z-n)lP) = 2P+
dx { f9(x)e--ixz-p+ - fQ(x)eixz-P+} . (12)
No information on the transverse position of partons is accessible here, Fig. 2.
4. Generalized parton distributions Both observables addressed in the previous two sections give only onedimensional slices of the nucleon since only the magnitude of scattering amplitudes is accessed in the processes but its phase is lost. These orthogonal spaces are probed simultaneously in generalized parton distributions (GPDs), which arise in the description of deeply virtual Compton scattering (DVCS) l N Py*N --+ PN’y in the Bjorken limit. In the same spirit as in deeply inelastic scattering, the latter consists of sending q2 = (q1 q2)’/4 4 --oo to the deep Euclidean domain while keeping A2 E ( p 2 - p 1 )2 << -q2 small and = - q 2 / p . q fixed, p = p l p z . By --+
+
<
+
the reasoning along the same line as in the previous section one finds that the Compton amplitude factorizes into GPDs parametrizing the twist-two light-ray operator matrix element (P214(-z-n)y+dz-
n>lPl>
and a handbag coefficient function, so that one gets
377
P.
Figure 3.
+
Geometric picture of deeply virtual Compton scattering.
where Fq = Hq, Eq and the contribution from a crossed diagram is omitted. GPDs depend on the s-channel momentum fraction x, measured with respect to the momentum p , and t-channel fraction q z q . A / q . p , which is the longitudinal component of the momentum transfer A M q p + A l , as well as its square A2 N” - (A: 4M$q2) / (1 - q 2 ) . Due to the reality of the final state photon q M -<. A geometric picture underlying DVCS is as follows, see Fig. 3. The electric field of lepton’s virtual fluctuation C -+ l’y* accelerates a quark localized in the transverse area ( 6 . ~ 1 ) ~ 1/Q2 at the impact parameter b l and carrying a certain momentum fraction of the parent nucleon. The accelerated parton tends to emit the energy via electromagnetic radiation and fall back into the nucleon, see Fig. 3. The incoming-outgoing nucleon system is localized at the center of coordinates b l = 0, however, due to non-zero longitudinal momentum exchange in the t-channel the individual transverse localizations of incoming and outgoing nucleons are shifted in the transverse plane by amountsa A b l q( 1 q )b l and Ab; q( 1 - q )b l , respectively 2 . Generally, GPDs are not probabilities rather they are the interference of amplitudes of removing a parton with one momentum and inserting it back with another. In the limit A = 0 they reduce to inclusive parton densities and acquire the probabilistic interpretation. This is exhibited in a most straightforward way in the light-cone formalism 3, where one easily identifies the regions -1 < x < -7 and 11 < x < 1 with parton densities while -q < x < 11 with distribution amplitudes. This latter domain precludes the density interpretation for q # 0. The first moment of GPDs turns into form factors (1). The second moment of Eq. (13) gives form factors of the quark energy-momentum
+
N
N
+
N
aNote the difference in the definition of our impact parameter space GPDs as compared to Ref. ’. In our frame pL2= -pll = A l / 2 . We define the Fourier transform with respect to A 1 which has its advantages that bL does not depend implicitly on 77.
378 splitter lens
laser
inmow em,,
reference beam
hologaphtc plate
k u n i diffraclul vtfn panoii
Figure 4. Left: Conventional setup for taking the holographic picture. Right: Nucleon hologram with leptoproduction of a photon: interference of the Bethe-Heitler (reference) and DVCS (sample) amplitudes.
QLv
qT{cLDv)q.Since gravity couples to matter via Q,, = these form factors are the ones of the nucleon scattering in a weak gravitational field
tensor,
s
=
Ad4z&GJF)L(2), &7rY
(P2lQ,ulPl) = A(A2)h{,Pv}
+ B(A2)e{,Pu} + C(A2)A,AU.
(15)
Analogously to the previously discussed electromagnetic case, the combination A(A2) A2/(4M&)B(A2)arising in the 8 0 0 component measures the mass distribution inside the nucleon 5 . It is different from the charge distribution due to presence of neutral constituents inside hadrons not accounted in electromegnetic form factors. The gravitomagnetic form factor A(A2) B ( A 2 ) at zero recoil encodes information on the parton angular = momentum d3.’ ‘.[ x 6](z)expressed in terms of the momentum flow operator 00i = 0i in the nucleon and gives its distribution when Fourier transformed to the coordinate space. These form factor are accessible once GPDs are measured:
+
+
s
dz z H(z,v , A2) = A(A2)
+ v2C(A2),
dz z E ( z ,77, A2) = B ( A 2 ) - q2C(A2)
GPDs regain a probabilistic interpretation once one sets 71 = 0 but P I # 0 6*7. When Fourier transformed to the impact parameter space they give a very intuitive picture of measuring partons of momentum fraction z at the impact parameter b l with the resolution of order 1/Q set by the photon virtuality in the localized nucleon state (6),
379
To visualize it, see Fig. 2, one can stick to the Regge-motivated ansatz H(rc,O, -A:) z-~R(-*:)(~ - z ) with ~ a linear trajectory cr~(-A:) = where a ~ ( 0 x ) 0.5 and a’ FS 1 GeV2. c x ~ ( 0) N
5. Hard leptoproduction of real photon and lepton pair
The light-cone dominance in DVCS is a consequence of the external kinematical conditions on the process in the same way as in deeply inelastic scattering. Therefore, one can expect precocious scaling starting as early as at -q2 1GeV2. It is not the case for hard exclusive meson production, giving access to GPDs as well, where it is the dynamical behavior of the short-distance parton amplitude confined to a small transverse volume near the light cone that drives the perturbative approach to the process. Here the reliability of perturbative QCD predictions is postponed to larger momentum transfer. Although GPDs carry information on both longitudinal and transverse degrees of freedom, their three-dimensional experimental exploration requires a complete determination of the DVCS amplitude, i.e., its magnitude and phase. One way to measure the phase at a given spot is known as holography, for visible light. This technology allows to make threedimensional photographs of objects, see Fig. 4: The laser beam splits into two rays. One of them serves as a reference source and the other reflects from the object’s surface. The reflected beam, which was in phase with the reference beam before hitting the “target”, interferes with the reference beam and forms fringes on the plate with varying intensity depending on the phase difference of both. (Unfortunately, the same method cannot be used for X-ray holography of crystals and scattering experiments due to the absence of practical “splitters”.) For the exclusive leptoproduction of a photon, however, there are two contributions to the amplitude: the DVCS one A D ~ ~wes are , interested in, and ABHfrom the ‘contaminating’ Bethe-Heitler (BH) process, in which the real photon spills off the scattered lepton rather than the quark, see Fig. 4. The BH amplitude is completely known since the only long-distance input turns out to be nucleon form factors measured elsewhere. The relative phase of the amplitudes can be measured by the interference of DVCS and BH amplitudes in the cross sec2 ~ADVCS A B H ~and, thus, the nucleon hologram can tion dUeN-,e/”-, be taken. The most straightforward extraction of the interference term is achieved by making use of the opposite lepton charge conjugation properties of DVCS and BH amplitudes. The former is odd while the latter N
-
+
380
Figure 5 . (right).
What is extractable from DVCS (left) and DVCS lepton pair production
is even under change of the lepton charge. The unpolarized beam charge asymmetry gives daelv-etN/r(+ee)
-
daehr+e~w,(-ee)
=
+
(ADVCS A;>vcs) ABH
and measures the real part of the DVCS amplitude modulated by the harmonics of the azimuthal angle between the lepton and photon scattering planes 4; If on top of the charge asymmetry one further forms either beam or target polarization differences, this procedure would allow to cleanly extract the imaginary part of the DVCS amplitude where GPDs enter in diverse combinations. These rather involved measurements have not yet been done. Luckily, since the ratio of BH to DVCS amplitude scales like [ A 2 / q f ( l- ~ ) ] l / ~ / for y , large y or small -A2, it is safe to neglect ( A D V C S ~ ~ as compared t o other terms. Thus, in such kinematical settings one has access to the interference in single spin asymmetries, ‘1’.
d ~ e r J - . e ~ w y ( + A e) daeru+eilvjy(-Ae)
M
(ADVCS- A;>vcs) ABH
which measure GPDs directly on the line x = E a s shown in Fig. 5. Experimental measurements of these asymmetries were done by HERMES l1>l3 and CLAS l 2 collabarations. The comparison to current GPD models is demonstrated in Fig. 6. In order to go off the diagonal x = J one has to relax the reality constraint on the outgoing y-quantum, i.e., it has to be virtual and fragment into a lepton pair L L with invariant mass qg > 0. Thus, one has to study the process.lN -+ PLLN’. In these circumstances, the skewedness parameter r] independently varies for fixed Bjorken variable since J x -v(/q:l - yZ)/(/y?/ y;), and one is able to scan the three-
+
38 1 0.6r
. 58
= 0.11 0.4
(b)
5B = 0.12
-Az =
0 . 2 7 GeV'
'
-0.2.
-0.4 -0.6'
HERMES '
-3
-2
-0.4.
PRELIMINARY HERMES
--/
l1
l3
I
-1
0
1
2
3
4;
4;
Figure 6. Beam spin asymmetry (a) in e + p + e+mand unpolarized charge asymmetry (b) from HERMES with E = 27.6 GeV are predicted making use of the complete twistthree analysis for input GPDs from Ref. ': model A without the D-term (solid) and C with the D-term (dashed) in the Wandzura-Wilczek approximation lo as well as the model B with the D-term (dash-dotted) and included quark-gluon correlations. The dotted lines on the left and right panels show 0.23 sin 4; and -0.05+0.11 cos 4!, HERMES fits, respectively. Note that a toy model for quark-gluon correlations while only slightly changing the beam asymmetry, however, strongly alter the charge asymmetry.
dimensional shape of GPDs, see Fig. 5. Unfortunately, the cross section for DVCS lepton pair production is suppressed by azm as compared to DVCS and also suffers from resonance backgrounds, see, e.g., 14. Finally, perturbative next-to-leading (NLO) and higher-twist effects are shortly discussed. Estimates of the former are, in general, model dependent. NLO contributions to the hard-scattering amplitude l5 of a given quark species are rather moderate, i.e., of the relative size of 20%, however, the net result in the DVCS amplitude can be accidentally large ',l6. This can be caused by a partial cancellation that occurs in tree amplitudes. Evolution effects l7 in the flavor non-singlet sector are rather small. In the case of gluonic GPD models we observed rather large NLO corrections to the DVCS amplitude for the naive scale setting = -qq '. For such models one also has rather strong evolution effects, which severely affect LO analysis. However, one can tune the factorization scale p~ so that to get rid of these effects. The renormalon-motivated twist-four and target mass corrections l9 await their quantitative exploration.
''
References 1. D. Muller et al., Fortschr. Phys. 42 (1994) 101; X. Ji, Phys. Rev. D 55 (1997) 7114; A.V. Radyushkin, Phys. Rev. D 56 (1997) 5524. 2. M. Diehl, hep-ph/0205208; 3. M. Diehl et al., Nucl. Phys. B 596 (2001) 33; S.J. Brodsky, M. Diehl, D.S. Hwang, Nucl. Phys. B 596 (2001) 99. 4. X. Ji, Phys. Rev. Lett. 78 (1997) 610.
382
A.V. Belitsky, X. Ji, Phys. Lett. B 538 (2002) 289. M. Burkardt, Phys. Rev. D 62 (2000) 071503. J.P. Ralston, B. Pire, hep-ph/0110075. A.V. Belitsky, D. Muller, A. Kirchner, Nucl. Phys. B 629 (2002) 323. M. Diehl et al., Phys. Lett. B 411 (1997) 193; A.V. Belitsky et al., Nucl. Phys. B 593 (2001) 289. 10. A.V. Belitsky, D. Muller, Nucl. Phys. B 589 (2000) 611; N. Kivel et al., Phys. Lett. B 497 (2001) 73; A.V. Radyushkin, C. Weiss, Phys. Rev. D 63 (2001) 5. 6. 7. 8. 9.
114012. 11. 12. 13. 14. 15.
A. Airapetian et al. (HERMES Coll.), Phys. Rev. Lett. 87 (2001) 182001. S. Stepanyan et al. (CLAS Coll.), Phys. Rev. Lett. 87 (2001) 182002. F. Ellinghaus, these proceedings. E.R. Berger, M. Diehl, B. Pire, Eur. Phys. J. C 23 (2002) 675. A.V. Belitsky, D. Muller, Phys. Lett. B 417 (1997) 129; L. Mankiewicz et al., Phys. Lett. B 425 (1998) 186; X. Ji, J. Osborne, Phys. Rev. D 58 (1998)
094018. 16. A. Freund, M. McDermott, Phys. Rev. D 65 (2002) 074008. 17. D. Muller, Phys. Rev. D 49 (1994) 2525; A.V. Belitsky, D. Muller, Nucl. Phys. B 537 (1999) 397; A.V. Belitsky, A. Freund, D. Muller, Nucl. Phys. B 574 (2000) 347. 18. A.V. Belitsky, A. Schafer, Nucl. Phys. B 527 (1998) 235. 19. A.V. Belitsky, D. Muller, Phys. Lett. B 507 (2001) 173.
383
-
Anatoly Radyushkin, Andrei Belitsky,Christian Weiss, and Latifa Elouadrhiri
Riad Suleiman and Steve Wood
DEEPLY VIRTUAL COMPTON SCATTERING AT JEFFERSON LAB, RESULTS AND PROSPECTS LATIFA ELOUADRHIRI Physics Division, Jefferson Lab, Newport News, Virginia, USA E-mail:
[email protected] Recent results from the Deeply Virtual Compton Scattering (DVCS) program at Jefferson Lab will be presented. Approved dedicated DVCS experiments at 6 GeV will be discussed.
1
INTRODUCTION
The recently developed formalism of “Generalized Parton Distributions” (GPDs) showed that information on quark-quark correlations, the transverse quark momentum distribution, and contributions of correlated quarkantiquark pairs (mesons) to the nucleon wave function can be obtained in hard exclusive leptoproduction experiments. GPDs provide a unifying framework for the interpretation of an entire set of fundamental quantities of hadronic structure, such as,the vector and axial vector nucleon form factors, the pcr larized and unpolarized parton distributions, and the spin components of the nucleon due t o orbital excitations. Deeply Virtual Compton Scattering (DVCS) is one of the key reactions to determine the GPDs experimentally, and it is the simplest process that can be described in terms of GPDs. One of the first experimental observation of DVCS was obtained from the recent analysis of CLAS data with a 4.2 GeV polarized electron beam in a kinematical regime near Q2= 1.5 GeV2 and ZB = 0.22 New measurements at higher energies are currently being analyzed, and dedicated experiments are planned. The high luminosity available for these measurements will make it possible to determine details of the Q2,ZB, and t dependences of GPDs. ‘j2v3
‘.
2
FIRST OBSERVATION OF EXCLUSIVE DVCS WITH THECLASDETECTOR
The DVCS/Bethe-Heitler (BH) interference has recently been measured using the CEBAF Large Acceptance Spectrometer in Hall B at Jefferson Lab *. The data were collected as a by-product of the 1999 run with a 4.25 GeV polarized electron beam. At energies above 4 GeV, the CLAS acceptance covers a wide
384
385
VCS
BH
Figure 1. Feynman diagrams for VCS and BetheHeitler processes contributing to the amplitude of ep -t epy scattering.
range of kinematics in the deep inelastic scattering domain (W 2 2 GeV and Q2 2 1 GeV2). The open acceptance of CLAS and the use of a single electron trigger ensures event recording for all possible final states. This experiment measures DVCS via the interference with the Bethe-Heitler (figure 1. At beam energies accessible at Jefferson Lab, the BH contribution in the cross section is predicted to be several times larger than the DVCS contribution in most regions of the phase space. The dominant BH process can be turned into an advantage by using a longitudinally polarized electron beam: one can measure the helicity-dependent interference term that is proportional to the imaginary part of the DVCS amplitude. In this case the pure real BH contribution is subtracted out in the cross section difference. For the present DVCS analysis, electron and proton were both detected in the CLAS detector, the reaction Zp -+ epX was studied and the number of single photon final states was extracted by fitting the missing mass ( M i ) distributions. The beam spin asymmetry was then calculated as:
Here P, is the beam polarization and, N T ( - ) is the extracted number of Z' -+ e p y events at positive (negative) beam helicity. The resulting qk dependence is shown in figure 2. A fit to the function
+
F ( 4 ) = Asin4 Bsin24 (2) yields A = 0.217 f 0.031 and B = 0.027 f 0.022. If the handbag diagram dominates, as expected in the Bjorken regime, B should vanish and only the contribution from transverse photons should remain, described by the parameter A. The GPD analysis including twist-3 contribution shows sensitivity of these data to ijGq correlations 5.
386 ,..........__ ...,_
0.41
..............
-0.4 l
0
50
u
l
100
,
l
150 0 9
,
l
200
,
l
250
,
l
300
,
L
350
deg
Fiwre 2. q5 dependence of the Zp --t em beam spin asymmetry at 4.25 GeV. Data are integrated over the range of Q2 from 1 to 2 GeV2, Z B fIom 0.13 to 0.35 (with the condition W > 2 GeV) and -t from 0.1 to 0.3 GeV2. The shaded region is the range of the fit function A(+) defined by statistical and systematical uncertanties. The curves are model calculations according to Ref.
’.
3
DEDICATED DVCS EXPERIMENTS AT JEFFERSON LAB
There are two dedicated DVCS experiments planned to run using the 6 GeV polarized electron beam. Both experiments plan to detect all three particles in the final state, the scattered electron, the recoil proton, and the photon. The first experiment E00-110 is a Hall A experiment which is expected to run in 2003. The DVCS beam spin asymmetries and cross section differences will be measured at three Q2 intervals, for a fixed interval of XB. The experiment will provide a precise check of the Q2dependence of the ep + epy cross section differences (for different beam helicities). The second experiment E01-113 is a dedicated CLAS DVCS experiment. The main goal of this experiment is to measure the t , 4, and X B dependence of the beam spin asymmetry for several fixed Q2 bins. This quantity is sen-
387
sitive to the model description of the GPDs. This will be the first time this dependence will be studied with high sensitivity using the DVCS process. A second goal will be to extract the helicity-dependent cross section difference, which directly determines the imaginary part of the DVCS amplitude. The results of these two experiments, Hall A and CLAS, on the Zp -i em cross section will allow tests of the &'-dependence to check the scaling behavior. As CLAS covers a broad kinematic range, we will be able to test the Q' dependence for different XB. This will verify that we are in a regime where a direct interpretation of the results in terms of GPDs is possible. Observation of significant scaling violations would provide important input for the analysis in terms of higher twist effects. 4
SUMMARY
A first measurement of the beam spin asymmetry in the exclusive electroproduction of real photons in the deep inelastic regime was presented. We see a clear asymmetry, as expected from the interference of the DVCS and BH processes. It has been shown that our results can be accomodated within a GPD analysis '. This supports the expectations that DVCS will allow access to GPDs at relatively low energies and momentum transfers. This opens up a new avenue for the study of nucleon structure which is inaccessible in inclusive scattering experiments. Dedicated DVCS experiments at 6 GeV electron beam energy are planned, which will allow significant expansion of the Q2 and ZJJ range covered in these studies. The high luminosity available for these measurements will make it possible to map out details of the Q', ZB, and t dependences of GPDs. References 1. D. Muller et al., Fortschr. Phys. 42 (1994) 2,101. 2. X. Ji, Phys. Rev. Lett. 78, 610 (1997); Phys. Rev. D 55, 7114 (1997). 3. A.V. Radyushkin, Phys. Lett. B 380, 417 (1996); Phys. RRv. D 56, 5524 (1997). 4. S. Stepanyan et al., Phys.Rev.Lett., 87 182002 (2001). 5. A. Belitsky, D. Muller, and A. Kirchner, Nucl.Phys., B629,323 (2002). 6. P. Bertin, C. HydeWright, F. Sabati6 et aZ., CEBAF experiment EOO110. 7. V. Burkert, L. Elouadrhiri, M. Garson, S. Stepanyan et al., CEBAF experiment Eo1-113.
TWIST-3 EFFECTS IN DEEPLY VIRTUAL COMPTON SCATTERING MADE SIMPLE C . WEISS Institut fiir Theoretische Physik Universitat Regensburg, 0-93053 Regensburg, Germany E-mail:
[email protected] We show that electromagnetic gauge invariance requires a “spin rotation” of the quarks in the usual twist-2 contribution t o the amplitude for Deeply Virtual C o m p ton Scattering. This rotation is equivalent to the inclusion of certain kinematical twist-3 (“Wandzura-Wilczek type”) terms, which have been derived previously using other methods. The new representation of the twist-3 terms is very compact and allows for a simple physical interpretation.
Deeply Virtual Compton Scattering (DVCS), r * ( q ) + N ( p )+ r ( q ’ ) + N ( p ’ ) at large q2 and finite t = (p’--p)’, is the simplest process which could probe the generalized parton distributions (GPD’s) in the nucleon. New experimental results for spin and charge asymmetries of the cross section have been reported at this meeting, allowing for a first comparison of GPD models with data The crucial property of DVCS (and a number of other hard electroproduction processes) is that the amplitude can be factorized in a hard photonquark amplitude, and a soft matrix element containing the relevant information about the structure of the nucleon. Technically, this factorization can be accomplished using QCD expansion techniques familiar from the theory of deep-inelastic scattering. Originally only the contribution from twist2 operators was i n ~ l u d e d .It~ was realized that in this approximation the amplitude is not transverse (electromagnetically gauge invariant); the violation is proportional to the transverse component of the momentum transfer, which is not suppressed at large q 2 . A gauge invariant amplitude up to terms O ( t / q 2 )is obtained by including certain “kinematical” twist-3 contributions. These have been derived in various approaches: Momentum-space collinear e ~ p a n s i o n ,coordinatespace ~ light cone e x p a n s i ~ n , ~ and > ~ a parton-model based a p p r ~ a c hIn . ~the usual formulation the twist-3 terms are parametrized by auxiliary GPD’s given by certain integrals over the basic twist-2 GPD’s, much like the Wandzura-Wilczek part of the spin structure function g 2 ( x ) in inclusive DIS. In addition to restoring gauge invariance of the twist-2 contribution, the twist-3 terms give rise t o new helicity amplitudes and strongly influence the predictions for the spin and charge asymmetries of the DVCS cross section.8
388
389
twist-2
+ crossed
+ crossed
(4
(b) Figure 1.
In this talk I would like to point out that the kinematical twist-3 terms in the DVCS amplitude have a simple physical interpretation as being due to a “spin rotation” applied to the twist-2 quark density matrix in the n u c l e ~ n . ~ This allows for a very compact representation of the twist-3 effects. Most important, it shows that, in spite of the apparent complexity of the amplitude at twist-3 level, DVCS is still a LLsimple” process. The results reported here have been obtained in collaboration with A. V. Radyushkin (Jefferson Lab and Old Dominion U.) Consider virtual Compton scattering off an electron in QED at tree level, see Fig. la. It is well-known that transversality of the amplitude, q,T’, = 0 and T,,q; = 0, requires not only the Ward identities relating the electromagnetic vertex and the free-field propagator, but also the on-shell conditions for the external particles, i. e., the Dirac equations for the electron spinors. Turning now to DVCS off a hadron, the twist-2 contribution to the amplitude in QCD is given by exactly the same diagrams its Fig. l a , describing virtual Compton scattering off a free quark, only the wave functions of the initial and final particle have been replaced by the transition matrix element of the appropriate non-local quark/antiquark density matrix between the hadronic states, see Fig. lb. The twist-2 part of the latter is defined as
plus a similar contribution with ,y- -+ 75ys^(a and i -+fy5. The density matrix is presented here in perhaps somewhat unusual form, in coordinate space, with the quark/antiquark “ends” located at X f ,212 (X is the center coordinate, z the separation); i and j are the Dirac spinor indices. Here $ and .J, are
390
+ crossed Figure 2.
the quark fields (we omit the flavor labels), and the bilinear operator is really a traceless QCD string operator, see Ref.g for details. What is important is that this-twist-2 density matrix does not satisfy the freefield Dirac equations with respect to the quark/antiquark LLends”; the violation is proportional to the momentum transfer A = p’ - p . The reason is, simply put, that in the twist-2 operator in Eq.(l) the quark spin is projected on a fixed direction, determined by the vector z , while the Dirac equations require that the spin projection changes between the two ends in accordance with the momentum transfer between the quark lines.a As a consequence, the twist-2 part of the DVCS amplitude alone is not electromagnetically gauge invariant; the amplitude violates transversality by terms proportional to A. It is not difficult to see what must be done in order to fix this problem. We must rotate the spin projection of the quarks in the density matrix (1) such as to align it with the momenta of the incoming and outgoing quark ends. This is achieved by a position-dependent rotation with a matrixg
The modified density matrix is
(x
1 - A)
aIn the usual collinear expansion around a fixed light-like direction, the vector operator in Eq.(l) would have a large “plus” component, while the quark/antiquark ends have transverse momenta because of A, # 0.
391
plus the same with T~ -+ ~~7~ and 2 + i y 5 . This “rotated” form satisfies the Dirac equations with respect to the external ends, up to terms proportional to t , see Ref.g for details. As a result, the DVCS amplitude obtained with Eq.(3) is gauge invariant up to terms of order O ( t / q 2 ) . Schematically, our modification of the twist-2 contribution to the DVCS amplitude can be represented as in Fig.2, with the spin rotation as an “intermediate step” between the twist-2 density matrix and the free quark Compton amplitude. In the terminology of the light cone expansion, the spin rotation of Eq.(3) amounts t o the inclusion of certain twist-3 operators, which, however, are completely given in terms of total derivatives of twist-2 operators (“kinematical twist-3”). When substituting parametrizations for the basic twist-2 matrix elements, Eq. (3) reproduces the Wandzura-Wilczek type relations for the twist-3 GPD’s, which were derived previously using other techniques.6 Thus, all the complexity of the kinematical twist-3 effects in DVCS can be reduced t o the simple spin rotation of Eq.(3). The effect of kinematical twist-3 terms on DVCS observables have been discussed in the literature.8 The twist-3 terms affect in particular the spin and charge asymmetries of the cross section. The spin rotation representation could be helpful in developing a more intuitive understanding of the twist-3 effects in DVCS observables. This problem certainly deserves further study. C.W. is supported by a Heisenberg Fellowship from Deutsche Forschungsgemeinschaft (DFG). References
1. A. Airapetian et al. [HERMES Collaboration], Phys. Rev. Lett. 87, 182001 (2001); G. van der Steenhoven, this meeting. 2. L. Elouadrhiri [CLAS Collaboration], this meeting. 3. X. Ji, Phys. Rev. D55 (1997) 7114; J. C. Collins, L. Frankfurt and M. Strikman, Phys. Rev. D56 (1997) 2982; A. V. Radyushkin, Phys. Rev. D56 (1997) 5524. 4. I. V. Anikin, B. Pire and 0. V. Teryaev, Phys. Rev. D62,071501 (2000). 5. A. V. Belitsky and D. Muller, Nucl. Phys. B589 (2000) 611. 6. A. V. Radyushkin and C. Weiss, Phys. Lett. B 4 9 3 (2000) 332; Phys. Rev. D 63 (2001) 114012. 7. M. Penttinen et al., Phys. Lett. B 4 9 1 (2000) 96. 8. N. Kivel, M. V. Polyakov and M. Vanderhaeghen, Phys. Rev. D 63, 114014 (2001). A. V. Belitsky, A. Kirchner, D. Muller and A. Schafer, Phys. Rev. D 64, 116002 (2001); Phys. Lett. B 510, 117 (2001). 9. A. V. Radyushkin and C. Weiss, Phys. Rev. D 63 (2001) 114012.
MEASUREMENT OF HARD EXCLUSIVE REACTIONS WITH A RECOIL DETECTOR AT HERMES R.. KAISER. (ON BEHALF O F T H E HER.MES COLLABOR.ATION) Department of Physics and Astronomy, University of Glasgow, Glasgow G i 2 SQQ, United Kingdom E-mail:
[email protected]. uk
The HERMES collaboration is planning to use a &coil Detector in combination with a high density unpolarized gas target to measure hard exclusive redions. This paper outlines the design of the detector and gives projedions for measurements of the beam spin and beam charge asymmetries in Deeply Virtual Compton Scattering (DVCS).
1
Exclusive Measurements at HERMES
Historically, the investigation of the spin structure of the nucleon in electron scattering has been synonymous with inclusive measurements, i.e. only the scattered electron was detected. In more recent times, semi-inclusive measurements have substantially extended the understanding of the nucleon spin. Nowadays, exclusive processes, where all reaction products are detected, are becoming a promising and powerful experimental tool. HERMES has already observed and investigated several different exclusive reactions, including the exclusive electroproduction of charged and neutral pions and of pmesons Recently, the beam-spin azimuthal asymmetry associated with Deeply Virtual Compton Scattering (DVCS) and, even more recently, the beamcharge asymmetry in DVCS were measured by HERMES for the first time. Both measurements rely on the interference between the DVCS and the BetheHeitler (BH) processes occurring at HERMES energies. However, the missing mass resolution of the HERMES spectrometer is not sufficient to identify exclusive events individually and to separate them e.g. from those about 10% of the events where an intermediate A-resonance was created '. For this reason, exclusivity can only be established at the level of a data sample and only on the basis of restrictive cuts. The main aim of the Recoil Detector is to substantially improve this situation by establishing exclusivity at the event level, i.e. to reduce the non-exclusive background to levels below 1%. 233.
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2
The HERMES Recoil Detector
The design requirements on the Recoil Detector are defined by the kinematics and the nature of the particles involved in the exclusive reactions, as well as by those of the expected background reactions. The main background results from events with intermediate A-production; events with higher resonances can be removed by an invariant mass cut. Hence the particle types that are in principle to be detected are protons, pions, neutrons and photons from TO-decay. All exclusive physics processes that will be investigated produce a low momentum recoil proton at large laboratory angles. The left panel of figure 1 shows the kinematic distribution of recoil protons from BH/DVCS events in terms of momentum y and polar laboratory angle 8 , as obtained from Monte Car10 simulations that include the correct relative weights. The equivalent distribution for exclusive pO-productionis shown in the right panel. The Recoil Detector consists of three active detector parts (cf. figure 2): A
Figure 1. LefkKinematic distribution of recoil protons from BH/DVCS in momentum p and polar angle 0. Right: Corresponding distribution for exclusive po production. Boxes indicate the acceptance of silicon and SciFi detector.
silicon detector around the target cell inside the beam vacuum, a scintillating fibre (SciFi) tracker in a longitudinal magnetic field of 1 Tesla and a photon detector consisting of several layers of scintillator strips inside and outside of the magnet. The photon detector uses an extra layer of lead, the cryostat and the return yoke of the magnet as shower material. The thickness of the target cell wall (75 pm, perhaps 50 pm) and of the beam pipe (1.2 mm) is kept to a minimum to achieve the lowest possible momentum thresholds for the silicon and the SciFi detector. The acceptance of silicon and SciFi detector in p and
394
3 is indicated by the boxes in figure 1. By measuring the energy deposition
of ;he emerging recoil particles the silicon detector will provide the momentum nformation for recoil protons with momenta below 450 MeV/c. The fact that t is located inside the beam vacuum makes it possible to detect momenta as ow as 135 MeV/c, corresponding to kinetic energies as low as 9 MeV. The kiFi-detector measures the momentum of recoil protons between about 250 tnd 1400 MeV/c. It also detects pions and provides particle identification PID) for the separation of pions and protons. The photon detector detects ieutral pions through their decay photons and improves the pion/proton s e p tration for momenta above about 400 MeV/c. The exclusivity of a given event s established through the positive identification of the recoil proton, the a b ence of additional pions and cuts utilizing mainly the transverse-momentum )alance that can then be established by comparing the measured recoil proon momentum to the missing momentum calculated from the spectrometer nformation. Monte Car10 studies shown that in this way more than 90% of vents with intermediate A-resonances can be rejected, reducing the overall iackground to below 1%.
395
3
Projections for DVCS Measurements
One of the main measurements at HERMES with the Recoil Detector will be the beam charge and the beam spin asymmetry in DVCS. Projections for these asymmetries based on an integrated luminosity of 2 ft-’ taken with an unpolarized hydrogen target are shown in figure 3 together with the published HERMES data and predictions based on different GPD models.
*
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3
fad
Figure 3. Left: Projection for a measurement of the beam helicity asymmetry at HERMES BS a function of the azimuthal angle, 4, between the scattering and the production plane, in comparison to the 1996/97 data (open points). Right: Projection of the statistical accuracy of the lepton charge asymmetry as a function of the azimuthal angle, 4. Preliminary results of HERMES 1998/2000 data are shown for comparison (open points). Both projections are based on 2 fb-l and we shown in comparison to different GPD models.
References 1. HERMES Collaboration, hepex/0104005 and DESY-01047. 2. HERMES Collaboration, Eur. Phys. Journ. C17, 389 (2000) 3. HERMES Collaboration, hep-ex/0102037 and DESY-0G189 4. HERMES Collaboration, Phys. Rev. Lett. 87, 182001 (2001) 5. F. Ellinghaus, proceedings at QCD-”02, Ferrara, 2002, to be published in Nucl. Phys. A 6. HERMES Collaboration, Nucl. Instrum. Meth. A 417,230 (1998) 7. HERMES Collaboration, DESY PRC 02-01, HERMES 02-003. 8. V. Korotkov and W.-D. Nowak, Eur. Phys. Journ. C, in press, [arXiv:hepph/O108077)
DISPERSION RELATION FORMALISM FOR VIRTUAL COMPTON SCATTERING OFF THE PROTON B. PASQUINI', D. DRECHSEL', M. GORCHTEIN', A. METZ3, M. VANDERHAEGHEN' ECT*,Villazzano (fiento), and Universitci degli Studi di Tknto, Thnto, Italy Institut fur Kemphysik, J . Gutenberg-Universitat, Mainz, G e m a n y Division of Physics and Astronomy, VU, Amsterdam, The Netherlands We describe a dispersion relation formalism to the virtual Compton scattering reaction off the proton as a new tool to analyze VCS experiments above pion threshold, where one observes increasing effects of the generalized polarizabilities.
In Virtual Compton scattering (VCS) off a proton target, y*+ p --t y + p , a spacelike virtual photon (y*)interacts with a proton and a real photon (y) is produced. At low energies, the real photon plays the role of an applied quasi-static electromagnetic field. On the other hand, the non-zero four momentum transfer squared of the virtual photon, Q 2 , allows one to study the spatial distribution of the polarization effects induced in the target, by means of generalized polarizabilities (GPs) which are functions of Q2. Unpolarized VCS observables have been obtained from experiments at MAMI and at JLab 2,3, and further data are currently under analysis at MIT-Bates '. VCS experiments at low outgoing photon energies can be analyzed in terms of lowenergy expansions (LEXs) '. In the LEX, only the terms to leading order in the energy of the real photon are taken into account. These terms can be parametrized by 6 GPs. However, in order to increase the sensitivity of the VCS cross sections to the GPs, it is advantageous to go to higher photon energies, provided one can keep the theoretical uncertainties under control when approaching the pion threshold. To this aim, we developed a dispersion relation formalism for VCS ', and here we report the essential of this analysis. The VCS process can be achieved through the e p + em reaction. In this process, the final photon can be emitted either by the proton, referred to as fully virtual Compton scattering (FVCS), or by the lepton, corresponding to the Bethe-Heitler (BH) process. The BH contribution is exactly calculable from QED in terms of the the proton electromagnetic form factors, while the FVCS amplitude contains the VCS subprocess y*p -+ yp. Furthermore, the scattering amplitude for VCS can be decomposed into a Born (B) and a nonBorn part (NB) . The Born amplitude, defined as in Ref. ', contains only properties of the proton in its ground state. The residual non-Born contribution contains the information of the excitation spectrum. These nucleon
396
397
structure information can be parametrized in terms of 12 non-Born invariant amplitudes, denoted by q N B ( Q 2 , v , ti) ,= 1, ...,12, which are functions of 3 invariants: Q 2 , v = (s - u)/(4M), and t ( s , t and u are the Mandelstam variables for VCS, and A4 is the proton mass). For the amplitudes one can write down the following unsubtracted dispersion relations (DRs)
FFB
) F?(Q2,v,t) ReFFB(Q2,v,t) = F r L e ( Q 2 , v , tv’ ImsFi(Q2,v’,t ) :P dv’ y” - v’
+
FF
J,trn
FrLe
,
where is the Born contribution, represents the nucleon-pole contribution, and Im,Fi are the discontinuities across the s-channel cuts of the VCS process, starting at the pion production threshold vo. To ensure the convergence of the unsubtracted DRs in Eq. (1), it is necessary that at high energies (v + 00 at fixed t and fixed Q’) the amplitudes ImsF,(&’,v,t) drop fast enough. It has been shown that unsubtracted DRs hold only for ten of the 12 amplitudes. For the remaining two amplitudes, denoted by Fl and F5,we close the contour of the integral in Eq. (1) by a semi-circle of finite radius v, in the complex plane, i.e. we evaluate the unsubtracted dispersion integrals for F1 and F5 along the real v-axis in a finite range (-vmaz5 v 5 +v,,,), and the remaining contribution from the finite semi-circle of radius v, in the complex plane is described by an “asymptotic contribution”. The imaginary parts of the amplitudes F, in Eq. (1) are obtained through unitarity from the dominant contribution of T N intermediate states, using as input the pion photo- and electroproduction multipoles of the phenomenological MAID analysis 7. The asymptotic contribution to the amplitude F5 results from tchannel nO-exchange, while the asymptotic contribution to the amplitude F I originates predominantly from t-channel nn intermediate states. In addition, it turns out that higher-energy dispersive contributions ( m N ,...) mainly affect the Fl and F 2 amplitudes. Since the dispersive terms beyond ?rN are very poorly known, we parametrize these contributions to F1 and FZby energy independent constants, fixed at arbitrary &’, v = 0 and t = -&’. In this way we introduce two free parameters which can be expressed in terms of the electric, a(&’), and magnetic, P(&’), GPs, which have to be fitted to experimental VCS data at each fixed value of Q’. However, in order to provide predictions for VCS observables at different values of Q 2 , we take the following parametrization for the &’ dependence of the scalar GPs
398
where the values at Q2 = 0 are fitted to real Compton scattering (RCS) data s. The present status of the analysis of the VCS experiments at JLab has been reported in this conference In particular, results for the unpolarized structure functions PLL- PTTf~ and PLT have been extracted from the analysis of JLab data below pion threshold, using both the LEX and the DR formalisms. A nice agreement between the results of both methods was found 2 . In Fig. 1, we show the results for PLL and PLT at Q2 = 1 GeV2 and at Q2 = 1.9 GeV2, from the JLab experiment at Q2 = 0.33 GeV2, from the MAMI experiment ’, and at real photon point, from the TAPS results s. To extract PLLfrom the data, we calculate the relatively small (spin-flip) contribution PTT in the DR formalism and subtract it from the measured value of PLL - PTT/E. By dividing out the form factor G E , PLL is proportional to a(&’),whereas PLT is proportional to P(Q2) plus some correction due to the spin flip GPs which are small in the DR formalism. One sees from Fig. 1 that the electric polarizability is dominated by the asymptotic contribution and has a similar Q2 behavior as the dipole form factor. The total result for PLT results from the interplay of a large dispersive B N term, related to the paramagneticxontribution of p(Q2),and a large asymptotic contribution, associated with a diamagnetic mechanism due to pion-cloud effects. These two contributions have a different Q 2 dependence and give rise to an interesting structure in PLT,in particular at low Q 2 . In order to show the potentiality of VCS above pion threshold to extract information on the GPs, in Fig. 2 we display the DR predictions for the cross sections in the A(l232)-resonance region, in MAMI kinematics. It is seen that the e p -+ epy cross section rises strongly when crossing the pion threshold, and the region between pion threshold and the A-resonance peak clearly displays an enhanced sensitivity to the GPs through the interference with the rising Compton amplitude due to A-resonance excitation. Therefore, this energy region is very promising to measure VCS observables with a larger sensitivity to the GPs. Such an experiment is underway at MAMI, and the first results from JLab about VCS in the resonance region at Q2 = 1 Gev2 have been shown in this conference 233. 213.
293,
References
1. J. Roche et al., Phys. Rev. Lett. 85, 708 (2000). 2. H. Fonvieille, these proceedings.
3. L. Van Hoorebeke, these proceedings; L. Todor, these proceedings. 4. R. Miskimen, spokespersons MIT-Bates experiment, 97-03.
5. P.A.M. Guichon, G.Q. Liu, A.W. Thomas, Nucl. Phys. A591,606 (1995). 6. B. Pasquini, D. Drechsel, M. Gorchtein, A. Metz, and M. Vanderhaeghen, Phys. Rev. C 62, 052201 (R) (2000); Eur. Phys. J. A 11, 185 (2001).
399
0
0.5
1.5
1
0
2
0.5
1
1.5
2
Q2 (GeV') Q2 (QV2) Figure 1. Results for the unpolarized VCS structure functions PLL (left panel) and PLT (right panel) divided by the proton electric form factor. Dashed lines: dispersive nN contributions. Dotted lines: asymptotic contributions calculated from Eq. (2) with A, = 0.92 GeV (left panel) and A0 = 0.66 GeV (right panel). Solid curves: total results, sum of the dispersive and asymptotic contributions. The RCS data are from Ref. 8 , the VCS data are: at Q2 = 0.33 GeV2 from Ref. ', at Q2 = 1 GeVZ and Q2 = 1.9 GeV2 from Refs. 233.
~ = 0 . 6 2 a=0.6GeV
0.1
0.2
0.3
-
O=Oo
b=O0
0.1
0.2
0.3
q' (GeV) 4'(QV) Figure 2. Left panel: differential cross section for the reaction e p -+ ep7 as function of the B contrioutgoing-photon energy q' in MAMI kinematics. Dashed-dotted curve: BH bution. The total DR results are calculated with the asymptotic contribution of Eq. (2) corresponding to a fixed value of A, = 1 GeV and three values of A@: h p = 0.7 GeV (dotted curve), Ap = 0.6 GeV (solid curve), and Ap = 0.4 GeV (dashed curve). Right where @ is a phase-space factor. The thick panel: Results for ( d 5 0 - d5~BH+Born)/@q', curves show the DR calculation with the full q' dependence and the thin horizontal curves are the DR results within the LEX formalism. The data are from Ref. l.
+
7. D. Drechsel, et d.,Nucl. Phys. A645, 154 (1999). 8. V. Olmos de Le6n et al., Eur. Phys. J. A 10, 207 (2001). 9. N. d'Hose and H. Merkel, spokespersons MAMI experiment, (2001).
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Session on Baryon Structure and Spectroscopy Convenors T. S. H. Lee M. Manley B. Schoch S. Simula
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MESON-PHOTOPRODUCTION WITH THE CRYSTAL-BARREL DETECTOR AT ELSA M. OSTRICK Physakalisches Institut der Universztat Bonn, Nussallee 12, 53115 Bonn, Gewnany E-mail:
[email protected] The photoinduced production of neutral mesons off protons has been studied with the Crystal-Barrel-detector at the electron stretcher facility ELSA. First data demonstrate that reactions with multi-photon final states can be reconstructed with high efficiency. Preliminary results on ~p -+ pnono and ~p + pnoq show evidence for successive decays of high mass states through different intermediate resonances.
1
Introduction
The excitation spectrum of baryons and even basic ground state properties are still not understood directly in the framework of QCD. Different models using constituent quarks and meson clouds as relevant degrees of freedom are able to reproduce the main features of the baryon mass spectrum at low excitation energies. However, it is still impossible to decide experimentally which of the proposed types of effective quark-quark interaction is realized in strong QCD 1*2,3.At higher energy most of these models predict many more baryonic states than observed so far. This may be due to the lack of experimental data different from KN-scattering, or due to additional symmetry breaking in the three quark system which reduces the relevant number of degrees of freedom. The intimate relationship between excited baryons and the photoproduction of mesons allows to study individual resonances in selective decay channels, different from K N and to search for contributions of "missing" states '. In this context, the production of neutral mesons is of special interest, as many non-resonant production amplitudes are strongly suppressed compared to reactions, where charged mesons are involved. The Crystal-Barrel-Experiment at ELSA focuses on photoinduced production of these neutral mesons and meson pairs, e.g. KO, q, q', w , KO, nono, n'q, vr],which decay into multi-photon final states. The accessible range in the center-of-mass energy reaches from the two pion threshold up to 2.6 GeV. In the following, the experimental setup is described and the status of analysis of the reactions -yp + nOnOpand y p + noqp is discussed.
403
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Experimental setup
The measurements were performed at the electron stretcher and accelerator ELSA in Bonn which provides an electron beam with a maximum energy of Eo =3.2 GeV. Quasi-monochromatic photons are produced by means of bremsstrahlung tagging. The tagging spectrometer covered a range in the photon energy from E7 = 0.22 - 0.95. Eo at a total flux of N7 = 2 . 106s-' in this energy range. Mesons are produced in a 5cm liquid hydrogen target which is surrounded
scintiIlatorwalls
scintillating fiber detector
/
Crystal-Barrel (1380 Csl, Crystals) Figure 1. detector setup
by three layers of scintillating fibers for the identification and tracking of charged particles. Decay photons can be measured with the Crystal-Barrel electromagnetic calorimeter which consists of 1380 CsI crystals and covers 98% of the full solid angle in the laboratory system (see Fig. 1). The large solid angle coverage together with the energy resolution of 2.5% at a photon energy of 1 GeV and the angular resolution of 1 . 2 O allows to reconstruct multi-photon final states efficiently. This basic detector arrangement can be completed by dedicated fast detectors for charged and neutral particles in forward direction. In 2001 a wall of plastic scintillators was used as time of flight spectrometer for forward going protons.
405
First data and status of analysis
3
In 2001 data including all reaction channels mentioned above have been taken simultaneously. In 4 weeks of data taking an integrated luminosity of Ltot M 5 . 1O5pbarn-l has been accumulated. The data are presently being analysed L
I
10'
10 10 10' 10
1o*
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10 10'
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1
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6w
WO 1wO 1200 1400
M /MeV
0
2 w a 0 6 w e m 1 w o
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a0 6w
em low
1200 1400 1wo
M m/MeV
Figure 2. Measured distributions of 27 and 3n0 invariant masses in p y y , paOy-yand pnOaOaOfinal states.
and all results presented here are preliminary, without flux normalisation and acceptance correction. Figure 2 shows events, where a proton has been identified together with two, four or six photons in the final state. In the first case (yp + my) the distribution of the yy invariant mass shows clear peaks from T O + yy and q + yy decays. Also signals from w + TOY and q' + yy decays can be observed. The w-meson appears here due to events, where one low energy photon escaped detection. The q-meson can also be clearly identified in its decay into three no mesons (right spectrum in Fig. 2). The spectrum in the center of Figure 2 contains yp + p4y events with one no meson already identified. The invariant mass distribution of the remaining yy-pair shows clear signals from TO- and q-decays, which demonstrates that the reactions yp + p2x0 and, for the first time, yp + pnoq can be clearly identified. The observation of the production of a meson pair allows to study transitions between high mass resonances and other excited (N*,A*) or ground states (e.g. A(1232)). Double TO production has recently been measured at MAMI up to a center of mass energy of & = 1.55 GeV '. The data confirm the sequential decay of the &3(1520) resonance with the A(1232) as intermediate state.
406
At ELSA higher excitation energies are accessible. As an example Figure 3 shows a Dalitz-plot for events at center of mass energies between 1.8 < f i < 2.2 GeV. The number of entries is plotted as function of squared invariant masses, calculated from the three particles in the final state. In case of double ro-production an event appears with two entries due to the two indistinguishable pions. Structures in the Dalitz-plot deviating from phase N
4.5
0
Nk ' I5 1
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2 15
1 1
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IE
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Figure 3. The Dalitz-plot for -yp + pno7ro events a t 1.8 y p + pn0v at 1.9 < , h < 2.3 GeV (right)
IS
2
25
< fi < 2.2 GeV
s
I
(left) and for
space indicate resonant intermediate states or, at least, correlations between the particles. In the example of Figure 3 not only a peak at the A(1232)mass but also a second peak around Adplr M 1.5 GeV is visible. This can be interpreted as the observation of a sequential decay of states around 2 GeV not only via the A resonance but also through excited states around 1.5 GeV. Similar decay chains are observed in the photoinduced r0v production. In this case, the isoscalar v meson connects states of the same isospin. As an example the Dalitz-plot at center of mass energies between 1.9 < & < 2.3 GeV is shown on the right side of Figure 3. The p r o mass peaks at the mass of the A( 1232), indicative for the observation of sequential decays of excited A*-states around 2 GeV. In addition, the structure at 1.52 GeV2 in the p17 invariant mass hints at the observation of the Sll(1535) as intermediate state. In order to determine the quantum numbers of the excited states involved and to identify contributions different from s-channel resonances a partial wave analysis of the data as well as a comparison to recent model calculations7 and measurements of observables including polarisation degrees of freedom' are in progress.
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Summary and outlook
The photoproduction of neutral mesons off protons has been measured up to center of mass energies of 2.6 GeV using the Crystal-Barrel-Calorimeter at ELSA. Reactions with multi-photon final states can be reconstructed with high efficiency. A first preliminary analysis of the reactions yp + p o 7 r o and yp + p7roq provides evidence for successive decays of high mass resonances via different intermediate states. Flux-normalisation, acceptance corrections and a partial wave analysis of the data are in progress. The measurements of photoinduced reactions off protons and nuclei with the Crystal-Barrel-Detector at ELSA will be continued in 2002/03 using the TAPS' calorimeter as detector for forward going charged and neutral particles. An improved tagging system and a coherent bremsstrahlung facility will provide linearly polarised photons at a total flux of N , = 107s-'.
References 1. S. Capstick, contribution to Baryon2002, Newport-News/USA 2. S. Capstick and N. Isgur, Phys.Rev.DS4, 2809 (1986) 3. U. Loring, B.C.Metsch, H.R.Petry, Eur.Phys.J. A10, 395 (2001) 4. A. d' Angelo, contribution to Baryon2002, Newport-News/USA 5. see, e.g., Aker et al. Nucl.1nst.Meth.A 321, 69 (1992) 6. M.Wolf et al., Eur.Phys.J. A 9, 1 (2000) 7. e.g., J.A.Gomez-Tejedor, E.Oset, Nucl.Phys.A600, 413 (1996) 8. C.Weinheimer, M.Ostrick et al., Proposal to PAC Bonn-Mainz, 2002 9. R. Novotny, IEEE Trans. on Nucl. Sc. 38, (1991) 378
408
Mina Nozar, Ulrike Thoma, and Michael Ostrick
Andrei Afanasev and Carl Carlson
K-MESON PRODUCTION STUDIES WITH THE TOFSPECTROMETER AT COSY WOLFGANG K. EYRICH Physikalisches Institut, Universitat Erlangen-Niirnberg, E.-Rommel-Str. 1. 91058 Erlangen Germany E-mail:
[email protected] FOR THE COSY-TOF COLLABORATION The associated strangeness production in elementary proton induced reactions is studied exclusively at the external COSY beam using the time-of-flight spectrometer TOF. The complete measurement of all primary and decay particle tracks allows the extraction of total and differential cross sections as well as Dalitz plots and invariant mass spectra of the subsystems for the channels p' K+&, K?E+p, K+,??p and KfFn.For all channels the full phase space is covered from the reaction threshold up to the COSY-limit of about 3.5 GeV/c. Especially the analysis of the Dalitz plots of the channel p p + K+Ap show a strong influence of N*-resonances. In parallel the production of the o - meson is studied in the reaction p'
PP 0.
1 Introduction The main interest in the investigation of the associated strangeness production in elementary reactions like pp+ KYN close to threshold is the insight into the dynamics of the Ss production. Meson exchange models appear to be the most appropriate way to describe strangeness production in the threshold region. Here the questions concern the contribution of the various strange and non strange mesons and especially the role of N*-resonances in the production mechanism. Moreover the YN final-state interaction (FSI) is known to be of special importance close to threshold. To come to conclusive results precise data are needed for different reaction channels. The measurements should concentrate on exclusive data covering the full phase space. Moreover, the data of the strangeness production in elementary nucleon-nucleon reactions are very useful as an input to explain strangeness production in nucleus-nucleus reactions including medium effects.
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2 Experiment The experiment COSY-TOF is a wide angle, non magnetic device with various start and stop detector components for time-of-flight measurement. The modular apparatus combines high efficiency and acceptance with an energy and momentum resolution of a few percent. The whole detector system together with a tiny liquid hydrogen target is installed inside a vacuum vessel. This ensures a rather precise definition of the interaction point and strongly reduced background reactions in air. The outer detector, serving as stop for the time-offlight, consists of several plastic scintillator hodoscopes. The inner detector, optimised for strangeness production, consists of two layers of thin segmented scintillators providing the start timing, a doublesided silicon micro-strip detector with a highly granulated ring and sector structure and two scintillating fibre hodoscopes. The full angular range of the reaction products is covered allowing a complete reconstruction of the p p + KYN events including the delayed decays. [I].
3 Results and discussion The reaction pp+ P A P has been investigated between 2.5 GeV/c and 3.2 GeV/c, that means from near threshold up to close to the COSY limit. For all measured momenta very clean event samples could be extracted. This is shown in fig. 1 for the momentum of 2.85 GeV/c.
58 15W
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Figure 1. A-missing mass spectrum for a beam momentum of 2.85 GeV/c.
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mpAZ[GeV2/c4]
*-u
*-u
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rii
*
% 3.22
3 E
2.8
3.2-
2 -2 E
-
2.8
-
2.6 -
2.6 2.4
3.4
.w
I
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mpA2 [GeV2/c4]
2.4
I
I
I
I
4.25
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m p A 2 [GeV2/c4]
Figure 2. Dalitz plots of the data at 2.85 GeVk (upper left) compared with calculations using the resonance model of Sibirtsev: full calculation (upper, right), only resonance contributions (lower, left), only FSI (lower, right).
By covering the full phase space various exclusive observables can be extracted model-independently. In particular Dalitz plot analyses turned out to be a powerful tool to investigate the reaction mechanism. This is demonstrated in figure 2 where the experimental data at 2.85 GeV/c are compared with a calculation of Sibirtsev [2]. where contributions from non resonant meson exchange are combined coherently with contributions from the N*(1650, 1710, 1720)resonances and the PA-FSI. Whereas the combination of the phase
412
unique way. This can be seen from fig. 3, where the projections of the Daltiz plot from fig. 2 are shown together with the calculations and a pure phase space. Obviously also here only the full calculation is reproducing the data in a satisfactory way. The distribution of the KAmass follows by "accident" the phase space, clearly showing that it is not sufficient to analyse the projections of the Dalitz plot.
2
2.05
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2.2
2.25
155
mpA[GeV/cZ]
1.6
1.65
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1.75
1.8
1.85
mu [GeV/cZ]
Figure 3. Invariant masses of the pA-(left) and KA-(right) subsystems at 2.85 GeVk together with calculations within the resonance model of Sibirtsev (drawn), resonances only (dotted), FSI only (dashdotted) and phase space (dashed).
Preliminary analyses of the Dalitz plots at 3.2 GeVk show that the influence of the N*( 1710)-resonancestrongly increases. As mentioned above the TOF detector for the first time also allows the measurement of the Z+-production in the channels pp+ p2?p and K + c n in the threshold region. Clean samples of a few hundred events could be extracted. The next steps will be the use of a polarized beam and the strangeness production in neutron proton scattering using a d-target. We gratefully acknowledge support by the l?L-Julich and the berman BMBF.
Keferences 1. A.Bilger et al., Strangeness Production in the Reaction pp+ K'Ap in the Threshold Region, Physics Letters B420 (1998) pp. 217-224 2. A. Sibirtsev, private communication (2002)
FIRST SIMULTANEOUS MEASUREMENTS OF THE TL AND TL‘ STRUCTURE FUNCTIONS IN THE r*P + A REACTION A.M. BERNSTEIN PHYSICS DEPARTMENT AND LABORATORY FOR NUCLEAR SCIENCE MASSACHUSETTS INSTITUTE O F TECHNOLOGY, CAMBRIDGE, MA 02139, USA
The first simultaneous measurements of both longitudinal-transverse structure functions (TL and TL’) in the p(Z, e‘p).lrOreaction in the A region are presented on behalf of the MIT-Bates OOPS Collaboration1. Measurement of the deviation of the proton shape from spherical symmetry is fundamental and has been the subject of intense experimental and theoretical interest2. This determination has focussed on the measurement of the electric and Coulomb quadrupole amplitudes (E2, C2) in the predominantly Ml(magnetic dipole -quark spin flip) y * N + A transition. The difficulty is the small E2/M1 and C2/M1 amplitudes (typically N -2 to -8 % at, low Q2). In this case the non-resonant (background) and quadrupole amplitudes are the same order of magnitude. This combination of small signal and signal/noise ratio requires both sensitive and accurate observations. The d state admixtures in the nucleon and A wave functions are caused in the quark model by the hyperfine tensor interaction between quarks3. In pion cloud model^^?^^^ it is caused by the p wave pion emission. This in turn is caused by the spontaneously broken symmetry of QCD in which the pion is an almost Goldstone Boson which primarily interacts with nucleons in the p wave. It has been shown that at low Q2 the pion cloud contributes significantly to the M1 amplitude and dominates the E2 and C2 contribution^^,^*^^ to the y*N Aitransition. The present experiment is performed near the predicted maximum of the pion cloud contribution6. To precisely determine the resonant quadrupole amplitude in the y * N A transition at low Q2, while addressing the issue of background contributions, a program has been developed at the MIT-Bates Linear Accelerator. For this purpose we have developed an out-of-plane magnetic spectrometer system (OOPS)7 in which the spectrometers are deployed symmetrically about the momentum transfer <. The present experiments is a first simultaneous measurement of both the TL and the TL’(po1arized) cross sections at and below the resonance energy. The TL‘ and the TL (transverse-longitudinal) response functions are the real and imaginary parts of the same combination of interference mu1t)ipole amplitudes. As has been previously demonstrated UTL is sensitive to the magnitude of the longitudinal quadrupole amplitude (C2)g.
413
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Adding a measurement of (TTL~ provides a stringent test of the background magnitudes and phases of the reaction calculations. It should be pointed out that a determination of the background amplitudes is an important part of the physics of the y7rN system. The experiment was performed at Q2 = 0.127 (GeV/c)2, W = 1232 MeV and 1170 MeV. which is close to the predicted maximum of the pion cloud contribution'?'.''. The experimental results* are compared to model calcuand to an empirical pion electroproduction multipole fit13 in lations Figs. 1 and 2. The dispersion" and MAID" calculations, Kamalov-Yang dynamical modello and empirical multipole fit (to previous electropion production data)13 have reasonable overall agreement with experiment with the exception of (TTL at W = 1170 MeV, at the center of mass angle O,, = 119" which is much larger than all of the calculations. This general agreement, is not too surprising since the MAID model provides a flexible way to fit the observed cross sections as a function of Q 2 . The Kamalov-Yang dynamical model" incorporates many features of the MAID model including the Born terms, the higher resonances, and the empirical x-N phase shifts in non-resonant channels. The dynamics of this model are for the resonant amplitudes only. Dispersion relation calculation^^^ are consistent with QCD and provide good agreement with photo-pion production data19720.The dispersion relations calculations for electro-pion production12 are in reasonable general agreement with our data. For U T L ~the errors are larger but since the calculations generally lie in a relatively small band this is not critical. In contrast to the general good agreement between the model calculations and our data the Sato-Lee dynamical model' is not in agreement with our data. This model is far more ambitious, calculating all of the partial waves in a dgnamical way. By contrast this model showed much better predictions for the recently reported JLab results15 for the p(C, e'p)7r' reaction in the A region for Q2 from 0.4 to 1.8 G e V 2 . This seems to indicate that the dominant meson cloud contribution, which is predicted to be a maximum near our values of Qz, is not quantitatively correct. Recently a measurement of ATL, for the p(Z,e'p)x0 reaction in the A region was performed at Mainzl*. The kinematics include a range of Q2 values from 0.17 to 0.26 (GeV/c)2 and backward Oxg angles. Somewhat surprisingly, compared to our results, none of the models agree with the data. The MAID" and Kamalov-Yanglo models are lower than the data and the Sato-Lee model is too high'. It is also of interest to compare the TL' results presented here with those of the induced polarization p , which are also related to the imaginary parts of interference multipole amplitudes. For the p ( e , e'p3x0 channel the outgoing 6,10y11,12
415 221
I
.
I
I
- iUAID2OOO Sam-Lee K-alO"-Y-g
O
110
120
130
14"
IS"
16"
17"
I*"
Figure 1. Cross sections for the p(Z,e'p)nO reaction for W = 1170 MeV, Q2 = 0.127 E U L . Panel (b) is for U T L (GeV/c)2 plotted versus Or,,. Panel (a) is for DO = UT and panel (c) is for U T ~ , .The curves are MAID", Sato-Lee', Kamalov -Yanglo, Aznauryan (dispersion theory)12, and empirical multipole fit t o previous pion electroproduction data(SA1D) 3.
+
h4AID 2000 sato-Lee ........ ..
... .
AznauwSAID
0
Figure 2. Cross sections for the p(Z,e'p)nO reaction for W = 1232 MeV, Q2 = 0.127 (GeV/c)* plotted versus Or,,. Panel (a) is for uo = UT E U L . Panel (b) is for UTL and panel (c) is for U T L , . See the Fig. 1 captions for an explanation of the curves.
+
416
proton polarization normal to the reaction plane has been observed, in parallel kinematics (the protons emitted along Gor O,, = 180') 16117. However, unlike the data we have presented, the reaction models are not in good agreement with this observable. In conclusion, we have performed a first measurement of both the real and imaginary parts of the transverse-longitudinal interference (TL) structure function for the p(Z, e'p)n" reaction in the A region. Several models'"~1'~'2 and the empirical multipole fit13 are in reasonable general agreement with these results but the discrepancy for UTL at W = 1170 MeV, 1 9 , ~= 119" remains to be understood. References
1. Information about the OOPS collaboration and experiments can be found on the Bates home page: http://mitbates.mit.edu/index2.stm 2. See e.g. NStar 2001, Proceedings of the Workshop on the Physics of Excited Nucleons, D. Drechsel and L. Tiator editors, World Scientific (2001) 3. N. Isgur, G.Karl, and R. Koniuk, Phys. Rev. D25, 2394 (1982). 4. D. H.Lu et al., Phys. Lett. C55, 3108 (1997). 5. M. Fiolhais et al., Phys. Lett. B373, 229 (1996). 6. T. Sato and T.-S. H. Lee, Phys. Rev. C63, 055201(2001). 7. S.M. Dolfini et d.,Nucl. Inst. Meth. A344, 571 (1994). J. Mandeville et a]., Nucl. Inst. Meth. A344, 583 (1994). Z.-L. Zhou et al., Accepted for publication in Nucl. Instr. Meth. 8. C.Kunz, Ph.D. Thesis, M.I.T.(2000). 9. C. Mertz et al., Phys. Rev. Lett. 86,2963(2001). 10. S.S.Kamalov and S.N. Yang, Phys. Rev. Lett.83, 4494(1999). 11. D. Drechsel et al., Nucl. Phys. A645, 145 (1999) and ht tp: / /www .kph.uni-mainz .de/MAID / 12. I. G. Aznauryan, Phys. Rev. 57,2727(1998) and private communications. 13. R.A.Arndt, 1.1. Strakovsky, and R.L. Workman, nucl-t,h/0110001 and http://gwdac.phys.gwu.edu 14. 0.Hanstein, D. Drechsel, and L. Tiator Nucl.Phys.A632,561(1998). 15. K. Joo et al., Phys.Rev.Lett.88,122001(2002) 16. G.A. Warren et al., Phys. Rev. C58, 3722 (1998). 17. Th. Popischil et al., Phys. Rev. Lett. 86, 2959(2001) 18. P.Bartsch et al., Phys.Rev.Lett.88,142001(2002) 19. G. Blanpied et nl., Phys.Rev.C64,025203(2001) 20. R. Beck et al., Phys. Rev. C61, 35204 (2000).
PHOTOPRODUCTION OF RESONANCES IN A RELATIVISTIC QUARK PAIR CREATION MODEL F. C A N 0 DAPNIA/SPhN, CEA-Saclay, 91191 Gif Sur Yvette Cedex, France
P. GONZALEZ Departamento de Fisica Tedrica and IFIC (Centro mixto CSIC- UVEG), 46100 Burjassot (Valencia), Spain S. NOGUERA Departamento de Fisica Tedrica, Universitat de Valencia, 46100 Burjassot (Valencia), Spain
B. DESPLANQUES Institut des Sciences Nucle'aires, F-38026 Grenoble Cedex, France
We study dynamical relativistic corrections to electromagnetic baryon transition operators in the quark model associated to 1qqq qQ) Fock-space components. We generate such components by means of a relativistic 3Po pair creation mechanism and we find sizeable contributions to photoproduction amplitudes of resonances.
1
Introduction
Electromagnetic baryon processes in the constituent quark model framework have been extensively studied in the literature, comprising non-relativistic as well as relativized approaches (see for instance Nevertheless the comparison to data makes clear that understanding of the relevant ingredients in its description may have not been reached yet. Our aim is to implement, starting from an elementary emission model description of the baryon transition process, the role of some dynamical relativistic corrections coming from the coupling of the photon to qq pairs in the baryon. To this purpose we shall assume a 3Po mechanism as a way to generate the I qqqqij > baryon components. Our treatment differs from previous ones following the same philosophy in the use of a relativistic 3Po model and the consideration of nog-resonant as well as resonant type contributions. ' 9 ' ) .
417
418
2
Themodel
The description of the process B + B’ y in the Elementary Emission Model (EEM) is based on the assumption that the photon is emitted by a quark of the baryon (figure la). In order to take into account the effects of the coupling of the photon to qq components in the baryonic medium we need a dynamical mechanism to generate such components. We shall assume a 3P0 mechanism, say that quark-antiquark pairs can be created from the vacuum, the hamiltonian for this process being given by
where b, d stand for quark and antiquark operators, u and u for the quark and antiquark quadrispinors, rn, $and Ep for the quark mass, momentum and energy. The sum over spin projections is implicit. p, the strength parameter, is the only free parameter of our model. A created pair recombines with the quarks of the baryon to couple the photon (figures l b and lc). Fig. l b is related to the standard Vector Meson Dominance phenomenology whereas Fig. lc stands for a non-resonant contribution. However a difficulty in assuring gauge invariance immediately arises since the non-resonant operator, at variance with the EEM and the resonant one (for this last diagram we choose a self gauge invariant coupling), is not expressed in terms of a conserved current. This difficulty can be surmounted by realizing that the 3P0 mechanism must be accompanied by a quark mass renormalization which we choose in such a way that a conserved current is obtained ‘. The transition matrix element is obtained by sandwiching the resulting operator between three-quark baryon wave functions as the ones provided by spectroscopic models. One could wonder whether the use of these wave functions altogether with relativistic operators is justified. To this respect one should realize that the wave functions are very effective ones in the sense that although they are derived from a non-relativistic form of the potential the parameters of this potential are not taken from the basic theory but from a fit to the baryon spectra. Therefore the wave functions contain implicitly in an effective way, at least in part, relativistic effects. Hereforth we shall assume Bhaduri-Cohler-Nogami wave functions very much detailed in the literature.
419
4
4 (a)
4
4 (b)
4
4 (c)
Figure 1 . Elementary Emission Model (a) and q q coupling to the photon in the 3Po model, (b) and ( c ) .
3
Results
Results obtained with our model for nucleon form factors have been published elsewhere '. They show a very significant improvement on the description of the form factors as compared to the EEM results. This improvement is also evident for the square mean radius and the magnetic moment of the nucleon. The EEM diagrams provides about 60% of the contribution. Non-resonant diagrams give no electric type contributions. They provide however a 40%of the magnetic moment of the proton when /3 is chosen to fit it. Resonant diagrams contribute to the square mean radii but not to the magnetic moments. Table 1 shows predictions for some photoproduction amplitudes. Leaving aside the first radial excitations for nucleon and delta, N ( 1440) and A ( 1600), which are very sensitive to the particular quark model under consideration due to the presence of a node in their wave functions, the results make clear on the one hand the relevance of qqqqTj contributions to the amplitudes (specially for the A(1232) + N y case), on the other hand the need to implement further corrections. These corrections may be of very different kinds. Improvements of the wave functions seems to be mandatory although there is not a clearcut way to carry them out. An anomalous magnetic moment of the quarks could be incorporated (work in preparation). New dynamics as the one associated to exchange currents can be considered although it may have been taken partially into account in our model through the effective value of /3. Kinematical factors as the ones coming from relativistic normalizations and boost effects should also be analyzed. Not withstanding it and the lack of a consistency check for strong and weak processes we think our minimal model may help to clarify the role of the coupling of the photon to qq pairs in the hadronic medium.
420 Table 1. Photoproduction amplitudes (in from each diagram in Fig. 1 are shown.
I A(1232)
4 1 2 4 1 2
N(1520) 4 1 2
A;"/z N(1535)
"I2 "?/2
I
Total
I
Exp.
1.a
1.b
1.c
-102 -59
-4
-2
-59 -34
8 5
-29 -16
65 -66 -19 -20
11 -3 0.5 -3
0
0 -30 10
76 -70 -48 - 10
166f5 - 1 3 9 f 11 -24 f 9 -59f9
97 -68
-15 5
21 -7
103
- 70
125 f 25 -59 f 22
A( 1600)
4 / 2
GeV-'12 units). Separate contributions
-258 f6 -140 f 5
-165 -95
I
-47 -27
1
- 9 f 21 -23f20
Acknowledgments
This work is partially funded by European Commission IHP program (contract HPR.N-CT-2000-00130). References 1. S. Capstick, Phys. Rev. D 46, 1965 (1992); Phys. Rev. D 46, 2864 (1992). 2. F. Cardarelli, E. Pace, G. Salmi: and S. Simula, Phys. Lett. B 397, 13 (1997). 3. F. Can0 and P. Gonzilez, Phys. Lett. B 431, 270 (1998). 4. F. Cano, B. Desplanques, P. Gonzilez and S. Noguera, Phys. Lett. B 521,225 (2001). 5. U. Meyer, E. Hernandez and A.J. Buchmann, Phys. Rev. C 64, 035203 (2001).
RELATIONSHIP OF THE 3P0 DECAY MODEL TO OTHER STRONG DECAY MODELS B. DESPLANQUES, A. NICOLET AND L. THEUSSL Institut des Sciences NuclLaires (UMR CNRS/IN2P3- UJF), F-38026 Grenoble Cedex, France E-mail: desplanqOisn.in2p3.fr The Po decay model is briefly reviewed. Possible improvements, partly motivated by the examination of a microscopic description of a quark-anti-quark pair creation, are considered. They can provide support for the one-body character of the model which, otherwise, is difficult to justify. To some extent, they point to a boost effect that most descriptions of processes involving a pair creation cannot account for.
1
Introduction
The 3P0 decay model, first introduced by M i a 1 , has been subsequently applied to the description of many processes by Le Yaouanc et al.'. Since then, it has been used extensively with a reasonable success, especially for the hadronic decays of mesons. Being described by a one-body operator, the model can be employed easily, while its strength is generally fitted to experiment. In these conditions, the agreement is not much better than a factor 2, which is too large to make stringent tests of the description of hadrons for instance. Improvements should therefore be introduced. This however requires to understand what the model accounts for. After reviewing the model, we will consider possible improvements, based on a microscopic description of a quark-anti-quark pair creation.
2
The 3P0 decay model
The 3P0 decay model assumes a creation of a quark-anti-quark pair from the vacuum with the corresponding quantum numbers, J = 0, L = 1, S = 1, T = 0. Represented in Fig. l a for a meson decay, it may be described by the following operator:
In comparison with the elementary emission model shown in Fig. l b , where a meson is emitted from a quark line, it offers the considerable conceptual
421
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a
b
Figure 1. Diagrams representing a meson decay with a one-body interaction: within the 3Po decay model (a) and an elementary emission model (b).
advantage that all hadrons are considered on the same footing. Among improvements, it has been proposed3 to introduce some momentum dependence in the strength y. A relativized version of the model has also been considered, involving the replacement of a‘. (6-5’) in Eq. (1) by 2 m ii(6)~(6‘)~. Some improvement is obtained but in absence of insight on the origin of the model, one cannot draw firm conclusions. Although it should be used in the c.m. of the decaying system, the creation of a pair from the vacuum without relation to the other particles is difficult to imagine. Moreover, a term like Eq. (1) can be absorbed in a redefinition of the quarks and their masses, producing elementary quark-meson couplings for instance. Kokosky and Isgur discussed the possibility that the 3Po decay model could account for a flux-tube breaking in some limit5. The strength is not known however. Another possibility is that the pair creation is closely related to the interaction between quarks6. This hypothesis, that we will develop in the following, is illustrated in Fig. 2a for a meson decay.
a
b
Figure 2. Diagrams representing a meson decay with a two-body interaction: emission of a meson (a) and a photon (b).
423
3
A key relationship
The calculation of the decay amplitude of a hadron H into another one H‘ and a meson M , as depicted in Fig. 2a for a particular case, implies an expression like the following:
) the meson wave function. V(f, f’) represents the where $ ~ ( f represents interaction responsible for a pair creation. Quite generally, its expression is complicated and without relation to the interaction between quarks. In one case, however, such a relation can be established. For spin-less particles, both interactions are the same (non-relativistic approximation). One can then use the equation that the meson wave function has to fulfill:
This can be used to replace the last factor in Eq. (2) by the wave function itself, obtaining:
where f has to be replaced appropriately in terms of the external momenta and This last expression looks very much like the one used when employing the 3Po decay model (spin put apart). It does not contain the interaction explicitly but involves a one-body operator. This one however appears with a well defined factor, “E - 2 e q ” , providing a clue for both the strength and the momentum dependence, often introduced on a phenomenological basis. The expression of the above amplitude corresponds to a particle-antiparticle pair creation that has the same form as the one appearing in a freeparticle interaction. It however differs by essential features. As already mentioned, such a term can be absorbed into the redefinition of the particle fields. The functional dependence of the front factor, “ E- 2 eq” , rules out this transformation here, since it cancels for free particles, consistently with the fact that it originates from an interaction term. This can solve one of the problems with the 3Po decay model, namely the creation of a pair without relation to the environment. With the above respect, it is worthwhile to mention another example where an interaction effect can be turned into a single-particle contribution. It concerns the Z-type contribution to the emission of a photon shown in Fig. 2b. This one evidently involves the interaction. However when the full
F”.
424
Feynman diagram corresponding to this figure is considered, it is found that the same contribution appears as a single-particle one. Consistency is achieved by the fact that this contribution involves a factor similar to the above one, “E- 2 e q l ’ . The details can be checked by looking at a simple model7. When applying the above ideas to spin 1/2 particles, one has to take into account that many terms of the order a . p’ are produced by the interaction, besides those appearing at the vertex where a quark-anti-quark pair is created. While the latter ones can be accounted for by the 3P0decay model, the other ones cannot. For that particular contribution, which could represent some average one, the structure of the operator is obtained as above for spin-less particles and is given by the replacement in Eq. (1):
a (fl- fl’) + “(E- 2 e4)” G ( f l ) v(fl’). ‘
2fi
(5)
If the meson is strongly bound ( E negligible) and eq approximated by the quark mass, the value 2 6 N 5 is obtained for y. This value compares well to the value that can be obtained from meson decays6 but is significantly smaller than the one derived from baryon decays4i8. Within conventions, the sign that is required in some cases is also known. A relativistic approach based on the description of mesons by BetheSalpeter amplitudes suggested some similarity with the quark-pair creation modelg. Comparison with the present work indicates a close relation which strongly supports the hypothesis that the 3P0 decay model, as completed here, would implement boost effects that an approximate (non-relativistic) description of hadrons cannot account for. The possibility that it still accounts for other effects remains open however. References
1. L. Micu, Nucl. Phys. B 10,521 (1969). 2. A. Le Yaouanc et al., Hadron Transitions in the Quark Model (Gordon and Breach, 1988). 3. W.Roberts and B. Silvestre-Brac, Phys. Rev. D 57, 1694 (1998). 4. F. Can0 et al., 2. Phys. A 359,315 (1997). 5. R. Kokoski and N. Isgur, Phys. Rev. D 35,907 (1987). 6. E.S. Ackleh, T. Barnes and E.S. Swanson, Phys. Rev. D 54,6811 (1996). 7. B. Desplanques, L. TheuBl and S. Noguera, Phys. Rev. C 65,038202 (2002). 8. L. TheuBl et al., Eur. Phys. J. A 12,91 (2001). 9. D.S. Kulshreshtha and A.N. Mitra, Phys. Rev. D 28,588 (1983).
DO WE SEE CHIRAL SYMMETRY RESTORATION IN BARYON SPECTRUM? LEONID YA. GLOZMAN Institute for Theoretical Physics, University of Graz, Universitatsplatz 5, A-801 0 Graz, Austria
THOMAS D. COHEN Department of Physics, University of Maryland, College Park, Maryland 20742-4111,USA The evidence and the theoretical justification of chiral symmetry restoration in high-lying baryons is presented.
I t has recently been suggested that the parity doublet structure seen in the spectrum of highly excited baryons may be due to effective chiral symmetry restoration for these states l . This phenomenon can be understood in very general terms from the validity of the operator product expansion (OPE) in QCD at large space-like momenta and the validity of the dispersion relation for the two-point correlator, which connects the spacelike and timelike regions (i.e. the validity of Kallen-Lehmann representation) Consider a two-point correlator of the current (that creates from the vacuum the hadrons with the given quantum numbers) at large spacelike momenta Q2, where the language of quarks and gluons is adequate and where the OPE is valid. The only effect that chiral symmetry breaking can have on the correlator is through the nonzero value of condensates associated with operators which are chirally active (ie. which transform nontrivially under chiral transformations). To these belong (qq) and higher dimensional condensates that are not invariant under axial transformation. At large Q 2 only a small number of condensates need be retained to get an accurate description of the correlator. Contributions of these condensates are suppressed by inverse powers of Q 2 . At asymptotically high Q2, the correlator is well described by a single term-the perturbative term. The essential thing to note from this OPE analysis is that the perturbative contribution knows nothing about chiral symmetry breaking as it contains no chirally nontrivial condensates. In other words, though the chiral symmetry is broken in the vacuum and all chiral noninvariant condensates are not zero, their influence on the correlator at asymptotically high Q2 vanishes. This is in contrast to the situation of low values of Q2, where the role of chiral condensates is crucial. This shows that at large spacelike momenta the correlation function be213.
425
426
comes chirally symmetric. The dispersion relation provides a connection between the spacelike and timelike domains. In particular, the large &' correlator is completely dominated by the large s spectral density. (The spectral density has the physical interpretation of being proportional to the probability density that the current when acting on the vacuum creates a state of a mass of &.) Hence the large s spectral density must be insensitive to the chiral symmetry breaking in the vacuum. This is in contrast to the low s spectral function which is crucially dependent on the quark condensates in the vacuum. This manifests a smooth chiral symmetry restoration from the low-lying spectrum, where the chiral symmetry breaking in the vacuum is crucial for physics, to the high-lying spectrum, where chiral symmetry breaking becomes irrelevant and the spectrum is chirally symmetric. Microscopically this is because the typical momenta of valence quarks should increase higher in the spectrum and once it is high enough the valence quarks decouple from the chiral condensates of the QCD vacuum and the dynamical (quasiparticle or constituent) mass of quarks drops off and the chiral symmetry gets restored This phenomenon does not mean that the spontaneous breaking of chiral symmetry in the QCD vacuum disappears, but rather that the chiral asymmetry of the vacuum becomes irrelevant sufficiently high in the spectrum. The physics of the highly-excited states is such as if there were no chiral symmetry breaking in the vacuum. One of the consequences is that the concept of constituent quarks, which is adequate low in the spectrum, becomes irrelevant high in the spectrum. If high in the spectrum (i.e. where the chiral symmetry is approximately restored) the spectrum is still quasidiscrete, then the phenomenological manifestation of the chiral symmetry restoration would be that the highly excited ~ hadrons should fall into the representations of the s U ( 2 ) ~x s U ( 2 ) group, which are compatible with the definite parity of the states - the parity-chiral multiplets In the case of baryons in the N and A spectra these multiplets are either the parity doublets (( 1/2,0) @ (0,1/2) for N * and (3/2,0) @ (0,3/2) for A*) that are not related to each other, or the multiplets (1/2,1) @ (1,1/2) that combine one parity doublet in the nucleon spectrum with the parity doublet in the delta spectrum with the same spin. Summarizing, the phenomenological consequence of the effective restoration of chiral symmetry high in N and A spectra is that the baryon states will fill out the irreducible representations of the parity-chiral group. If (1/2,0) @ (0,1/2) and (3/2,0) @ (0,3/2) multiplets were realized in nature, then the spectra of highly excited nucleons and deltas would consist of parity doublets. However, the energy of the parity doublet with given spin in the nucleon spectrum a-priori would not be degenerate with the doublet with the 'p4.
'i3.
427
same spin in the delta spectrum; these doublets would belong to different representations , i e . to distinct multiplets and their energies are not related. On the other hand, if (1/2,1) @ (1,1/2) were realized, then the highly lying states in N and A spectrum would have a N parity doublet and a A parity doublet with the same spin and which are degenerate in mass. In either of cases the highly lying spectrum must systematically consist of parity doublets. We stress that this classification is the most general one and does not rely on any model assumption about the structure of baryons. What is immediately evident from the empirical low-lying spectrum is that positive and negative parity states with the same spin are not nearly degenerate. Even more, there is no one-to-one mapping of positive and negative parity states of the same spin with masses below 1.7 GeV. This means that one cannot describe the low-lying spectrum as consisting of sets of chiral partners. The absence of systematic parity doublets low in the spectrum is one of the most direct pieces of evidence that chiral symmetry in QCD is spontaneously broken. However, as follows from the discussion above, there are good reasons to expect that chiral symmetry breaking effects become progressively less important higher in the spectrum. As a phenomenological manifestation of this smooth chiral symmetry restoration one should expect an appearance of systematic parity-chiral multiplets high in the spectrum. Below we show all the known N and A resonances in the region 2 GeV and higher and include not only the well established baryons (“****” and “***” states according to the PDG classification), but also “**” states that are defined by PDG as states where “evidence of existence is only fair”. In some cases we will fill in the vacancies in the classification below by the “*” states, that are defined as “evidence of existence is poor”. We mark both the 1-star and 2-star states in the classification below. 1
J
=2 : N’(2100) (*), N-(2090) (*), A’(1910) 3 2
J = - : N+(1900)(**), N-(2080)(**), A’(1920)
5
J
= - : N+(2000)(**), N-(2200)(**), b’(1905) 2
7
J = - : N’(1990)(**), N-(2190) 2
, A’(1950)
, A-(1900)(**);
, A-(1940) (*); , A-(1930) , A-(2200) (*);
;
428
J
9
= - : N’(2220) 2
11 J = y :
, N-(2250)
, A+(2300)(**), A-(2400)(**);
, A’(2420)
, N-(2600)
?
13 J = - : N+(2700)(**), 2
?
9
?
,
?
,
, A-(2750)(**);
15 ? ? , A+(2950)(**), ? 2 The data above suggest that the parity doublets in N and A spectra are approximately degenerate; the typical splitting in the multiplets are 200 MeV or less, which is within the decay width of those states. Of course, as noted above,“nearly degenerate’’ is not a truly well-defined idea. In judging how close to degenerate these states really are one should keep in mind that the extracted resonance masses have uncertainties which are typically of the order of 100 MeV. If the mass degeneracy between N and A doublets is accidental, then the baryons are organized according to (1/2,0) @ (0,1/2) for N and (3/2,0) @ (0,3/2) for A parity-chiral doublets. This possibility is supported by the fact that one observes systematic parity doublets in the nucleon spectrum as low as at M 1.7 GeV, while there are no doublets at this mass in the A spectrum. If the mass degeneracy between the highly-lying nucleon and delta doublets is not accidental, then the highly lying states are organized according to (1/2,1)@(1,1/2) representation. It can also be possible that in the narrow energy interval more than one parity doublet in the nucleon and delta spectra is found for a given spin. This would then mean that different doublets would belong to different parity-chiral multiplets. While a discovery of states that are marked by (?) would support the idea of effective chiral symmetry restoration, a definitive discovery of states that are beyond the systematics of parity doubling, would certainly be strong evidence against it. The nucleon states listed above exhaust all states (“****”, I L * * * ” , LL**X , “*”) in this part of the spectrum included by the PDG. However, there are some additional candidates (not established states) in the A spectrum. In the J = 5/2 channel there are two other candidate states A+(2000)(**) and A-(2350)(*); there is another candidate for J = 7/2 positive parity state - A+(2390)(*) as well as for J = 1/2 negative parity state A-(2150)(*). J=-:
1
-
-
429
Certainly a better exploration of the highly lying baryons is needed. This task is just for the facilities like in JLAB, BNL, SAPHIR, SPRING-8 and similar. Recent data on the highly excited mesons give a very strong evidence of chiral symmetry restoration in meson spectra too '. References
1. L. Ya. Glozman, Phys. Lett. B475 (2000) 329. 2. T . D. Cohen and L. Ya. Glozman, Phys. Rev. D65 (2002) 016006. 3. T. D. Cohen and L. Ya. Glozman, Int. J . Mod. Phys. A17 (2002) 1327. 4. L. Ya. Glozman, Phys. Lett. B539 (2002) 257.
VIRTUAL COMPTON SCATTERING: RESULTS FROM JEFFERSON LAB L. VAN HOOREBEKE (FOR THE JEFFERSON LAB HALL A/VCS COLLABORATION) Dept. Subatomic and Radiation Physics - RUG, Pmeftuinstmat 86, 9000 Gent, Belgium Virtual Compton Scattering off the proton has been studied at Q2-values of 1.0 and 1.9 (GeV/c)' in Hall A at the Thomas Jefferson National Accelerator Facility (JLab). Data were taken below and above the pion production threshold as well as in the resonance region. Results obtained below pion threshold at Q2 = 1.0 (GeV/c)2are presented in this paper.
1
Virtual Compton Scattering and Generalized Polarizabilities
Virtual Compton Scattering (VCS) off the proton refers to the reaction y*p + yp' where y* stands for an incoming virtual photon. Below pion threshold this reaction allows access to 6 new observables called Generalized Polarizabilities (GPs)'l2. They are a function of Q2 or q (the modulus of the cm virtual photon three-momentum) only and are extensions of the electromagnetic polarizabilities a: and obtained from Real Compton Scattering (RCS, Q 2 = 0 (GeV/c)2). VCS off the proton can be accessed experimentally through the photon electro-production reaction e p + e'p'y. The real photon y (with q' the modulus of its cm three-momentum) can be emitted either by the incoming or the outgoing electron (the Bethe-Heitler contribution) or by the proton itself (the actual VCS process, containing the Born and Non-Born contributions). The Non-Born contribution contains the new physics and can be parametrized in terms of the 6 GPs. The Bethe-Heitler and Born (BH B ) contributions can be accurately calculated using QED if the electromagnetic form factors of the proton are known. The ep + e'p'y reaction cross section d o 5 / d k ~ , , d n $ b d S 2 depending ~~ on q, q', E (the virtual photon polarization), 0 and cp (the spherical angles indicating the cm direction of the outgoing photon relative to the virtual photon direction) can then conveniently be arranged as
+
+
wherein d5aBH+B is the BH B cross section and @$!Po is the lowest order polarizability effect where @ is a phase space factor. Qo contains the GPs and
430
431
in case of an unpolarized experiment at fixed q one can write
Here the PIJ are structure functions which consist of linear combinations of five (out of six independent) GPs3 and v1 and v2 are known kinematical coefficients depending on q, c, 8,cp. An experiment performed at fixed q and e allows to deduce PLL - $PTT and PLT. First such results were obtained from data measured below pion production threshold at MAMI/Mainz4 at q = 600 MeV/c ( Q 2 = 0.33 (GeV/c)2). The VCS experiment (E93-050)6performed at JLab has taken data below and above pion threshold at Q2 = 1.0 and 1.9 (GeV/c)28,9. Meanwhile, Pasquini et aL5 have developed a dispersion relation formalism for VCS which can be used as a tool to extract GPs from data measured in the A(l232)-resonance region and below. In this paper we restrict ourselves to JLab results obtained at Q2 = 1.0 (GeV/c)2below pion threshold at the present stage of the analysis. 2
Experimental Method and Data Analysis
The experiment was performed in Hall A of JLab using a beam energy of 4 GeV and a liquid hydrogen target. The scattered electron and recoil proton were detected in coincidence in two high-resolution magnetic spectrometers. Real photon production events were identified by missing-mass reconstruction. For the determination of the absolute cross section, the detector acceptance was accurately determined using an extensive Monte Car10 simulation7 which generates events starting from the B H B cross section and incorporates all resolution deteriorating effects. The cross section behaviour in the simulation was iterated using a lowest-order polarizability effect on top of the B H B cross section until convergence was obtained. Radiative corrections have been fully appliedlO.
+
+
3
Results
- Discussion
The JLab VCS experiment allows to obtain cross sections in and out of the leptonic plane. The left-hand panel of fig. 1shows the cross section determined in the leptonic plane as a function of 8 for q' = 45,75 and 105 MeV/c (solid points), the full curve representing the B H + B cross section. At low q' the data are in near agreement with the B H + B cross section (as they should according to Eq. (l),this indicates the quality of the data analysis method),
432
r ‘ l
n
‘,,
20
2e$ 1 5 1
s
_/ % -
PLL-PJ
E
= 2.32 f 0.22 f 7 GeV.’
PL,=-0.42f0.11f7GeV”
xz s 1.00
c---
-2
Figure 1. Left-hand panel: absolute cross sections (solid points) for the ep + e’p’y reaction obtained in the leptonic plane as a function of 0 at q = 1080 IMeV/c (Q2= 0.923 (GeV/c)2) and e = 0.95, for three different values of q’. The curve represents the BH B cross section. Right-hand panel: fit according to Eq. (2) to the data obtained in and out of the leptonic plane. The slope and intercept yield the two combinations of GPs. The errors indicated are statistical only, the systematic error (indicated by question marks) has still to be determined.
+
while with increasing q’ one observes an increasing deviation from the B H +B cross section due to the polarizability effect. This behaviour is also observed for the data obtained out of plane. For each combination of angles ( 0 , ~ XI!o ) should fullfill Eq. (2). In case one makes the assumption that higher order terms do not play a role in Eq. (l), one can determine the value of 90as the mean over the three q‘ values of (d5aeZp- d 5 a ~ ~ + ~ ) / [ ’ P(low q ’ ]energy expansion (LEX) analysis, exactly the same approach was taken for the MAMI experiment4). Doing this for 12 data points obtained in the leptonic plane and 20 data points out of the leptonic plane, one can plot the left-hand side of Eq. (2) as a function of V I / V ~ , as shown in the right-hand panel of fig. 1. The data points are reasonably
433
well aligned and a linear fit to the data yields PLL - ~ P T Tas slope and PLT as intercept. The indicated errors on the obtained values are statistical only, the systematic errors still have to be determined. The obtained values for the two structure functions are about 1/10 of the values measured at Q2 = 0.33 (GeV/c)2 ‘. Concluding, it is clear that the klose t o final” results presented here are very promising and indicate a strong Q2 dependence of the structure functions PLL - $PT, and PLT. To finalize the analysis, the systematic errors have t o be determined and additional stability checks of the data have to be performed. In addition to the LEX analysis, it is also planned to use the data obtained below pion threshold to extract GPs using the new dispersion relation formalism5. Acknowledgments
This work was supported by DOE, NSF, by contract DE-AC05-84ER40150 under which the Southeastern Universities Research Association (SURA) operates the Thomas Jefferson National Accelerator Facility for DOE, by the French CEA, the Universith Blaise Pascal de Clermont-Ferrand and the CNRS/IN2P3 (France), the FWO-Flanders (Belgium), the BOF-Gent University (Belgium) and by the European Commission ERB FMRX-CT96-0008. References 1. P.A.M. Guichon, G.Q. Liu and A.W. Thomas, Nucl. Phys. A 591, 606
(1995). 2. D. Drechsel, G. Knochlein, A. Metz and S. Scherer, Phys. Rev. C 55, 424 (1997); D. Drechsel et al., Phys. Rev. C 57, 941 (1998). 3. P.A.M. Guichon and M. Vanderhaeghen, Prog. Part. Nucl. Phys. 41, 125 (1998). 4. J. Roche et al., Phys. Rev. Lett. 85, 708 (2000). 5. B. Pasquini et al., Eur. Phys. J. A l l , 185 (2001), and also B. Pasquini, these proceedings. 6. P.Y. Bertin, P.A.M. Guichon and C. Hyde-Wright, spokespersons JLab E93-050 proposal, (1993). 7. L. Van Hoorebeke et al., in preparation. 8. H. Fonvieille, these proceedings. 9. L. Todor, these proceedings. 10. M. Vanderhaeghen et al., Phys. Rev. D 62, 025501 (2000).
VIRTUAL COMPTON SCATTERING AND NEUTRAL PION ELECTRO-PRODUCTION FROM THE PROTON IN THE NUCLEON RESONANCE REGION L.TODOR Carnegie Mellon University, Pittsburgh, PA 15213 VCS COLLABORATION Jefferson Lab, Newport News, VA 23606 The Experiment (E93-050) at Jefferson Lab measured the e p --$ epy and e p -+ epno cross sections in the nucleon resonance region, from threshold to W = 1.9 GeV at Q 2= 1 GeV2 for backward emission of the y or no.
1
Introduction
The electro-production of resonances from the proton followed by photodecay, known as Virtual Compton Scattering (VCS) is a necessary element of the study of resonances together with the meson decaying channels. The p ( e , e’p’)y amplitude is the coherent sum of VCS and Bethe-Heitler(BH) amplitudes. In the BH process, the final real photon is emitted by the electron either before or after the interaction with the proton. The BH amplitude peaks in the directions of the incident and scattered electron. The experimental kinematics were chosen such that for the VCS reaction, the virtual photon and the final photon were back to back. In this case the BH amplitude is minimized
’.
2
Experimental Details
The experiment ran in March-April 1998 and used the TJNAF 4 GeV electron beam incident on Hall A liquid hydrogen target with a luminosity 2 4 . cm-’ s-’. The scattered electron and proton were detected in coincidence with the two Hall A high resolution spectrometers (HRS). Each HRS consists of a QQDQ magnetic system and a detection package with scintillators, wire chambers, and a electromagnetic calorimeter. The electron spectrometer was set to detect scattered electrons corresponding at a fixed 4-momentum transfer of Q2 = 1 GeV’. The energy transfer from the electron was varied so that for the VCS reaction, the invariant mass for the virtual photon plus proton system ranged from 1.0 GeV to 1.9 GeV. We identified the true coincidences using both time and space coincidence. For the coincidence timeof-flight resulting
434
435
from back-projecting the detected particles to the target we reconstruct the true coincidence with a FWHM of 1.2 11s. Comparing the transverse vertex position as determined from the crossing of the detected charged particles trajectories with the instantaneous beam position we reconstruct the true coincidence with a FWHM of 2.0 mm. We identified the undetected particle in the final state (noor 7) using the missing mass technique. Although the purpose of the experiment was to measure the p ( e , e‘p’)y cross-section, within the acceptance we measured the p ( e , e‘p’).rro cross-section in a kinematic region poorly covered previously.
3 p ( e , e‘p’)y Cross-section
I
-9
I
I
1
I
I
I
1.2
1.4
1.6
I
I
1.8
W (GeV)
Figure 1. p ( e , e’p’)y cross-section function of center of mass energy W for Q 2= 1GeV2, and cosOcm = -0.975. @ is the azimuthal angle between the leptonic and hadronic scattering planes. Ocm is the polar angle between the emitted photon and the direction of momentum transfer from the electron. The black curves represent the calculated BH+Born cross-section and the blue are the values calculated with the dispersion relation formalism.
The 5-fold differential cross section was evaluated in the phase-space W , Q2, &, O,,, a. We compared our results with the model prediction using
436
dispersion relation formalism and the BH plus Born (proton in intermediate state) calculation. We note at @ = 15’ and 165”, the destructive and constructive interference, respectively, of the BH and VCS amplitudes near W = 1 GeV. At large W we also note the agreement between the data and the BHfBorn calculation, suggesting a cancellation of the the contributions of excited intermediate states. 4
p ( e , e’p’)7r0 Cross-section
The 5-fold differential cross section is usual described (Hand convention) as a product between a photon flux and the 2-fold differential cross section. Using the angular distribution we extract the transverse and longitudinal terms of the cross section.
We used the MAID2000 (Unitary Isobar Model) parametrisation in our simulation to extract the p ( e , e’p’)7ro differential cross-sections. From our results, the MAID photon point parameters were readjusted; substantial differences were noticed for &1(1535), S31(1620) and &3(1700) parameters (Fig. 4). Similar comparison was performed for SAID model. 5
Conclusion
The 7ro and y electro-production reactions were measured simultaneously, in the H ( e , e’p)X at Q2 = 1 GeV2, with the proton detected parallel to the virtual photon direction. These are the first ever measurements of the excitation function of the VCS process in the resonance region. The VCS data show a strong interference between the Compton and Bethe-Heitler processes at low W , and a smooth convergence towards the Born cross-section at high W . In ~ , and the 7ro electroproduction case, the three cross sections daT + ~ d a dcq-L, duTT are separated. Above the A resonance, there are strong disagreements between the data and the MAID2000, and SAID parameterizations. This reflects the limited previous data set on 7ro electroproduction.
Acknowledgments The collaboration thanks to Hall A technical staff for their support during this experiment. The Southern Universities Research Association (SURA)
437 I
L
v! i
n
-1
b
u -1
10
1
I
0.4
0.2 0.0
-0.2
0.1
0.0 -0.1
-0.2 -0.3
1
1 2
MAID old set
14
16
__ MAID new set
18
2
W (GeV)
Figure 2. p ( e , e'p')ro separated cross-sections as functions of center of mass energy W, at 1 GeV2, and cosBcm = -0.975..
Q2 =
operates the Thomas Jefferson National Accelarator Facility for the United States Department of Energy under contract DEAC05-84ER40150. References 1. P.Y. Bertin, C. Hyde-Wright and P.A.M.Guichon, Jefferson Lab
PR93050, (1993). 2. B. Pasquini et al.,Phys. Rev. C 62, 052201 (2001). 3. D.Drechse1 et al., Nucl. Phys. A 645, 145 (1999).
THE HYPERCENTRAL CONSTITUENT QUARK MODEL M. M. GIANNINI, E. SANTOPINTO, A. VASSALLO Dipurtimento &i Fisica dell’Universita’ di Genova und Istituto Nazionale di Fisica Nucleare, Sezione di Genova, via Dodecaneso, Genova, I--16146, Italy E-mud: gia7-Lriiwi~~e.infn.it,
[email protected],
[email protected] The hypercentrd constituent quark model contains a spin independent three-quark interaction inspired by lattice QCD calculations which reproduces the average enThe splittings are obtained with a residual generalergy of SU(6) multiplets ized SU(6)-breaking interaction including an isospin dependent term The long standing problem of the Roper is absent and all the 3- and 4-star states are well reproduced. The model has been used in a systematic way for transverse and longitudinal electromagnetic transition form factor of the 3- and 4- star and also for the missing resonances. The prediction of the electromagnetic helicity amplitudes agrees quite well with the data except for low Q 2 , showing that it can supply a realistic set of quark wave functions. In particular we report the calculated helicity amplitude A1j2 for the S11(1535), which is in agreement with the TJNAF data 3.
’.
1
’.
Introduction
The baryon spectrum is usually described quite well by different Constituent which have in common the three constituent quark spatial Quark Models degrees of freedom and the underlying SU(6) spin-flavour structure. However they differ for the chosen potential, that is for the wave functions, and in particular also for the way in which the S U ( 6 ) symmetry is broken. By comparing various models one can see that each of them has different predictions concerning the position and number of the missing resonances under 2 GeV, giving the possibility of discriminate among them, but due to the difficulties of the analysis of the experimental data this is not always possible. In this respect the study of hadron spectroscopy is not sufficient to distinguish among the various forms of quark dynamics and to this end one has to consider other observables more sensitive to the wave functions and to the way in which SU(6) is broken such as the e.m. transition form factors, the so called helicity amplitudes. 114,5,
2
The Model
The hypercentral Constituent Quark Model (hCQM) consists of a hypercentral quark interaction containing a linear plus coulomb-like term, as sug-
438
439 gested by lattice QCD calculations
where x is the hyperradius defined in terms of the standard Jacobi coordinates p and A. We can think of this potential both as a tjwo body potential in the hypercentral approximation (which, as shown by Fabre de la Ripelle ‘,is a good approximation for the lower states) or as a true three body potential. A hyperfine term of the standard form is added and treated as a perturbation. The paramet,ers a , T and the strength of the hyperfine interaction are fitted to the spectrum ( a = 1.61 fm-’, T = 4.59 and the strength of the hyperfine interaction is determined by the A - Nucleon mass difference). Having fixed the values of these parameters, the resulting wave functions have been used for the calculation of the photocouplings (J,the transition form factors for the negative parity resonances lo, the elastic form factors l1 and the ratio between the electric and magnetic form factors of the proton l 2 and now also for the longitudinal and transition form factors for all the 3- and 4-stars and the missing resonances 13.
3
The electromagnetic transition form factors
The helicity amplitudes for the electroexcitation of baryon resonances, A l l 2 , A312 and S112 are calculated as the transition matrix elements of the transverse and longitudinal electromagnetic interaction between the nucleon and the resonance states given by this model. A non relativistic current for point, quarks is used. In particular, in Fig.1, one can see the predictions (full line) for the AY12 for the Sll(1535) lo which are in agreement with the new TJNAF data ’. The results for the helicity amplitudes for all the negative parity resonances are reported in Ref.l0. The prediction of the electromagnetic helicit,y amplitudes agrees quite well with the data showing that the hCQM can supply a realistic set of quark wave functions. In general the Q2 behaviour is reproduced, except for discrepancies at small Q 2 , specially in the A:,2 amplitude of the transition to the &(1520) state. These discrepancies could be ascribed to the non-relativistic character of the model, and to the lack of explicit quark-antiquark configurations which may be important at low Q 2 . The longitudinal and transverse transition form factors for all the 3- and 4-stars and the missing resonances have been calculated 13. The computer code is at disposal under request and it can be used also with other models. In this way it can be a useful tool for the forcoming analysis of the experimental data.
440 /
'
'
'
~
I
'
200 -
150
-
100
'
I
'
'
'
'
l
N(1535)S,,
-
-
-
-
-
-3-
z
s
"
A",,,
' I -Q
50 -
.* -.
----_--_ -
-
. .
0
-
0 -
1
1
,
,
,
1
,
,
,
,
1
1
1
1
,
I
-
Figure 1. Comparison between the new TJNAF data for the helicity amplitudes the Sil(1535)
and the calculations with the hCQM
for
g.
The relativistic corrections at the level of boosting the nucleon and the resonances states to the EVF or the Breit frame are important but not sufficient 15. These boost effects are indeed important for the elastic e.m. form factors, giving origin to the decreasing behaviour of the ratio R of the electric and magnetic proton form factors, as shown by the recent TJNAF data 16. 4
SU(6)-breaking residual interaction.
There are different motivations for the introduction of a residual flavour dependent term in the threequark interaction. The well known GuerseyRadicati mass formula l7 contains a flavour dependent term, which is essential for the description of the strange spectrum. In the chiral Constituent Quark Model 6 1 the non confining part of the potential is provided by the interaction with the Goldstone bosons, giving rise to a spin- and isospin-dependent interaction. More generally, one can expect that the quark-antiquark pair production can lead to an effective residual quark interaction containing an isospin (or flavour) dependent term and with these motivations in mind, we have introduced isospin dependent terms in the hCQM hamiltonian. The complete interaction used is given by Hint =
V(z)
+ H s + HI + HSI
1
(2)
were V(x) is the linear plus hypercoulomb SU(6)-invariant potential, already described in Eq.(l), while Hs HI H S I , is a residual SU(6)-breaking in-
+ +
441
teraction that can be treated as a perturbative term leading to an improved description of the spectrum. 5
Conclusions
We have presented various results predicted by the hypercentral Constituent Model compared with the experimental data. We have shown that the hCQM can supply a realistic set of quark wave functions. References 1. M. Ferraris, M.M. Giannini, M. Pizzo, E. Santopinto and L. Tiator, Phys. Let,t,.B364, 231 (1995). 2. M.M. Giannini,E. Santopinto,A. Vassallo, Eur.Phys.J. A12, 447 (2001); Nucl.Phys.A699,308 (2002). 3. R.A. Thompson et al., Phys. Rev. Lett. 86, 1702 (2001). 4. N. Isgur and G. Karl, Phys. Rev. D18, 4187 (1978); D19, 2653 (1979); D20,1191 (1979); S. Godfrey and N. Isgur, Phys. Rev. D32,189 (1985); 5. S. Capstick and N. Isgur, Phys. Rev. D 34,2809 (1986). 6. L. Ya. Glozman, et al., Phys. Rev. C57, 3406 (1998). 7. Gunnar S. Bali, Phys. Rep. 343,1 (2001). 8. M. Fabre de la Ripelle and J. Navarro, Ann. Phys.(N.Y.)123, 185 (1979). 9. M. Aiello, M. Ferraris, M.M. Giannini, M. Pizzo and E. Santopinto, Phys. Lett. B387, 215 (1996). 10. M. Aiello, M. M. Giannini, E. Santopinto, J. Phys. G: Nucl. Part. Phys. 24, 753 (1998) 11. M. De Sanctis, E. Santopinto, M.M. Giannini, Eur. Phys. J. A l , 187 (1998). 12. M. De Sanctis, M.M. Giannini, L. Repetto, E. Santopinto, Phys. Rev. C62,025208 (2000). 13. to be published. 14. E. Santopinto, F. Iachello and M.M. Giannini, Nucl. Phys. A623, 100c (1997); Eur. Phys. J. A1,307 (1998). 15. M. De Sanctis, E. Santopint,o, M.M. Giannini, Eur. Phys. J. A2, 403 (1998). 16. M.K. Jones et al., Phys. Rev. Lett. B84,1398 (2000). 17. F. Guersey and L.A. Radicati, Phys. Rev. Lett. 13,173 (1964); 18. Particle Data Group, Eur. Phys. J. C15, 1 (2000).
442
Fritz Klein and Peter Barnes
Rolf Ent, Frank Dohrmann,Jorg Reinhold,andBen Zeidman
NEW SEARCH FOR THE NEUTRON ELECTRIC DIPOLE MOMENT P. D. BARNES Los Alamos National Laboratory, N.M. 87545, USA for the NEUTRON EDM COLLABORATION We report on a new experiment to search for the neutron electric dipole moment which has the potential to lower the current limit by a factor of 50 to 100. A unique approach to this measurement is described including the results of recent measurements at LANSCE of the mass diffusion coefficient for 3He in superfluid 4He.
1. Introduction
The possible existence of a nonzero electric dipole moment, EDM, of the neutron is of great fundamental interest in itself and directly impacts our understanding of the nature of electro-weak and strong interactions. The experimental search for this moment has the potential to reveal new sources of T and CP violation and to challenge calculations that propose extensions to the Standard Model l . In addition, the small value for the neutron EDM continues to raise the issue of why the strength of the CP violating terms in the strong Lagrangian, are so small. This result seems to suggest the existence of a new fundamental symmetry that blocks the strong CP violating processes. Searches for the EDM of the neutron date back to a 1957 paper of Purcell and Ramsey2. This led to an experiment using a magnetic resonance technique at ORNL, where they established a value3 of d, = - 0.1 - 2.4 x 1 F2'e cm. An MIT/BNL experiment used Bragg scattering of neutrons from a CdS crystal to search for the neutron EDM, and obtained a value4 of d, = 2.4 - 3.9 x 10 -22e cm. In the intervening 30 years, a series of measurements with increasing precision have culminated in the current best limit of d, < 0.63 x 10 -25e cm [90% C.L.] obtained in measurements at the ILL reactor at Grenoble5. Thus there has been an impressive reduction with time, of the experimental limit for d, as illustrated in Fig 1.
443
444
2. Measurement Strategy The new experiment6, is based on the magnetic resonance technique of rotating magnetic dipole moments in a magnetic field and requires a precision measurement of the neutron precession frequency under the influence of an electric field. The apparatus, shown in Fig. 2, includes two cells that contain neutrons, 3He, and 4He. The strategy6 features: a) using a dilute mixture of polarized 3He in superfluid 4He as a working medium for the very high electric field environment; b) determining in situ the magnetic field experienced by the neutrons, using a direct SQUID measurement of the precession frequency of the 3He magnetic dipoles; and, finally, c ) making a comparison measurement of changes in the precession frequency, under E field reversal, of the neutron and 3He components of the fluid, where the neutral 3He atom does not have an EDM. 1 -1
E
S
l
1
Year Fig. 1. Upper limits of the neutron EDM plotted as a function of year of publication. The solid circles correspond to neutron scattering experiments. The open squares represent in-light magnetic resonance measurements, and the solid squares signify UCN magnetic resonance experiments
445
Additional features include loading two identical neutron traps with UCNs through a superfluid 4He-phonon recoil process, introducing highly polarized He atoms into the trap in order to confirm alignment of the trapped UCN spins, operating the trap at extremely cold temperatures (-300 mK) to minimize UCN losses at the walls, and, finally, detecting the precession frequency difference, independently of the SQUID detectors, by viewing the w3He absorption reaction with photomultitipliers, through the induced 4He scintillation light. The process of validating these techniques and determining their limits is well started. 3. Experimental Apparatus
The technique relies on simultaneous precession of trapped ultra-cold neutrons and 3He atoms in a bath of superfluid 4He at a temperature of 300 mK. The relative precession frequencies of the neutrons and the 3He atoms in a B field, are compared in each of two traps. For one the electric field is parallel to B, for the other, antiparallel.
-
A schematic of the heart of the experiment in the main cryostat, is shown in Fig. 2. The pair of neutron cells are placed in the gaps between the three electrodes as shown in Fig. 3 . The cells consist of two rectangular acrylic tubes, each with dimensions of approximately 7 cm x 10 cm x 50 cm long. The cold neutron beam enters along the long axis of the cell and passes through either deuterated acrylic or deuterated polystyrene windows attached to each end. The beam exits at the rear of the cell and is absorbed outside the cell in a beam stop made from a neutron absorbing material. The difference in the neutron precession frequency in the two traps (of the order of ~ H zis) directly proportional to the neutron EDM. 4. 3He Diffusion in 4He
An important technical issue for the EDM measurement is the physics of 3He propagation through the superfluid 4He, where it has both diffusion and ballistic characteristics. These features are very temperature dependent. To clarify this, we used a neutron tomographic technique at flight path 11B at LANSCE7, to
446
Light Guides
Cells Between
itrari ce
c cIS 8 Coil
Fig 2. Experimental cryostat. The neutron beam enters from the right. Two neutron cells are between the three electrodes. Scintillation light from the cells is monitored by the light guides and photomultipliers.
study the spatial and temperature dependence of the 3He density. By irradiating a 3He-superfluid 4He cell with a narrow neutron beam (-2mm) we were able to measure the n-3He absorption yield as a function of position. Specifically we made a study of the changes in density of 3He near a heater as a function of applied heat current and were able to infer, with 20% accuracy, values of the mass diffusion coefficient, D, for 3He in 4He. At temperatures below 0.7 K, D was measured for the first time. At the lowest temperatures, D can be characterized7 as D = DT T-7 = (1.6 - 0.2) T-7 cm2/sec. We conclude that at temperatures below 0.6 K, ballistic 3He collisions with phonons provide the dominate mechanism for 3He scattering. At the very low temperatures (0.3 K) of the EDM experiment discussed above, the 3He atoms will rapidly traverse the neutron cell as required for an effective co-magnetometer. The design and construction of this neutron EDM experiment is in progress, for measurements at a new beam line at LANSCE.
447
Be Exit Ground Entrance
Stop or
Measuring
Window
TPB Walls Entrance Window
Cryostat Wall
Fig 3 The path of the neutrons through the cryostat. The beam enters from the right. It is about 3.1 m through the cryostat, wall to wall.
References I . G. Buchalla et al., NZK!Phys. B370, 69 (1992); A. J. Buras et al., N k ! Phys. B408, 209 (1993); M.
Ciuchini, N z d Phys. Proc.Sup@ 59, 149 (1997); 1. I. Bibi and A. I. Sanda, CP Vio/utiun (Cambridge University Press, 2000), p. 355.
2. E. M. Purcell and N. F. Ramsey, Phys. Rev. 78,807 (1950). 3. J. H. Smith, E. M. Purcell, and N. F. Ramsey, Phys. Rev. 108, 120 (1957). 4. C. G. Shull and R. Nathans, Phys. Rev. Lett. 19,384 (1967). 5 . P. G . Hams et al., Phys. Rev. L d f . 82,904 (1999). 6. G . Golub and S. K. Lamoreaux, Phys. Rep. 237, 1 (1994), I. B. Khriplovich and S. K. Lamoreaux, CP Vidution withour Strungmess (Springer Verlag, 1997).
7. S. K. Lamoreaux et al, submitted to Europhy. Lett. 58,718 (2002).
qq
LOOP EFFECTS ON BARYON MASSES DANIELLE MOREL* AND SIMON CAPSTICK’ Department of Physics, Florida State University, Tallahassee, FL 32306-4350, USA *E-mail: dmorelQdescartes.physics.fsu.edu E-mail: capstackOcsit.fsu.edu
Corrections to the mass= of baryons from baryon-meson loops are calculated using a pair-creation model to give the momentum-dependent vertices, and a model which includes configuration mixing to describe the wave functions of the baryons. A large set of baryon-meson intermediate states are employed, with all allowed SU(3)f combinations, and excitations of the intermediate baryon states up to and including the second hand of negative-parity excited states. It is found that roughly half of the splitting between the nucleon and Delta ground states arises from loop effects, and the resulting splittings of negative-parity excited states are sensitive to configuration mixing caused by the residual interactions. With reduced-strength one-gluon-exchange interactions between the quarks, there is a reasonable correspondence between model masses and the bare masses required to fit the masses extracted from data analyses.
1
Introduction
In QCD there are qqq(qq) configurations possible in baryons, and these must have an effect on the constituent quark model, similar to the effect of unquenching lattice QCD calculations. These effects can be modeled by allowing baryons to include baryon-meson (B’M) intermediate states, which lead to baryon self energies and mixings of baryons of the same quantum numbers. A calculation of these effects requires a model of baryon-baryon-meson (BB’M) vertices and their momentum dependence. It is also necessary to have a model of the spectrum and structure of baryon states, including states not seen in analyses of experimental data. This model will provide wave functions for calculating the vertices and knowledge of the thresholds associated with intermediate states containing missing baryons. Baryon self energies due to B‘M intermediate states and B’M decay widths can be found from the real and imaginary parts of loop diagrams. The size of such self energies can be expected t o be comparable to baryon widths. For this reason, they cannot be ignored when comparing the predictions of any quark model with the results of analyses of experiments. Since the splittings between states which result from differences in self energies can be expected to be comparable to those that arise from the residual interactions between
448
449
the quarks, a self-consistent calculation of the spectrum needs to adjust the residual interactions, and with them the wave functions of the states used t o calculate the BB‘M vertices, to account for these additional splittings. 2
Baryon Self Energies and Mass Spectra
The energy-dependent self-energy contributions to the mass of baryon B of a set of intermediate states B’M calculated in the center-of-momentum frame of baryon B is
where MLB,M,k, and mi are the BB‘M vertex, relative momentum, and masses of the intermediate hadrons respectively. Since the self energies are energy-dependent, it is necessary to solve for the ‘bare’ mass Eg required to reproduce the known physical mass mB of a given baryon B by solving the equation Eg + CB(EB) = m g over a wide range of bare energies EB. In the present work, a study of the self energies of ground and negativeparity excited N and A states is carried out using a 3Po pair-creation model with a modified operator 1,2 to calculate the momentum-dependent BB‘M vertices, and wave functions obtained from a relativized model with variable-strength spin-dependent (one-gluon exchange) contact and tensor residual interactions between the quarks. Learning from previous work this calculation takes into account a full set of spin-flavor symmetry related intermediate states B’M with M E {T,K , q,q’,p, w , K * } and B’E { N , A, N * ,A*, A, C, A*, X*}, including all excitations of the intermediate baryons up to and including the second band (N=3) of negative-parity states. Figure 1 shows how the ‘bare’ mass Eg [which solves EB +CB(EB)= mB for the ground state N and A] changes with the addition of intermediate states. Ground state (N=O) and negative-parity excited (N=l) baryons are seen to have the greatest effect while larger sets of intermediate states have little additional effect. This indicates that results have converged with the inclusion of the N = l band intermediate baryons. Similar results are obtained for the negative-parity excited states studied (not shown here) but with convergence requiring the inclusion of at least the N=2 band baryons in the set of intermediate states. Although results for the ground-state N and A are mostly independent of the choice of residual interactions included in the Hamiltonian, this is not the case for the negativeparity states, where configuration mixing in the wave functions plays an important role in the splitting between these states and in their respective self energies. 435,
450 4000
I
-
I
I
I
,
I
I
-,;
..
N112+(938)
3000 -
3000 -
2000
-1000
'
1.7
/!
- A312+(1232)
a
'
1.9
1
'
2.1
'
2.3
E (GeV)
'
"
2.5
2.7
-1000
-
'
1.7
' 1.9
2.1
2.3
E (GeV)
2.5
2.7
Figure 1. Sum of bare and self energies for the ground state N and A with contact residual interactions only. The long-dashed curve is calculated with only ground state intermediate baryons B', the short-dashed curve adds N = l band baryons, the short-dashed long-dashed curve adds N=2 band baryons, and the solid curve adds N = 3 intermediate baryons. Eg C B ( E B )= mg is solved where each curve intersects the horizontal solid line at the physical mass VZB.
+
Figure 2 presents a comparison between the spectrum of 'bare' masses Eg extracted from graphs similar to Fig. 1, and model masses generated by a Hamiltonian which includes both contact and tensor residual interactions. Reasonable overall agreement can be seen between the two spectra although the string tension or the quark mass needs to be adjusted to decrease the shift between the average mass of the ground-state N and A and the average mass of the P-wave baryons. Since some splittings resemble spin-orbit effects, further studies including spin-orbit residual interactions are required to complete the picture.
3
Conclusions
The results presented demonstrate that the bare energies required to fit the physical masses of the initial baryon states studied have converged, using a full set of SU(6)-related B'M intermediate states with excited baryons B' up to the top of the N=3 band. The ground-state N - A splitting has also converged and is found to be roughly 150 MeV, a result largely independent of the choice of inter-quark Hamiltonian used to generate the wave functions which can affect the vertices used to evaluate the self energies. Convergence of the bare energies required to fit the P-wave non strange baryon spectrum was also reached using this same set of B'M states. In contrast to the situation with the ground states, a larger set of intermediate states was found to be required for convergence. These bare energies are not 617
45 1 2900
16uO
2800
ISW
Figure 2. Bare energies (in MeV) of ground and P-wave excited state non-strange baryons required to fit their masses from analyses of data, calculated using wave functions which are eigenfunctions of a Hamiltonian with contact and tensor residual interactions (lightly shaded boxes, left scale) compared to model masses (in MeV) from the same Hamiltonian (dark-shaded boxes, right scale).
degenerate, and are found to depend on the inter-quark Hamiltonian used. This indicates that it is necessary t o use a self-consistent calculation of both the spectrum with its corresponding wave functions and the strong vertices in the calculation of the self energies. An extension of the present work to the ground-state and negative-parity excited A and C baryons is currently in progress. The mixing of both nonstrange and strange baryons with the same quantum numbers due to these B'M intermediate states is also under investigation. 4
Acknowledgments
This work is supported by the U.S. Department of Energy under contract DEFG02-86ER40273. References
1. B. Silvestre-Brac and C. Gignoux, Phys. Rev. D43, 3699 (1991). 2. P. Geiger and N. Isgur, Phys. Rev. D 44, 799 (1991). 3. S. Capstick and N. Isgur, Phys. Rev. D34, 2809 (1986). 4. P. Zenczykowski, Ann. Phys. (NY) 169,453 (1986). 5. M. Brack and R. K. Bhaduri, Phys. Rev. D35,3451 (1987). 6. D. Morel and S. Capstick, nuc-th/0204014, submitted to Phys. Rev. D. 7. D. Morel, PhD thesis (Florida State U., January 2002), nuc-th/0204028.
LEARNING FROM DISPERSIVE EFFECTS IN THE NUCLEON POLARISABILITIES HARALD W. GRIEDHAMMER T39, Technische Universitat Miinchen, 0-85747Garching, Germany EMail: hgrieophysik.tu-muenchen. de
Static nucleon polarisabilities gauge the stiffness of the nucleon against an external electro-magnetic field, parameterising the part of the real Compton amplitude at zero energy which is not explained by the pole terms, i.e. by the successive interactions of two photons with a point-like nucleon of anomalous magnetic moment n. Dynamical nucleon polarisabilities are the energy dependent generalisation to real Compton scattering and thus provide more information about the low energy effective degrees of freedom inside the nucleon. Here, I sketch their definition and interpretation in terms of the low energy degrees of freedom, referring to for particulars and references. Investigating in more detail the nucleon polarisabilities at non-zero photon energy, one first subtracts the “nucleon pole” effects from the real Compton amplitude T, writing T ( w , z ) = A 1 (w, z ) (Z‘* .Z) + A2(w, z ) (2 * . (Z. . . , for the two spin-independent structure amplitudes in the centre of mass (cm) frame, with the non-Born part already subtracted. w is the cm energy of an incident (outgoing) real photon with momentum (2) and polarisation 7 ( E l ) , scattering under the cm angle 8 off the nucleon, with z = cos 8. At fixed real photon energy, the structure dependent part of the amplitude is then analysed by expanding it in multipoles. In terms of the first four electric and magnetic (dipole and quadrupole) polarisabilities of definite multipolarity, c ~ E ~ ( wp) , ~ ( w1) , & E 2 ( W ) and p ~ 2 ( w )the , amplitudes read ‘i2
i) it)
+
w is the total cm energy and M the nucleon mass. where W = w + d The multipolarities are dis-entangled by their angular dependence. The prefactors are chosen such that at zero photon energy, the definitions of the static
452
453
-
polarisabilities are recovered, e.g.: &E = ~ E I ( W= 0),BM = ,BMI(W = 0). Dynamical polarisabilities test the temporal response of the global, low energy excitation spectrum of the nucleon at non-zero energy. They therefore contain information about dispersive effects induced by internal relaxation mechanisms, baryonic resonances and meson production thresholds of the nucleon. This is also clearly seen in Figs. 2, where the result of a dispersion theory analysis of the four leading dynamical polarisabilities is compared to a chiral effective field theory describing the nucleon at low energies, called Modified Small Scale Expansion MSSE. The latter is a rigorous, model-independent and systematic approach to low energy QCD. It incorporates the nucleon, the A(1232) and their respective pion clouds as explicit low energy degrees of freedom, see Fig. 1 for the dominant contributions Short distance physics
’.
Figure 1. The diagrams contributing at leading one loop order in MSSE. Graphs obtained by permuting vertices or external lines are not displayed. Double line: A(1232).
-
is sub-sumed into local counter terms whose strengths are na’ively given by dimensional analysis to be of the order of (daE1,dBMll 1 - 2n which would make them higher order effects. However, fitting these two free parameters to reproduce the static values of the dipole polarisabilities shows that they are indeed much larger, d a ~ 1M -5, 681211 M -10, i.e. of leading order in accord with the MSSE power counting. It is at this point that the new dimension of the dynamical polarisabilities comes into play by allowing for a parameter-free prediction of the energy dependence after the zero energy value is fixed. For example, a large dia-magnetic but only very weakly energy dependent contribution is needed in the magnetic dipole polarisability to cancel the well known large para-magnetism coming from the strong M 1 + M1 transition between nucleon and A which clearly rules this channel. As the shape of BM I ( W)is dominated by the A already below the pion production threshold w,, the good agreement between its experimentally measured value at zero energy (P~l(0) = 1.5) and the result of Heavy Baryon Chiral Perturbation aAll dipole polarisabilities here given in the “natural units” of lo-* fm3.
454 W,
W.
Y L
0 .
w,
30
.
wA
-
B
h 20
0 -5
_---
-10
p 10
-15
I
-20
0 50
100
1.50 200 w [MeV]
w"
250
300
50
0
175
22.5 w [MeV]
200
2.50
200
IS0
250
300
w [MeV] W&
I50
1.50
100
wn
WA
275
300
1.50
175
17.5
200
225 w IMeVl
200
225
--------i 250 275
300
2.50
300
275
w [MeV]
Figure 2. Comparing the Dispersion Relations results (thick solid line) of the real (top four) and imaginary (bottom four) parts of the iso-scalar dynamical electric and magnetic dipole and quadrupole polarisabilities with the leading one loop order MSSE prediction. Dashed: HBxPT prediction (nucleons and pions only); dotted: A pole contribution added; dot-dashed: pion cloud around A added; thin solid: total MSSE result (counter terms for the dipole polarisabilities fixed to the static values of the dipole polarisabilities). For the imaginary parts, the MSSE and HBxPT predictions are identical at this order.
455
Theor HBxPT with only pions and nucleons as low energy degrees of freedom = 1.2) can be seen as accidental. The energy dependence of the dynamical polarisabilities demonstrates therefore that the underlying physics mimicked at zero energy by the counter term is in a large range insensitive to derailed dynamics at short distances. No genuinely new degrees of freedom are missed at low energies. As the A has no width at leading order in MSSE, the result for / 3 ~ (lw ) diverges close to the A resonance energy W A . For this reason, the imaginary part of / ~ M I ( wabove ) the one pion production threshold is also ill reproduced in MSSE. Dispersion theory shows that it is clearly dominated by the non-zero width of the A(1232). The cusp strength and structure at wr is well captured in MSSE, and very well so for a y ~ l ( w ) . Thanks to the contribution from the pion cloud around the A, the agreement for C Y E ~ ( Wat ) low energies is good. N o t surprisingly, there is no residue of the famed E2 + E2 transition due to its smallness. No counter term is used or necessary in this channel to account for short distance physics. A nucleon resonance might be seen in the discrepancy between the DR and chiral calculations at very high momenta w > 250 MeV. Albeit there is some improvement by adding the Ax continuum, nearly half of the static strength of / 3 ~ 2 ( w is ) still missing. Introducing a counter term to reproduce the correct static value, as was done for the dipole polarisabilities but is for the quadrupole polarisabilities inconsistent with the MSSE power counting, is of no help in the magnetic quadrupole polarisability because the slope of the dispersion theory result is much steeper than the one obtained in MSSE. Not even the physics of the pion production threshold seems to be reproduced correctly. This analysis is an overall success for MSSE: In the rkgime at low energies where it is supposed to work, the agreement is surprisingly good, and the deviation around W A is clearly related to the fact that the “natural” power counting must be modified in order to account for the non-zero width of a resonance by summing a sub-class of diagrams. Dynamical polarisabilities do not contain more or less information than the corresponding Compton scattering amplitudes, but as with any multipole decomposition, the facts are more readily accessible and easier to interpret. Stringent constraints for models and model-independent power countings of a low energy effective field theory of the nucleon follow from their analysis.
(/3EXgT(O)
References
1. H. W. Grieflhammer and T. R. Hemmert: Phys. Rev. C65, 045207. 2. R. Hildebrandt, H. W. Grieflhammer, T. R. Hemmert and B. Pasquini, forthcoming.
DYNAMICAL EARYON RESONANCES WITH CHIRAL LAGRANGIANS C . BENNHOLD Center for Nuclear Studies, Department of Physics, The George Washington University, Washington, DC 20052, USA E-mail:
[email protected]
A. RAMOS Departament d’Estructura i Constituents de la Matdria, Universitat de Barcelona, Diagonal 64 7, 08028 Barcelona, Spain E-mail:
[email protected] E. OSET Departamento de Fisica Tedrica and IFIC, Centm Mixto Universidad de Valencia-CSIC, Institutos de Investigacidn de Paterna, Aptd. 22085, 46071 Valencia, Spain E-mail:
[email protected] The s-wave meson-baryon interaction is described using the lowest-order SU(3) chiral Lagrangian in a unitary coupled-channels Bethe-Salpeter equation. The entire octet of ground-state J p = 1/2- resonances, the A(1670), C(1620), Z(l620) and N(1535) states, along with the SU(3) singlet A(1405), is found t o be dynamically generated through meson-baryon rescattering.
1
Overview
Since the discovery of the first baryon resonance, the A(1232), over fifty years ago, there has been a persistent question regarding the nature of such resonances: Are these genuine states that appear as bare fields in the driving term of the meson-baryon scattering matrix? Or can they be generated dynamically, i.e., by iterating an appropriate nonpolar driving term t o all orders, just like the deuteron appears as a bound state when the nucleon-nucleon interaction is solved t o all orders? Early attempts by Chew and Low t o generate the A(1232) by iterating a crossed nucleon pole term were eventually overtaken by the success of the SU(3) quark models which established the A(1232) as part of the SU(3) ground-state decuplet. The subsequent discovery of over 100 additional baryon resonances and their mostly successful incorporation into quark models appeared t o have settled the question in favor of treating them as genuine fields. However, one persistent exception for many years was the lowest-lying S = -1 resonance, the SU(3) singlet A(1405), which appeared quite naturally as a dynamical pole in the K - p scattering matrix using a va-
456
457 riety of approaches (see the discussion by R. Dalitz in Ref!). The advent of chiral Lagrangians combined with unitarization techniques placed these efforts on more solid theoretical g r o ~ n d d , ~ ? ' ~ . In order to search for dynamically generated resonances we construct the set of coupled channels from the SU(3) octets of ground-state baryons and pseudoscalar mesons. Using the lowest-order chiral Lagrangian
where @ and B are the SU(3) matrices for the meson and baryon fields, respectively, we solve a coupled-channel Bethe-Salpeter equation
T = [l-VG]-'V,
(2)
with the driving terms given by the lowest-order contact terms that depend on SU(3) coefficients and kinematic variables and the function G appearing in Eq. (2) is a diagonal matrix accounting for the loop integral of a meson and a baryon propagator and in dimensional r e g u l a r i ~ a t i o n ~depends ,~ on a subtraction constant for each channel, coming from a subtracted dispersion relation. 2
Strangeness S = -1 sector
Invoking the same framework used for the SU(3) singlet A(1405) and the threshold E N interaction, Ref? investigated the I = 0 parts of the K N -+ K N and K N 4 TE amplitudes at higher energies. Both channels clearly display a signal from the A(1670) resonance. Just like the large coupling of the A(1405) to the KN channel allows identifying this resonance as a quasibound K N state, Ref? identifies the A(1670) excitation as a quasibound K E state due to its large coupling to this channel. Searching for the I = 1 member of the SU(3) octet, the I = 1 amplitudes are calculated in our model to be smooth and featureless without any trace of resonance behavior, in line with experimental observation. To explore this issue further we conducted a search for the poles of the E N -+ E N amplitudes in the second Riemann sheet. As expected, two poles are identified in the I = 0 amplitude at (1426 i16) MeV and (1708 221) MeV, corresponding to the A(1405) and A(1670) states, respectively. Examination of the 1 = 1 amplitude also reveals a pole at (1579 i296) MeV, corresponding - most likely - to the C(1620) resonance, designated as a 1-star state by PDG. The large width obtained for this resonance in our model and suggested experimentall? may
+
+
+
458
explain why there is no trace of this state in the scattering amplitudes. Thus, the extension to higher energies within the chiral unitary framework in the the S = -1 sector leads naturally t o the dynamicnl generation of the A(1670) and C(1620) resonances as two additional members of the same J p = l / 2 - octet. Not surprisingly, an examination a t even higher energies came up empty, there was no trace of the next two s-wave resonances, the A(1800) and C(1750) stat,es, indicating that the dynamics included in the lowest-order chiral Lagrangian is limited t o the lowest-lying octet.
3
Strangeness S = -2 sector
Within SU(3) the chiral meson-baryon Lagrangian naturally extends to the S = -2 sector. Thus, the dynamics of the K A , K C ,7rZ and 778 interactions can be predicted within the same approach. Ref6 indeed finds a E resonance with an energy around 1606 MeV and a width at the pole position around 100 MeV. Due t o a significant threshold effect the apparent (Breit-Wigner) width is much smaller and compatible with experimental findings quoted in Ref.' for the 5 resonances in question. Of the two relevant E states with isospin 1/2, the 1-star rated E(l620) and the 3-star rated E(1690), Ref6 argues that the Z(1690) must be ruled out because, on the one hand, it was impossible to find a pole with an energy close t o 1690 MeV and, on the other hand, we found large disagreements between the resonance couplings t o meson-baryon final states found here and the information given in F k f ? for the partial decay widths t o those states. These findings support the assignment of the quantum numbers J p = 1/2- to the E(1620) resonance. 4
Strangeness S
=0
sector
For completeness we briefly mention here the work done in the S = 0 sect^?^^^^, where the N*(1535) was generated dynamically within the same approach. This resonance is known t o be unusual as the only 4-star state that does not have a peak in the speed plot due t o its proximity t o the 7N threshold. In order to reproduce the phase shifts and inelasticities for 7rN scattering in isospin I = 1/2 around the energy region of the "(1535) resonance, four subtraction constants are adjusted to the data. The dynamical N*(1535) state is found t o have strong couplings to the KC and $V final states. The lowest-lying I = 3/2 state, the S31(1620) resonance is not reproduced in this approach, unless the irN -+ 7r7rN channel is introduced, requiring additional assumptions that go beyond the lowest-order chiral approach. In conclusion, the computation of the E(l620) along with its partners, the N*(1535), the A(1670) and the C(1620), within the chiral unitary approach
459
completes the J p = l / 2 - octet of dynamically generated s-wave resonances. We believe that the dynamical generation of all states belonging to the lowestlying J p = l / 2 - SU(3) octet, along with the SU(3) singlet R(1405), demonstrates the extraordinary power of the chiral unitary approach. That these states should appear especially with as simple a driving term as provided by the first-order chiral Lagrangian with very few open parameters is truly remarkable and suggests that the nature of these states can be well described through the meson-baryon components of their wave functions.
5
Acknowledgments
This work is supported in part by DGICYT contract numbers BFM2000-1326, PB98-1247, by the EU-TMR network Eurodaphne, contract no. ERBFMRXCT98-0169, and by the US-DOE grant DE-FG02-95ER-40907.
6
References 1. D. E. Groom et al., Eur. Phys. Jour. C 15,1 (2000). 2. N. Kaiser, P. B. Siege1 and W. Weise, Nucl. Phys. A 594,325 (1995); Phys. Lett. B 362,23 (1995). 3. E. Oset and A. Ramos, Nucl. Phys. A 635,99 (1998). 4. J.A. Oller and U.G. Meissner, Phys. Lett. B 500,263 (2001) 5. E. Oset, A. Ramos and C. Bennhold, Phys. Lett. B 537,99 (2002). 6. A. Ramos, E. Oset and C. Bennhold, submitted to Phys. Rev. Lett. 7. J.C. Nacher et al., Nucl. Phys. A 678,187 (2000); 8. T. Inoue, E. Oset and M.J. Vicente Vacas, Phys. Rev. C 65, 035204 (2002).
PION ELECTROPRODUCTION IN THE SECOND RESONANCE REGION USING CLAS HOVANES EGIYAN Jefferson Lab, Newport News, Virginia, USA INNA AZNAURYAN Yerevan Physics Institute, Yerevan, Armenia FOR THE CLAS COLLABORATION The differential cross sections and the single beam asymmetries have been measured for the single pion electroproduction on the proton at Q2 = 0.4 GeV2 using CLAS. The large phase space coverage of CLAS and the high statistical accuracy of the data allowed us to perform the analysis of single pion electroproduction observables and to obtain the Al12 amplitudes for the Sll(1535). The preliminary results of this analysis are in good agreement with the q-meson production data.
1
Introduction
Single pion electroproduction process is one of the most suitable exclusive channels for studying the excitation of the resonances in the first and second resonance regions because of the large K N coupling for these states. The detection of the two out of three outgoing particles allows us to extract the amplitudes for the individual resonances. The kinematics of the single pion electroproduction is completely defined '. The cross section for the by five independent variables Q 2 , W , E , 8*, single pion electroproduction on unpolarized target can be written as 2:
The U T , U L , UTT, C T L and ffTLi structure functions are bilinear combinations of the amplitudes, depending only on Q 2 ,W and 8*. The last term in Eq. (1) is due to the polarization of the electron beam. The quantities of interests that can be derived from the study of the pion electroproduction in the second resonance region are the transition amplitudes for P11(1440), DI3(1520) and Sll(1535). These three isospin I = !j states favor the decays into r+n channel, and the measurement of the ep + e ' d n is crucial for determining the electroproduction amplitudes for the transitions into these excited states. The lack of the high quality data in d n prevented
460
461
Figure 1. Unpolarired structure functions versus 0” for single n+ electroproduction at Q2 = 0.4 GeV2. The solid curves are from MAID2000 the dashed curves are the result of our isobar fit 7 .
’,
a precise extraction of the electro-excitation amplitudes for the states in the second resonance region using coupled channel analysis techniques. 2
Experiment
The experiment was carried out using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Laboratory located in Newport News, Virginia. CLAS is a nearly 47~detector, providing almost complete angular coverage for both e p + e’7r+n and ep + e‘rOpreactions in the hadronic center-of-mass frame. CLAS and the continuous beam produced by CEBAF provides an excellent opportunity for measuring the pion electroproduction cross section by detecting the outgoing electron and one hadron in coincidence. The main magnetic field of CLAS is provided by six superconducting coils, which produce a toroidal field primarily in the azimuthal direction. The spaces between the cryostats are filled with six identical detector packages, also referred to as “sectors”. Each sector is instrumented with three regions (Rl, R2,R3) of drift chambers to determine the trajectories of the charged particles, Cerenkov counters for electron identification, scintillator counters for charged particle identification, and an electromagnetic calorimeter used for electron identification and detection of neutral particles. < 0.5% momentum resolution for The CLAS detector can provide p = 1 GeV charged particles 3 , and M 80% of 47r coverage of the solid angle. The efficiency of the detection and the reconstruction for the charged particles
%
462
w
Figure 2. Beam spin asymmetry versus 9’ for single AO electroproduction at Q 2= 0.4 GeV2 and W = 1.54 GeV. The solid curves are from MAID2000 l , the dashed curves are the result of our isobar fit ?.
’.
in the fiducial regions is greater than 95% The combined information from the tracking in DC and the scintillator counters allows for a reliable separation of protons from positive pions for momenta up to 3 GeV To obtain cross sections the experimental yields were corrected for the detector acceptance and efficiency, binning, kinematic and radiative effects 8 .
’.
3
Results
The unpolarized structure functions O T T , I J T L and the linear combination OT EIJLwere obtained by fitting the rp*-dependenceof the unpolarized cross sections to a function of the form:
+
F($*)= A
+ BCOS$*+ C C O S ~ ~ * .
(2)
The structure functions for ep + e ’ d n are shown in Fig. 1. One can see that the MAID2000 calculations overestimate the CTTTstructure function in the second resonant region. The IJTL structure function in MAID is almost flat and close to zero, while the experimental data indicate a significant structure in the 8*-dependence for W > 1.32 GeV. The 4*-dependences of the beam spin asymmetry at W = 1.54 GeV are shown in Fig. 2. Although MAID2000 describes the cross sections well, the experimental and calculated beam spin asymmetries do not match, and even have opposite signs. The CLAS data set can be used to adjust the appropriate
463
u-Op*lto
~
........ ... .. ...
0.5
0
1
1.5
2
wK-Wh
2.4
3
1.5
a', G.!
Figure 3. A1/2 photon coupling amplitudes for Sll(1.535). The large full square is from the CLAS combined data analysis. The full circles only include CLAS data on n+n channel. The open markers are from previous analyses 9,10.
parameters in the MAID model by fitting both the cross sections and the beam spin asymmetries. The combined data set from CLAS was fitted with a program based on the MAID model to obtain the optimal value for the multipole amplitudes. The preliminary result for the All2 amplitude for ,511 (1535) is shown in Fig 3. One can see that the points from CLAS pion production data are in a good agreement with the q-meson production results. This is in contrast with the earlier results a t the Q2 = 0, where the pion and q production analyses gave different results
'
'.
References
1. D. Drechsel, 0. Hanstein, S.S. Kamalov, L. Tiator, Nucl. Phys. A 6 4 5 , 145 (1999). 2. F. Foster and G. Hughes, Rept. Prog. Phys. 46, 1445 (1983). 3. M.D. Mestayer et al, Nucl. Inst. and Meth. A 4 4 9 , 81 (2000). 4. G. Adams et al, Nucl. Inst. and Meth. A 4 6 5 , 414, (2001). 5. E.S. Smith et al, Nucl. Ints. and Meth. A 4 3 2 , 265 (1999). 6. M. Amarian et al, Nucl. Inst. and Meth. A 4 6 0 , 239 (2001). 7. I. Aznauryan, S. Stepanyan, JLab Analysis of Nucleon Resonances (JANR); Private communications. 8. H. Egiyan, Ph.D. Thesis, unpublished, (2001) 9. V. Burkert in Perspectives in the Structure of Hadronic Systems, ed. M.N. Harakeh et a1 (Plenum Press, New York, 1994); Private communications. 10. R. Thompson et al, Phys. Rev. Lett. 86, 1702 (2001)
ELECTRON BEAM ASYMMETRY MEASUREMENTS FROM EXCLUSIVE no ELECTROPRODUCTION IN THE A(1232) RESONANCE REGION K. JOO FOR THE CLAS COLLABORATION Jefferson Lab, 1ZOO0 Jeflerson Avenue, Newport News, VA 23606, USA E-mail: kjoo Qjlab.org The polarized longitudinal-transverse structure function U L T ~ in the p ( S , e'p)nO reaction has been measured for the first time in the A(1232) resonance region for invariant mass W = 1.1 - 1.3 GeV and at four-momentum transfer Q 2 = 0.40 and 0.65 GeV2. Data were taken at the Thomas Jefferson National Accelerator Facility with the CEBAF Large Acceptance Spectrometer (CLAS) using longitudinally polarized electrons at an energy of 1.515 GeV. This newly measured o ~ provides new and unique information on the interference between resonant and nonresonant amplitudes in the A(1232) resonance region. The comparison to recent phenomenological calculations shows sensitivity to the description of non-resonant amplitudes and higher resonances.
1
Introduction
A precise study of the y*p + A+(1232) transition has been of special interest for many years. The transition is usually described using three electromagnetic multipoles: the magnetic dipole ( M I + ) ,and the electric (El+)and scalar (&+) quadrupoles. SU(6) symmetric quark models describe M I + as a quark spin flip , while El+ and S1+ are identically zero. Small but finite contributions to El+ and S1+ may arise from interactions with the pion cloud at large and intermediate distances. Quark models that include hyperfine interactions from one-gluon exchange also predict small contributions. In addition, there is the prediction, resulting from quark helicity conservation in perturbative QCD, that MI+ = El+ at asymptotic Q 2 , while S1+ remains constant. The p(e,e'p)xo reaction has been the major tool in probing the y*p + A+( 1232) transition. However, unpolarized experiments are unable to separate the reaction mechanisms which contribute to the excitation of the A( 1232) from non-resonant backgrounds and contributions of higher mass resonances. Spin observables, which access the imaginary parts of interfering amplitudes, provide promising new information to address these issues. The imaginary parts vanish identically if the final state is determined by a single
464
465
complex phase, which is the case for an isolated resonance. Thus spin observables are especially useful to study contributions from other resonances and non-resonant terms which may interfere with the A+(1232) amplitudes. In this report, we report a measurement of the longitudinal-transverse polarized structure function CLTf obtained in the A(1232) resonance region using the p(Z, e'p)r0 reaction. 2
Experiment
The data were taken using a 1.515 GeV beam of longitudinally polarized electrons incident on a liquid hydrogen target at 100 % duty factor. The electron polarization was measured frequently with a Mdler polarimeter and was typically 69.0 %. Scattered electron and proton were measured using the CLAS detector. Electrons were selected by a hardware trigger using a coincidence of the gas Cerenkov counters and the lead-scintillator electromagnetic calorimeters. Protons were identified using momentum reconstruction in the tracking system and time of flight from the target to the scintillators. Software fiducial cuts were used to exclude regions of non-uniform detector response. Kinematic corrections were applied to account for drift chamber misalignments. The p 0final state was identified by the missing mass cut of -0.01 5 Mz(GeV2)5 0.05. Background from elastic Bethe-Heitler radiation was suppressed to below 1% using a combination of cuts on missing mass and 4: near 4; = Oo. Target window backgrounds and proton multiple scattering were suppressed with cuts on the reconstructed e'p target vertex.
3
Data analysis
The electron beam asymmetry ALT, is directly proportional to the polarized longitudinal-transverse structure function U L T ~:
A L T ~=
-
d2a' - d 2 K d 2a+ d 2a-
+
(1)
&GJiZjaLTl 00
sin
e;
sin
4:
,
(2)
where d 'af is the differential cross section for positive and negative electron beam helicities. Experimentally, ALp was determined by scaling the measured asymmetry Am by the magnitude of the electron beam polarization P,:
466
where N,' is the number of K O events for each electron beam helicity state. Acceptance and normalization factors cancel in A,, making this observable largely free from systematic errors. Radiative correction were applied using the program recently developed by Akusevich et al. for exclusive pion electroproduction. Corrections were also applied to compensate €or cross section variations over the width of a bin. ALT, was determined for individual bins of ( Q 2 ,W,case:, 4;) then multiplied by the unpolarized cross section no. A parameterization of go was used, obtained from fitting previously measured CLAS data '. The structure function (TLTI was then extracted by fitting the r#P distributions. The major systematic errors for ( T L T ~come from the electron beam polarization P, (3%)and the measured unpolarized cross section no (5%). The systematic error for A , is negligible in comparison. Figure 1 shows the comparisons of (TLT and ( T L T ~ extracted at Q2=0.40 GeV2, where the cos 0: dependence is plotted for W bins of 1.18, 1.22 and 1.26 GeV. The top plots of each figure show OLT from our previous measurements and the bottom plots show the newly extracted (TLTJ-Also shown are recent model calculations of (TLT and (TLT' using the Sat0 and Lee (SL) dynamical model 3, the Dubna-Mainz-Taipei (DMT) model 4 , and the Mainz unitary isobar model (MAID2000) Both OLT and (TLT' measure the same combination of amplitudes, but the former probes the real part while the latter probes the imaginary part of the interference. As shown in the top row of Figures 1 and ??, the calculations of (TLT from all three models agree well with the data and with each other near the peak of the A(1232) resonance. Discrepancies become evident away from the peak, especially at W = 1.18 GeV, suggesting that while all three models describe the A(1232) resonance well, their prescriptions of non-resonant and higher-resonance contributions may differ significantly. While this effect is , shown subtle for CTLTnear the peak of the A(1232), it is amplified in o ~ pas in the bottom row of Figures 1 and ??. DMT model calculations generally describe our results well, whereas MAID2000 calculations are generally higher and those of the Sato-Lee model are lower.
'.
4
summary
In summary, the polarized structure function OLTI has been measured for p(e',e'p)7ro in the A(1232) resonance region at Q2 = 0.40 and 0.65 GeV2. This structure function is significantly different from zero in the entire range
467 W=1.18GeV
W=l.22 GeV
W=1.26 GeV
$ 4
4 2
0 r
b -2 -4
-6
-8 ~6
$ 5 i
4
.
2
3
2 1 0 -1
-0.5
0.5
CLAS Data (a2=0.4 GeV') - MAID2000
-0.5
0.5
-0.5
0.5
cosd', .....
s,,:o..L*e
--.--DMT
Figure 1. Structure functions, (TLT and ( T L versus ~ cm0; extracted at Q2= 0.40 GeV2. Various curves show model predictions. Shaded bars show systematic errors.
of the A(1232) resonance region, indicating that they are sensitive to nonresonant and higher-resonance processes in the A( 1232) resonance region. The measured structure function differentiates between recent theoretical calculations. For higher Q2, contributions from non-resonant processes and higher-resonances become more important in extracting the information of the A(1232) resonance since the strength of the A(1232) resonance decreases rapidly as Q2 increases. These new measurements will provide additional valuable information towards a more detailed understanding of the y * p + A+(1232) transition. References
1. 2. 3. 4. 5.
A. Afanasev,I. Akushevich, V.D. Burkert, K. Joo, PRD 66,074004 (2002) K. Joo et al., Phys. Rev. Lett. 88, 12 (2002). T. Sat0 and T.-S.H. Lee, Phys. Rev. C 63, 055201 (2001). S.S. Kamalov and Shin Nan Yang, Phys. Rev. Lett. 83, 4494 (1999). D. Drechsel, 0. Hanstein, S.S. Kamalov, and L. Tiator, Nucl. Phys. A 645, 145 (1999).
?rNN*(1440) A N D o N N * (1440) COUPLING CONSTANTS FROM A MICROSCOPIC N N + N N * ( 1440) POTENTIAL P. GONZALEZ Dpto. de Fisica Te6rica and IFIC Universidad de Valencia - CSIC, E-46100 Burjassot, Valencia, Spain E-mail: pedro.gonzalez8uu. es
B. JULIA-D~AZ,A. VALCARCE, F. FERNANDEZ Grupo de Fisica Nuclear lJniuersidad de Salamanca, E-37008 Salamanca, Spain E-mail: bjuliaQusal.es, ualcarceOmozart.usal.es, f d z 8 u s a l . e s
The N*(1440): or Roper resonance, plays an important role in nucleon and nuclear dynamics as an intermediate state. The excitation of a Roper may mediate pion electro- and photoproduction processes pion and double pion production in N N reaction^^:^: heavy ion collisions4, etc. In this context: the knowledge of the N N + NN*(1440) interaction and the ?rNN*(1440)and a N N * (1440) coupling constants should be of great help. The usual way to determine meson-NN coupling constants is trough the fitting of N N scattering data with phenomenological meson exchange models. Therefore: a consistent way to obtain meson-NN* (1440) coupling constants is from a transition N N + NN'(1440) potential, in particular when ratios over meson-" coupling constants are to be considered. In order to derive the transition potential we shall follow the same quark model approach previously used for N N scattering 5 : 6 : this is we shall start from a quark-quark (qq) interaction containing confinement! one-gluon exchange (OGE) one-pion exchange (OPE) and one-sigma exchange (OSE) terms and carry out a BornOppenheimer approximation. The quark treatment presents two main advantages, on the one hand once the parameters of the qq potential are fixed from N N data, there is not any free parameter: on the other hand it allows all the baryon-baryon interactions to be dynamically considered on an equal footing (actually the same framework has been applied to the A excitation case'). Explicitly, the N N + NN*(1440) potential at interbaryon distance R is obtained by sandwiching the qq potential, Vqq7between N N and N N * (1440) states: written in terms of quarks, for all the pairs formed by two quarks belonging to different baryons. The qq potential has been very much detailed elsewhere 5,6. It reads:
':
468
469
where <j is the interquark distance. VCONis the confining potential taken to be linear ( r i j ) and VOGEis the usual perturbative one-gluon-exchange interaction containing Coulomb ($): spin-spin (& Z j ) and tensor (S,) terms. For future purposes we detail the central part of the one-pion: VOPE:and exchange : interactions given by: one-sigma, V O ~ E
-
where O,-h is the chiral coupling constant and A is a cutoff parameter. The values chosen for the parameters are taken from Ref.6. The N* (1440) and N states are given in terms of quarks by IN* (1440)) =
{ fi"l(OS)2(1~))
IN) = I[31(os)3) c3 P3Ic where [l3Icis the completely antisymmetric color state: [3] is the completely symmetric spin-isospin state and 0s: Is: and Op: stand for harmonic oscillator orbitals. The transition potential obtained can be written at all distances in terms of baryonic degrees of freedom '. One should realize that a qq spin and isospin independent potential as for instance the scalar OSE, gives rise at the baryon level, apart from a spin-isospin independent potential, to a spin-spin, an isospin-isospin and a spin-isospin dependent interactions 5 . Nonet heless for distances R 2 4 fm, where quark antisymmetrization interbaryon effects vanish: we are only left with the direct part, i.e. with a scalar OSE at the baryon level. The same kind of arguments can be applied to the OPE potential. Thus asymptotically ( R 2 4 fm) OSE and OPE have at the baryon level the same spin-isospin structure than at the quark level. Hence we can parametrize the asymptotic central interactions as (the A depending exponential term is negligible asymptotically as compared to the Yukawa term)
and
-
&31~O~)(OP)2)}
@ P3Ic and
470
where g i stands for the coupling constants at the baryon level and M , is the reduced mass of the N N * (1440) system. By comparing these baryonic potentials with the asymptotic behavior of the OPE and OSE previously obtained from the quark calculation we can extract the T N N *(1440) and (rNN*(1440) coupling constants. The A2/(A2 - m:) vertex factor in expressions (4) and (5) comes from the vertex form factor chosen in momentum space as a square root of monopole
';
(
A2'$2) the same choice taken at the quark level, where chiral symmetry requires the same form for pion and sigma. A different choice for the form factor at the baryon level: regarding its functional form as well as the value of A: would give rise t o a different vertex factor and eventually to a different functional form for the asymptotic behavior. Then, the extraction from any model of the meson-baryon-baryon coupling constants depends on this choice. We shall say they depend on the coupling scheme. For the OPE and for our value of A = 4.2 fm-', ~ 2 - m = ~ ,1.0286, pretty close to 1. As a consequence: in this case the use of our form factor or a modified monopole form at baryonic level makes little difference in the determination of
*'
the coupling constant. This fact is used when fixing value of
(z)2
2from the experimental LIZ
extracted from N N data. The value we use for (x,h = ln2
&*e-* 471 4mN
2
= 0.027 corresponds to
$$ = m-2
= 14.8.
To get &"*(1440) we turn to our numerical results for the 'SO OPE potential and fit its asymptotic behavior (in the range R : 5 + 9 fm) to Eq. (4). We obtain g n N N g n N N *(1440)
&L *
grNN'(1440L
&L
A* = -3.73: A2-m:
- -0.94. Let us note that the sign comes out from the arbitrary
1.e. fi choice of the overall phase of the "(1440) wave function with respect to the N wave function. Hence it is more appropriate to quote the absolute value. Furthermore the coupling scheme dependence can be explicitly eliminated if with gn" extracted from the N N + N N potential we compare gn"*(1440) within the same quark model approximation. Thus we get
The value obtained for this ratio is similar to that obtained in Ref. and a factor 1.5 smaller than the one obtained from the analysis of the partial decay
47 1
width. By proceeding in the same way for the OSE potential we have
I
g u N N * ( 1440)
I
= 0.475.
(8)
This result agrees quite well with the only experimental available result, obtained in Ref. lo from the fit of the cross section of the isoscalar Roper excitation in p(cx,ct') in the 10-15 GeV region. Furthermore, we can give a very definitive prediction of the magnitude and sign of the ratio of the two ratios, g n N N * (1440) gnNN
= 0.53
g u N N * (1440) goNN
(9)
which is an exportable prediction of our model. We should finally notice that for dynamical applications our results should be implemented including the "(1440) width. Quantum fluctuations of the two baryon center-of-mass: neglected within the Born-Oppenheimer approach, could also play some role. Though these improvements will have a quantitative effect we think, as suggested by the values we get, our predictions will not be very much modified. In this sense they could serve either as a first step for more refined calculations or as a possible guide for phenomenological applications.
Acknowledgments We thank to E. Oset for suggesting discussions. This work has been partially funded by Junta de Castilla y Le6n under Contract No. SA-109/01, and by EC-RTN, Network ESOP, Contract HPRN-CT-2000-00130. References
1. H. Garcilazo and E. Moya de Guerra: Nucl. Phys. A 562: 521 (1993). 2. M.T. Peiia et al, Phys. Rev. C 60, 045201 (1999). 3. L. Alvarez-Ruso, Phys. Lett. B 452, 207 (1999). 4. B.A. Li et al, Phys. Rev. C 50, 2675 (1994). 5. F. Ferndndez et al, J. Phys. G 19: 2013 (1993). 6. D.R. Entem et al: Phys. Rev. C 62,034002 (2000). 7. A. Valcarce et al, Phys. Rev. C 49: 1799 (1994). 8. K. Holinde, Nucl. Phys. A 415: 477 (1984). 9. D.O. Riska and G.E. Brown: Nucl. Phys. A 679, 577 (2001). 10. S. Hirenzaki et al: Phys. Lett. B 378: 29 (1996); Phys. Rev. C 5 3 , 277 (1996).
7)
ELECTRO-PRODUCTION AT AND ABOVE THE S11(1535) RESONANCE REGION WITH CLAS HALUK DENIZLI Department of Physics and Astronomy University of Pittsburgh, Pittsburgh, PA 15260, USA E-mail:
[email protected] New cross section measurements for the electro-production are reported for total center of mass energy from threshold to 2 GeV and invariant momentum transfer Q 2 between 0.13 and 3.2 ( G e V / c ) 2 . This large kinematic range and increased statistics allow to study the response functions and Q2 evolution of photo-coupling amplitude.
1 Introduction and Motivation When we look at the the inclusive excitation spectra ep->eX along with the masses of known baryon resonance, the picture is complicated. The excited states of proton are broad and overlapping above the second resonance region. This makes the extraction of their physical properties very difficult. But this situation is considerably simplified in the case of the r]p final state. There are fewer resonances involved since it couples to nucleon resonance with isospin I = 1/2 only. Therefore, this process is cleaner for distinguishing certain resonance than other processes. In addition, The cross section appears to be dominated by &(1535) resonance near the threshold. This is the only known resonance to have a large branching ratio. Past experiments1i2 showed that the photocoupling amplitude pA1/2 for the &1(1535) has an unusual slow falloff with Q2 which indicates more compact object than other resonances. A structure at W around 1700 MeV has been seen by Thompson et a12. He also showed that RTT and RLT are small compared to RT. Longitudinal amplitudes are small compared to transverse in the Mainz prediction. In this paper, I will show new measurements of r] electro-production with CLAS. This data has more than quadrupled the statistics and doubled the Q2 coverage of the first CLAS data. This experiment produces precise measurements over the range 0.13
472
473
2 Experiment and Results This experiment has been performed in Hall-B with CLAS detector. Data has taken during January-March, 1999 with luminosity 2 - 7 1033cm-2s-1. Liquid Hydrogen 5 cm in length was used as a target. Data from 4 different beam settings are presented here. A total of 1.5 billion triggers gave 600k 77 events. This is 10 times more than the previous CLAS publication2. CLAS has 6 identical sectors, each covering 54" in 6. Drift Chambers (DC) measure angles and momenta of the charged particles in CLAS. Scintillator Counters (SC) which are located outside of the DC provide time-of-flight measurements with which we can separate the charged hadrons into pions, kaons, and protons. For this analysis, events were selected with an identified electron and proton. A fiducial cut is applied to these particles and the momentum of the electron was required to be above 400 MeV. Events were binned according Q2,W, and the center of mass angles of 7 ( C O S ~and , , &). Yields were determined by fitting the missing mass spectrum t o a function which is the sum of a gaussian peak with aradiative tail and a simple polynomial background function modified by geometric acceptance for this reaction. Acceptance for this reaction was calculated using a GEANT based Monte Carlo simulation. Cross sections have been corrected for radiation. For each W, Q2 and cos8, bin the d,, dependence of the differential cross sections was fit to extract the response functions RT CLRL,RTT,RLT.
+
+
Results for RT CLRLare shown in figure 1. In this figure, the results have been scaled by the average value for that W and Q2 in order to more clearly show the shape of the distributions. A new model based on the MAID formalism6 has been developed for 71 electro and photoproduction using the data of previous experiments as input. The predicted shape of RT ELRL from this model is also shown in figure 1. The model does not match the linear behavior of the data for W around 1.7 GeV. This feature of the data can be seen more clearly by expanding RT CLRLas a series of Legendre Polynomials
+
+
+
+
RT C LRL = A B .cos8, + C . P~(cos~,) + .... (2) The B parameter is plotted versus W in figure 1. The simplest explanation for a non-zero B is interference between S and P partial waves. In that case, the rapid change in B around 1.7 GeV, would be due to changing phase difference between the S and P waves. The P11(1710) resonance is close and provides the necessary phase motion; it has no known qN decay.
474
1.8
1.2
B
W
I
W
1.64 GeV
=
1.10 GaV
*
Q2=0.70 - Qz=0.70
I
0.4
0.0
W = 1.68 U V
W=I.K?G#V
2.4
I
0.8
T
T -0.4
0.0
'
-0.8-0.4
I 0.0 0.4 0.8 -0.8-0.4
1 0.0 0.4 0.8
-0 8
~
1.5
1.6
1.7
1.8
1.9
2.0
W (GeV) Figure 1. The result of the fit to the differential cross section using eqn 1. This is for Q2 = 0 . 7 ( G e V / ~ )Curves ~. are predictions from Mainz calculation.
Angle integrated cross sections are shown in Fig 2 for three Q2 values.For each Q2 bin the maximum cross section used to determine A l p with the assumption that longitudinal contribution is small. For consistent comparison, a full width of &1(1535) of 150 MeV and a branching ratio of 7 of 0.55 were used.The results of this experiment of All2 are shown in Fig 2 with some previous results converted to be consistent with our choice of width and b,. The calculation of A112 depends on the choice of parameters r, b, and contributing resonances. This will affect the overall normalization but the shape is determined with the full coverage of Q2 up to 3 GeV. 3 Conclusion New 7 electroproduction measurements from the elc running period taken at Jlab with CLAS are presented. We have broadened the kinematic coverage and increased the statistics dramatically. It covers the W region at and above the Sll(1535) resonance region. Structure at W around 1700 MeV in the B term that was seen in Thompson2 is confirmed here. It is indicative of resonance structure around 1700 MeV.The shape of RT CLRLshows significant deviations from the predictions of the MAID model. Unlike MAID, the data shows no indication of any D wave contribution around 1.7 GeV. It is unfortunate that we did not see any obvious structure above W = 1.8 GeV. Q2 dependence of the Sll(l535) photocoupling amplitude is mapped out between
+
475
0.13 and 3.2 (GeV/c)2.This allows us to determine accurately the shape of the slow fall off in this transition form factor. I60 140
.
I20
::loo
Q2=0.6 (GeV/c)’
0
”
2 80 s 60
7 . l
.............
0.0
40
Q2=1.4 (GeV/c)’
a.01 0.0
0
p.,..................... 1.5
1.6
1.7
1.8
1.0
20 ’ 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
I
4.0
Q2 (CeV’) 2.0
Figure 2. Integrated data at 3 different Q 2 values shown on the left. The curves corrosponding to single-resonance Breit-Wigner fits with an energy-dependent width over the energy range shown. Values of the A l l 2 from integrated cross section data of this experiment compared to previous data and various CQM calculations’
References 1. F. Brrasse et al.,Z. Phys. C 22, 33 (1984),H. Breuker et al.,Phys Lett B 74, 409 (1978), F. Brrasse et al.,Nucl. Phys. B 139, 37 (1978),P. Kummer et al.,Phys Rev. Lett. 30, 873 (1973),.U. Beck et al.,Phys Lett B 51, 103 (1974),J. Alder et al.,Nucl. Phys. B91, 386 (1975), C.S. Armstrong et al.,Phys Rev. D 60, 052004 (1999). 2. R. Thompson et al., Phys Rev. Lett. 86, 1702 (2001). 3. B. Krusche et al., Phys Rev. Lett. 74, 3736 (1995). 4. W. Brooks et al., Nucl. Phys. A 663-664, 1077 (2000). 5. G. Knochlein, D.Dechse1, L.Tiator,Z. Phys. A352, 327 (1995);L.Tiator, C. Bennhold, S.S. Kamalov,Nucl. Phys. A 580, 455 (1994) 6. W. Chiang, S. Yang, L. Tiator, D. Drechsel Nucl.Phys. A700,429 (2002) 7. S. Capstick, B.D. Keister, Phys. Rev. D51,3598 (1995);W. Konen, H.J. Weber,Phys. Rev. D41, 2241 (1990);F.E. Close, Z. Li,Phys. Rev. D42, 2194 (1990);M. Aiello, M.M. Giannini, E. Santopinto, J.Phys. G24, 753 (1998)
g PHOTOPRODUCTION FROM THE PROTON USING CLAS E. A. PASYUK, M. R. DUGGER, B. G. RITCHIE Arizona State University, Department of Physics and Astronomy, Tempe, A 2 85287, U S A
and the CLAS collaboration E-mail:
[email protected] Differential cross sections for the reaction 7 p + q p have been measured for incident photon energies from 0.75 to 1.95 GeV. Data were taken using the CLAS spectrometer and tagged photon facility at Jefferson Lab. The data provide the first extensive measurements of angular distributions for this process above the 5’11(1535) resonance in the range up to W = 2.1 GeV.
Much effort is presently devoted to the study of the structure of the nucleon and its different modes of excitation, the baryon resonances. At first, information in this field came from T N scattering. Now, a large amount of information has begun to come from electro- and photoproduction experiments. In spite of extensive study over decades, many of the baryon resonances are still not well established and their parameters (e.g., mass, width, couplings to various decay modes) are poorly known. In addition, some of the resonances predicted by various quark models have not been observed so far. Photoproduction of g-mesons provides a valuable “isospin filter.” Because of the quantum numbers of the g-meson this process directly couples only to isospin I = f resonances. While the Sll(1535) resonance is known to dominate the reaction near threshold there are still many questions concerning its properties. Our knowledge for the coupling of the higher resonances to g N channel is very limited. We report here measurements of the differential cross sections for the reaction yp + gp for incident laboratory photon energies w extending from 750 to 1950 MeV. The data were obtained using the CEBAF Large Acceptance Spectrometer (CLAS) and the bremsstrahlung tagged photon facility in Experimental Hall B of the Thomas Jefferson National Accelerator Facility. The tagged photon beam was incident on a liquid hydrogen target placed at the center of CLAS. Tracking of the charged particles through the CLAS magnetic field by the drift chamber system provided a determination of their momentum and scattering angle. This information, together with time-of-flight information, was used for particle identification. Photoproduced mesons were identified using the missing mass technique; missing mass being obtained using
476
477 L
L
L
I
Figure 1. Differential cross sections for y p + q p measured in this experiment. Only statistical uncertainties are shown. Also shown are results from Ref. [l] (triangles) and Ref. [2] (squares). The dashed curve is the multiple resonance fit. The solid curve shows preliminary results of chiral quark model approach from Ref. [ll].
the momentum of the recoiling proton reconstructed in CLAS and assuming a two body final state (i.e.: y p + p X ) . The missing mass resolution is sufficient to clearly identify the no,q , p + w and q' mesons peaks atop of the multi-pion background. The data were binned in 50 MeV wide bins in incident photon energy in the range from 750 to 1950 MeV and 0.2 wide bins in C O S O ~in. ~ . the range -0.8 5 COSO,.,. 5 0.8. The resulting differential cross sections for q photoproduction for photon energies w from 775f25 to 1925f25 MeV are presented in Figure 1. In the lowest portion of this energy range, data from other experiments at approximately the same w are available and are shown for comparison. In general, where previous data exist, agreement is good. While these differential cross sections span a wide range in C O S O ~ . ~ . , nonetheless, to determine total cross sections an extrapolation to unmeasured regions of solid angle must be done. With the limited available experimental data, especially lack of data at most forward and most backward angles it is impossible to make this extrapolation model-independent. As a first attempt, we performed a multiple s-channel resonance fit to the differential cross sections reported here, the differential cross sections of Refs. [1,2,3], beam asymmetry from Ref. [4] and target asymmetry from Ref. [5]. We used the formalism described by Hicks with coworkers.[6] The resulting fit is shown in Figure 1. This fit reproduces measured differential cross sections
478 18 1
&
16 14
-3 8
(A)
I CLAS
A G
12
A 10
8
W
TAPS HICKS MODEL
i
6 4
2
W (MeV)
Figure 2. (a) Total cross sections estimates for ~p -+ q p reaction determined in this work (squares). Also shown are results from Ref. [l](solid triangles) and Ref. [2] (open triangles). The solid curve is the multiple resonance fit as described in the text. (b) The Baldin sum rule running integral using Hicks model cross section estimates from (a).
reasonably well, and was used to estimate our total cross sections, which are shown in Figure 2(a). GRAAL data hint possible “bump”-like structure around W = 1700 MeV. Similar behavior was observed in g-electroproduction data from CLAS at Q2=0.625 GeV2/c2.[7] Our measurements do not show any prominent structure in this range. This apparent discrepancy around W = 1700 MeV in part could be attributed to the difference in extrapolation procedure. With these total cross section estimates, the g contribution to the Baldin sum rule [8] may be determined. This sum rule relates the electric and magnetic polarizabilities of the nucleon (aand p, respectively) to the total photo absorption cross section by
WO
where wo is a threshold and a ( w ) is the total cross section. Due to the limitations of available data, attempts to use this sum rule integral have usually
479
dealt only with pion photoproduction contributions. The running Baldin integral for the reaction yp + rp is shown in Figure 2(b). This integral appears to saturate at about 6 x lop6 fm3. While the contribution from 77 photoproduction is only about 0.5% of that from pion photoproduction, this first measurement of this quantity may provide new possibilities for an isospin decomposition of the polarizabilities. As an example of QCD-based approaches to exploration of meson photoand electroproduction, one can look at a chiral constituent quark model developed by Saghai and Li.[9] Their approach was applied to 77 photoproduction data then available.[lO]The results of their analysis suggested that excitation of a third 5’11 in the second resonance region is necessary to describe data. With the CLAS data presented here added to the data base, Saghai [ll]has performed a new fit using this model. The preliminary results of this analysis are shown in Figure 1. In general, these calculations are in a good agreement with the data for lower energies but diverge at higher energies. In particular, the model does not reproduce the increasing forward peak in the observed angular distribution. In summary, we have presented here new experimental data for the differential cross section for the reaction yp -+ q p spanning a previously unmeasured energy range above the Sll(153.5) resonance, with a broad coverage in COS~,,,,. This data set has been extracted from the so-called “gla” running period, the first run of the CLAS with a tagged photon beam. A subsequent data run with 20 times more statistics is currently being analyzed. Work by Arizona State University is supported by U.S. National Science Foundation. References 1. B. Krushe, et al., Phys. Rev. Lett. 74, 3736 (1995) 2. F. Renard, et al., Phys. Lett. B 528, 215 (2002) 3. S. Dytman, et al., Phys. Rev. C 51, 2710 (1995) 4. J. Ajaka, et al., Phys. Rev. Lett. 81, 1797 (1998) 5. A. Bock, et al., Phys. Rev. Lett. 81,534 (1998) 6. H. R. Hicks, et al., Phys. Rev. D 7,2614 (1973) 7. R. Thompson, et al., Phys. Rev. Lett. 86, 1702 (2001) 8. A. M. Baldin, Nucl. Phys. 18, 310 (1960) 9. Z. Li and B. Saghai, Nucl. Phys. A 644, 345 (1998) 10. B. Saghai and Z. Li, Eur. Phys. J. A 11, 217 (2001) 11. B. Saghai, http://arXiv.org/abs/nucl-th/O202007
WHY IS THE WAVELET ANALYSIS USEFUL IN PHYSICS OF RESONANCES? EXAMPLE OF p’ AND w’ STATES V.K. HENNER, P.G. FFUCK AND T.S. BELOZEROVA Perm State University and ICMM, Perm, Russia E-mail:
[email protected] We use wavelet analysis (WA) to reduce statistical noise in experimental data t o clear out resonances contribution. With these ”cleaned up” data, we find p’ and w’ parameters with generalized coupled-channel Breit-Wigner method that preserves unitarity in case of overlapping states.
1. The properties of p’ and w’ states and even their number are not well defined. The major difficulties are poor statistics and overlapping of states with the same quantum numbers. Correspondingly, our goals are to resolve structures in the data (to do that, we give the first, to our knowledge, application of WA for the problems of physics of resonances), and then to find parameters of the states related to these structures with a preserving unitary for overlapping states Breit-Wigner (BW) formalism. We apply the WA that is a very efficient multi-scale technique, to resolve structures in e+e- annihilation and in pwave m~scattering from experimental noise and background. The WA is much less sensitive to the noise than any other analysis and allows us to substantially reduce the role of fluctuations and to make more reliable conclusion about the resonances. An interference of resonances with the same decay channels is the key aspect of any analysis and interpretation. It is often taken into account by relative phases for BW terms which are treated as free parameters (the most often just Oo or 180O). Whether or not these phases are included, such a sum of BW terms violates unitarity which is the basic point in BW description. The BW approach has the advantage of almost complete model independence and contains only masses, widths and branching fractions of the resonances. Because of that, results of any coupled-channel analysis (such as K-matrix, T-matrix, N / D method) would be desirable to compare to BW. A common place in a literature is that there is no unitary BW multiresonance method. But such method does exist and the scattering amplitudes look as standard BW expressions: N
fZj(S)
=
c r=l
rnTrTgTigTj
s - rn?
+ imJT
-
c N
e i ( q p , i + q p , j ) rnTrT
r=l
I
s - rnz
gT2
I I gTj 1
+ irnTrr ’
(1)
where the phases p r k are not independent parameters and should be deter-
480
481
mined in such a way that preserves unitarity (the number of free parameters is smaller or equal then in a "naive" BW or K-matrix approach). Details and connection to different methods are described in 111. 2. The continuous wavelet transformation of a function f(E) representing the data is defined as: +a
w(a, E ) = c;+a-i
$J*
("-")a
f(E')dE'.
-a
Decomposition (2) is performed by convolution of the function f(E) with a biparametric family of self-similar functions generated by dilatation and translation of the analyzing function + ( E ) ,called wavelet: $Ja,a(t) = +((E b ) / a ) where a scale parameter a characterizes the dilatation, b characterizes the translation, C, is a constant defined through the Fourier transformation of ?,b(E).High frequency wavelets are narrow (due to the factor l / ~while ) ~ low frequency wavelets are much broader. Contrary to Fourier analysis, the w ( a ,E ) depends both on E and frequency l l a . When a goal of the WA is to find the parameters of dominating structures (location and scale/width) then the wavelets with a good localization and small number of oscillations are used, such as "Mexican Hat" (MH), $ ( E ) = (1- E 2 ) e - E 2 / 2 . I 00
a
30
7
25
-
20
-
-
a
-
=Is-
0 10
6
10
5-
0 01
-
-
-
0 1.0
1.2
1.4
E. GeV
1.6
1.8
2.0
1.0
1.2
1.4
1.6
1.8
2.0
E.GeV
Figure 1. e+e- + 2?r+27r-. Wavelet plane and reconstruction of the data [3,5] for cutoff value aCutoff = 0.018.
The wavelet plane w ( a , E ) shows the frequency (scale) contents of the data as a function of energy. The location of a dark spot on a scale axis, a , corresponds to the width of the maximum. The intensity of spots shows the amplitudes of maxima. If the reconstructed data are stable under smdl perturbations, that enables one to distinguish between "useful" large scale stains (low frequencies
482 I00
a 0 10
0 01
1.4
1.2
1.6
1.8
2.0
1.2
1.4
E, GeV
1.6
2.0
1.8
E. GeV
Figure 2. e+e- + 7r+7r-27r0 with subtracted contribution from w7ro. Wavelet plane and two reconstructions of the data [3,5] for different cutoff values acutoff.
in Fourier space) and contributions of the small scale features usually generated by noise. The noise is located at the bottom of the wavelet plane (small scale regions, or high frequencies). In order to separate noise, the wavelet reconstruction is performed for scales greater than a certain boundary scale acutoff.
To clear out p' and w' contributions we perform the WA (with MH wavelet) of efe- + hadrons data relevant to those excitations, and pwave ITIT scattering data. The main p' decay channels are ~ 7 r 2, 7 r + 2 ~ - , 7r+7r-27r0, WT', q7r+7r-. The WA indicates p' states with masses 1.1-1.25, 1.4 and 1.6-1.85 GeV and widths of about 100-200 MeV. I.oo
a 0.111
1.0
1.2
1.4
1.6
E, GeV
1.8
2.0
2.2
1.0
1.2
1.4
1.6
1.8
2.0
2.2
E. GeV
Figure 3 . e+e- -+ 7 r + s - 7 r o . Wavelet plane and reconstruction of the data [3,4] for cutoff value acutoff= 0.02 (solid line); fits with two u' (dashed line) and three w' (dotted line).
483 I00
30-
a 0 10
0 01
00
I .4
I .6
I .8
E, GeV
2.0
2.2
, , I .4
,
,
I .6
1
,
I .8
I
,
2 .o
,
1 2.2
E , GeV
Figure 4. e+e- + w m r . Wavelet plane and reconstruction of the data [4] (multiplied by the factor 1.5 to include unobserved W?TOSO state) for cutoff value aCutoff = 0.02 (solid line); fits with two w' (dashed line) and three w' (dotted line).
The WA shows that some of the considered experimental data are statistically inadequate in sense they do not allow to separate the noise contribution. The WA gives the criteria for distinguishing between stable and unstable data - the latter do not reproduce the same essential structures when acutoff value changes slightly. A high sensitivity to noise might be one of the explanations why the low mass ~'(1200)is hard to observe and to confirm. In this short paper we only have room for two related to p' states figures. On Figs.1 and 2 for e+e- + 21r+27r- and e+e- + 7~+~-27r'cross-sections, two stable to variation of acutoffvalue maxima are seen: around 1.45 and 1.7 GeV with widths about 120 and 150 MeV. On Fig.2 there are also two rather sensitive to acutoff structures at about 1.2 and 2.0 GeV. Besides that, they do not belong to any particular value a (no evident central zone), i.e. they can hardly be associated with a state having some width. 3. For a sake of clarity we give the BW analysis of w' states only. A coupled-channel unitary analysis is important because even "cleaned up" data give the masses and widths that might be shifted from the physical values due to overlapping of the states. The main w' decay channels are T+A-T' and w m . Here we use the data, some of which are rather recent, 3,4,5, that lead to w' states with masses rather different from those cited most often (at about 1.45 and 1.6 GeV). The w' masses reported from the SND detector are 1.25, 1.40 and 1.77 GeV. In the previous work of the same team 3 , the ~ ' ( 1 2 0 0 ) state was reported as a replacement for ~ ' ( 1 4 2 0 ) .The WA, Figs.3 and 4, gives w' states at around 1.2, 1.6, possible at 1.4, and maybe a weaker state at 1.8 GeV. The 1.2 GeV state is clearly seen on the wavelet plane in Fig.3,
484
but the ~ ' ( 1 4 2 0 )is rather sensitive to acutoffvalue. A comparison of the reconstructed with the WA data and BW unitary expression (1) gives good fits for both cases of two and three w' with the X2/noabout 1.3. In the case of two w' the masses and widths (in GeV) are: ml = 1.153 f 0.018, rl = 0.176 f0.039, m2 = 1.652 f0.017, r2 = 0.303 f0.032. In the case of three w' the masses and widths are: ml = 1.204f0.014, I'l = 0.250f0.048, m2 = 1.55ofo.019, r2= 0.212fo.077, m3 = 1.7oofo.021, r3= 0.30ofo.039. Table 1. Branching ratios of two w' states (in %) and relative (to w ; ) phases (in deg) Channel e+ep?r WiTT
BW: (11% 9) . 13.8f' 10.2 86.2f 10.2
Bw; f 1 5 f 11)10-5 ' 6.19f 3.02 93.8% 3.02
'PWk
- 2 3 f 13 20f 6 -22f 3
Table 2. Branching ratios of three w' states (in %) and relative (to w ; ) phases (in deg) Channel e+eP WKK
BW; (1.9% 1) 83.2% 35.1 16.8%35.1
BW& ( l . l f .5) 81.6% 11.8 18.4f 11.8
VW&
-24 f 9 -34 f 6 -28 f 11
BY; ( 1 . 3 f 1) 15.7% 10.5 84.34~10.5
'Pw;
-16 f 2 -11 f 6 -21 f 6
References
1. V.K.Henner and TSBelozerova, Yad.Fizika 60, 1998 (1997); Physics of Particles and Nuclei 29, 63 (1998). 2. E.C.Poggio, H.R.Quinn and S.Weinberg, Phys.Rev.Dl3, 1958( 1976). 3. M.N.Achasov et al., Phys.Lett.B462, 365 (1999). 4. A.Antonelly et al., Zeit.Phys.CB6, 15 (1992). 5. M.N.Achasov et al., Hadrons 2001 conference, Protvino, 2001, Proceedings, p.30.
L = l BARYON MASSES IN THE 1/Nc EXPANSION C. L. SCHAT Jefferson Lab, 12000 Jefferson Avenue, Newport News, VA 23606, USA Department of Physics, Hampton University, Hampton, VA 23668, USA E-mail:
[email protected] The mass spectrum of the 70-plet of negative parity baryons is studied using the l/Nc expansion of QCD. It is found that the A(l405) is well described as a threequark state and a spin-orbit partner of the A(1520). Singlet states with higher orbital angular momentum L are also briefly discussed.
The l/Nc expansion is an appropriate tool for the study of some longstanding problems of the quark model in a model independent way. In those cases where the quark model does not agree with phenomenology, such as the problem of the mass splittings between spin-orbit partners in the negative parity baryons (spin-orbit puzzle), it is not clear whether the problem is due to the quark model itself or to specific dynamical properties of the states involved. This situation is clarified in the l / N c expansion where the presence of other operators, the leading one being of U(N:), solves the contradictions that arise in the quark model when the spin-orbit interaction is considered. In the N , + 00 't Hooft limit QCD has a contracted dynamical spinflavor symmetry SU(ZF), for the ground state baryons ( F is the number of light flavors). This is a consequence of unitarity in pion-nucleon scattering in that limit and at fixed energy of order U(N:) l. The excited baryons are expected to reveal further the details of strong QCD and are therefore of current theoretical interest3i4 and also a central goal of lattice QCD studies5. This provides a strong motivation to extend the l / N c techniques beyond the ground state baryons6>'. Most of the known baryons of negative parity seem to fit very well in the (3,70) irreducible representation (irrep) of 0 ( 3 ) @ S U ( 6 ) . The l/Nc operator expansion for the full 70-plet can be implemented along the lines developed for two flavors7 and shows that the leading order spin-flavor breaking (O(N:)) is indeed small, thus justifying SU(2F) as an approximate symmetry useful for classifying excited baryons3. A basis of mass operators can be built using the generators of O ( 3 ) @I S U ( 2 F ) 7. A generic n-body mass operator has the general structure O(") = N:-" 0~0, 0, , where the factors Oc, 0,, and 0, can be expressed in terms of products of generators of orbital angular momentum (&), spin-flavor of the excited quark (si,t, and gia _= sit,) and spin-flavor of the core of N , - 1 nonexcited quarks (Sf,T: and Gt,,G C2=A1~ ! ~ ) t k " 'respectively. )), The explicit
485
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l/Nc factors originate in the n - 1 gluon exchanges required to give rise to an n-body Operator'. The 70-plet mass operator up to C?(ENZ),where E is the strength of the S U ( 3 ) symmetry breaking, has the most general form 11
M ~= o CciOi i= 1
4
+ E XbiBi i=l
,
(1)
where ci and bi are unknown coefficients which are reduced matrix elements (of a QCD operator) that are not determined by the spin-flavor symmetry. Calculating these reduced matrix elements is equivalent to solve QCD in this baryon sector. Fortunately, the experimental data available in the case of the 70-plet is enough to obtain them by making a fit. A more detailed discussion and a full presentation of results (e.g. mixings and splitting relations) has been published elsewhere3. Here I only present the masses of the particles with one unit of strangeness in Fig.1 and restrict the discussion to the singlets. The singlet Lambdas are the two lightest states of the 7O-plet, something that has its natural explanation in the dominant effect of the hyperfine interaction". The chief contribution to spin-flavor breaking stems from the O(l/Nc) hyperfine operator 0 6 = NLIS;S;, as in the ground state baryons. Since 0 6 is purely a core operator, the gross spin-flavor structure of levels is determined by the two possible core states. In particular, the two singlet As are not affected by 0 6 , while the other states are moved upwards, explaining in a transparent way the lightness of these two states. The long standing problem in the quark model of reconciling the large A(1520) - A(1405) splitting with the splittings between the other spin-orbit partners in the 70-plet is resolved in the large N , analysis. The singlet As receive contributions to their masses from 01 = N,1 and e . s while the rest of the operators give vanishing contributions because the core of the singlets carries S" = 0. The splitting between the singlets is, therefore, a clear display of the spin-orbit coupling. The problem with the splittings between spin-orbit partners in the non-singlet sector, illustrated by the fact that the e - s operator gives a contribution to the A112 - A3/2 splitting that is of opposite sign of what is observed, is now solved by the presence of the operators 0 4 , 0 5 , 0 9 and 011, with the contribution from 0 4 = e h t, G;, being the dominant one in accordance with the l/Nc counting3. While O2 = e . s and O4 are of order N," separately, their sum 0 2 + 0 4 is of order l/Nc for the non-singlet states. 0 4 is therefore the natural operator that cancels the effect of 0 2 at large N,. In principle, a similar situation would be expected for states with one quark excited at higher angular momentum L > 1. It is interesting to note that the splittings of the observed states (A(1405)+-,A(1520);-),
&
487
1800
--
1700
a,
m
1600
1500
1
-
i
1400
1300
Figure 1. L = l baryons with one unit of strangeness. The shaded (green) boxes correspond t o the experimental data8, the black lines are quark model predictionsg and the hatched boxes are the l / N c results3.
)'p
(A(l890)2+, A(2110)$+), (A(1830)$-, A(2100)$-), (A(2020)5+,A(2350) are in a relation 3.0 : 5.7 : 7.0 : 8.6 while the l? . s operator predicts 3.0 : 5.0 : 7.0 : 9.0. The largest discrepancy corresponds to the L = 2 states, which seem to lie on a different Regge trajectory. Thus, the observed data also hints that c2 may be of approximately the same size in different spin-flavor multiplets. Further support to this picture can be drawn from scaling down to the strange sector the mass splitting between the (Ac(2593)i-, Ac(2625):-) as suggested by Isgur". The results reported here were obtained in collaboration with J.L. Goity and N.N. Scoccola. The author acknowledges financial support from CONICET(Argentina).
488
References 1. R. Dashen and A. V. Manohar, Phys. Lett. B 315, 425 (1993); B 315,
438 (1993); E. Jenkins, Phys. Lett. B 315,431 (1993); B 315,441 (1993); B 315, 447 (1993); R. Dashen, E. Jenkins, and A. V. Manohar, Phys. Rev. D 49,4713 (1994); D 51,3697 (1995); E. Jenkins and R. F. Lebed, Phys. Rev. D 52, 282 (1995); E. Jenkins and A. V. Manohar, Phys. Lett. B 335, 452 (1994); J. Dai, R. Dashen, E. Jenkins, and A. V. Manohar, Phys. Rev. D 53, 273 (1996). 2. C. D. Carone, H. Georgi and S. Osofsky, Phys. Lett. B 322, 227 (1994); C. D. Carone, H. Georgi, L. Kaplan and D. Morin, Phys. Rev. D 50,5793 (1994); A. Luty and J. March-Russell, Nucl. Phys. B426, 71 (1994); M. A. Luty, J. March-Russell, M. White, Phys. Rev. D 51, 2332 (1995). 3. C.L. Schat, J.L. Goity and N.N. Scoccola, Phys. Rev. Lett. 88, 102002 (2002). C. L. Schat, hep-ph/0204044. 4. Yu. A. Simonov, hep-ph/0203059; F. X. Lee and X. Liu, nucl-th/0203051; E. Oset, A. Ramos and C. Bennhold, Phys. Lett. B 527, 99 (2002); M. F. Lutz and E. E. Kolomeitsev, Nucl. Phys. A 700, 193 (2002); E. Klempt, nucl-ex/0203002. 5. D. G. Richards et al.,(QCDSF/UKQCD/LHPC Collaboration), Nucl. Phys. Proc. Suppl. 109, 89 (2002); M. Gockeler et aZ., (QCDSF/UKQCD/LHPC Collaboration), Phys. Lett. B 532, 63 (2002); W. Melnitchouk et al., heplat/0202022; Nucl. Phys. Proc. Suppl. 109, 96 (2002); J. M. Zanotti et al. (CSSM Lattice Collaboration), Phys. Rev. D 65, 074507 (2002); S. Sasaki, T. Blum and S. Ohta, Phys. Rev. D 65, 074503 (2002). 6 . D. Pirjol and T.-M. Yan, Phys. Rev. D 57, 5434 (1998); D 57, 1449 (1998); C. E. Carlson and C. D. Carone, Phys. Lett. B 441, 363 (1998); Phys. Rev. D 58,053005 (1998); Phys. Lett. B 484,260 (2000); Z. Aziza Baccouche, C. K. Chow, T. D. Cohen and B. A. Gelman, Nucl. Phys. A 696, 638 (2001). 7. J. L. Goity, Phys. Lett. B 414, 140 (1997); C. E. Carlson, C. D. Carone, J. L. Goity, and R. F. Lebed, Phys. Lett. B 438,327 (1998); Phys. Rev. D 59, 114008 (1999). 8. Particle Data Group (D.E. Groom et al.), Eur. Phys. J. C15, 1 (2000). 9. N. Isgur and G. Karl, Phys. Rev. D 18, 4187 (1978); S. Capstick and W. Roberts, Prog. Part. Nucl. Phys. 45, S241 (2000). 10. A. De Ri?ula, H. Georgi and S. L. Glashow, Phys. Rev. D 12, 147 (1975). 11. N. Isgur, in Proc. of the Conference on Baryons '95, ed. by B. F. Gibson et aE. (World Scientific, 1995), p.275; Phys. Rev. D 62, 014025 (2000).
SEARCH FOR RESONANCE CONTRIBUTIONS IN MULTI PION ELECTROPRODUCTION WITH CLAS F. KLEINA,V. BURKERTB, H. FUNSTENc, M. RIPANID FOR THE CLAS COLLABORATION A Catholic Uniu. of America, Washington, D. C. 20064; T J N A F , Newport News, Virginia 23606; College of William and Mary, Williamsburg, Virginia 23185; DINFN, Sezione d i Genova, 16146 Genova, Italy Electroprodution data from CLAS a t Jefferson Lab are being analyzed in order to identify resonant couplings to baryon resonances decaying into TA, p N , or w N . A multi-dimenional fit to the new two-pion electroproduction data not only provides better determined photocouplings of several resonances, but also implicates a significant correction of the hadronic couplings of resonances at W M 1.7 GeV. The electroproduction of w shows strong indications of u- and s-channel contributions at W below 2 GeV.
1 Introduction Quark model calculations' indicate that many of the so-called missing baryon resonances at W > 1.7 GeV are expected to couple strongly t o yN as well as 7rA, pN,or wN. Due t o their low cross section and difficult separation from other production processes, predominantly diffractive and o/r-exchanges, these multipion channels have not yet been investigated with electromagnetic probes for s-channel contributions. The CLAS detector at Jefferson Lab has accumulated a large amount of events for Zp t e'W+.rr- and Zp t e'p7r+7r-7ro, for a large range in invariant hadronic mass (1.74 < W < 2.5 GeV) and photon virtuality Q2 (0.5 < Q 2 < 3.5 GeV2) and with complete angular coverage. The multi-pion analyses examined outgoing electron tracks detected in CLAS in coincidence with a proton and 7r+ track. Missing mass techniques were applied to identify the two-pion channel and w p channel. The following sections present results from the well elaborated analysis of the two-pion channel which will soon be published, followed by preliminary results for the wp channel which is still being analyzed. 2
The reaction channel y * p -+ X t p7r+.rr-
The two-pion channel has been analyzed for a major fraction of the accumulated data (for W = 1.4 - 1.9 GeV and Q2 = 0.5 - 1.5 GeV2) by means of a phenomenological model.2 The model describes the reaction y*p + px+fn-
489
490
as a sum of amplitudes for y*p -+ nA + pn+n- and y*p -+ pop + pm+n(at tree level) and a phase space factor representing all other possible mechanisms. The resonant part includes 12 states rated as 3' and 4* with sizeable n A and/or p p coupling^,^ based on a Breit-Wiper ansatz. Non-resonant contributions to p p (diffractive ansatz) and n A were implemented as well.4 The partial LS decay widths of the included resonances are taken from an analysis of nnN data by M. M a n l e ~ Where .~ available, the electromagnetic couplings Al l2,A3/2 are determined through parameterizations extracted from previous experiments; for the other resonances the results of Single Quark Transition Model (SQTM) fits6 and Quark Model predictions' are used. In each W and Q 2 bin, the model was fitted to the following three differential cross sections simultaneously: da/dM,,+, du/dM,+,- , and dc/dO,-. The fitting procedure was performed in two steps: (A) The model parameters representing the non-resonant and phase space contributions were fitted to CLAS data, whereas the resonant parts were kept fixed using available information on resonances in the fitted W range. (B) Restricted W ranges where we observed discrepancies between the CLAS data and the model calculation, were re-fitted by allowing for variation of the resonant coupling parameters within the SQTM fitting uncertainties of 10-20 %.
c30
E 25 b
20
15
10
5
0
O
w GeV
'
'1:4
'
'1:s
'
'$'
'
'117
'
'is' '119 ; '
' '
'
'
'2
I
W GeV
Figure 1. Total cross section for y * p + pn+s- for 3 Q 2 ranges. The curves on the left plot result from a fit using fixed resonant parameters (step A). The curves on the right plot result from a fit allowing for variation of resonance couplings (step B). The errors in the CLAS data are statistical only.
49 1
Figure 1 shows the total cross section and the model calculation for the three analyzed Q2 bins: 0.5-0.8 GeV2, 0.8-1.1 GeV2, and 1.1-1.5 GeV2. The description of the cross section is considerably improved by allowing for variations of N' couplings in step B (plot on right side). The only exception is the W range around 1.7 GeV where a reasonable variation (10-20 %) of established resonance parameters fails t o fit the CLAS data.
2 100
A
50 25
50 D
- 3 0 \
-
1
W
1.25 1.5
-
1 1.25 1.5
1 1.25 1.5
M+ ,
2
= b
(GeV)
\ 100
75
50
40
25 T J O
20 0
A
?
0.25 0.5 0.75
&..-..
40
'
..Q
0.25 0.5 0.75
I
U
0.25 0.5 0.75
M,+n-
\ 13
b
20 0
O
100
0
,
100
,
,
0
0 +CM,-
(GeV)
1 0
r d eg )
Figure 2. Differential cross sections duldM,,+, du/dM,+,- , and du/dO,- (from top t o bottom) at W=1.70-1.725 GeV and Q2 bins: 0.5-0.8 GeV2 (left), 0.8-1.1 GeV' (mid), 1.11.5 GeV2 (right). Curves show the fit result when varying either the couplings of 013(1700) (solid) or P11(1710) (dotted) or Pi3(1720) (dashed line).
Allowing for a wide variation of coupling parameters of either 013(1700) or P11(1710) or P13(1720) result in better fits t o the data as shown in Fig. 2. Whereas the variation of &(1700) parameters fails t o fit the angular distri-
492
bution and the variation of 5 1 (1710) overestimates dn/dM,, at M,+,- M 0.7 GeV, the best fit is obtained by a significant change of the p13(1720) coupling parameters. In comparison with the PDG values3 (mass: 1650-1750 MeV, r = 100-200 MeV, BR(pN)=70-85 %), we find that its coupling to .rrA clearly dominating over the pN coupling: BR(.rrA)=63f12 % and BR(pN)=19&9 % with its mass and width at mR = 1725 f 20 MeV and r = 114 f 19 MeV. Apart from such drastic changes in established resonance parameters, we considered the possibility that an unknown resonant state may couple to electromagnetic probes which has not been visible in .rrN scattering. Such a state is - according to our fits, keeping the established resonance parameters fixed - most likely a PI^ state at 1720 MeV with I? = 88 f 17 MeV and BR(nA)=41f13 %, BR(pN)=17flO %. The isospin could not be determined.
3
The reaction y'p
+ wp + .rr+r-nop
According to quark model predictions,l>gthe w N channel is another promissing channel in the search for undiscovered N*. Due to its zero isospin this vector meson only couples to I = states. Omega electroproduction data was extracted analyzing (e,e'pr+) events with cut on missing mass MMetp,+X > 2m,. As shown in Fig. 3, the w mass peak in the resulting missing mass distributions MMe,,x was sufficiently narrow ( M 30 MeV FWHM) to permit fits in the immediate omega mass neighborhood using a 3ndorder polynomial to represent the underlying 37r phase space background. 0
1 . 7 < W < 1.8 G e V
._
=-
1 . 8 < W < 1.9 G e V
~MK)
1.9<W<2.0
GeV
2000
1000
500 '0.4
0.6
0.4
0.8
MM(e'pX)
[GeV
0.6
0.8
MM(e'pX)
[GeV
Figure 3. Missing mass distributions M M , l p x for ( e , e ' p s + ) events with cut on M M e t p , + > 2mr. T h e w signal is extracted In each kinematical bin separately.
Figure 4 shows the preliminary differential cross section for selected W ranges. The angular distributions are characterized by a monotonic fall off with increasing production angle, indicating diffractive and/or T exchange process(es). However, in the W ranges around 1.8 GeV and 1.9 GeV, the
493
cross section shows additional strength in intermediate and backward direction, an indication for a strong nucleon pole (u-channel) and possible N * resonance (s-channel) contributions. Due to statistical limitations, we required in this analysis only one pion of the w decay being detected. The data set is currently being enlarged to allow for smaller W - and Q2-bins and additional investigations on d* dependence and angular momenta.
Figure 4. Preliminary results from CLAS for omega electroproduction: differential cross section for selected W ranges.
References
S. Capstick and W. Roberts, Phys. Rev. D 49, 4570 (1994). V. Mokeev et aE, Phys. of Atomic Nucl. 64, 1292 (2001). D.E. Groom et all Eur. Phys. J. C 15, 1 (2000). M. Ripani et all Phys. of Atomic Nucl. 63, 76 (2000). 5. D.M. Manley and E.M. Salesky, Phys. Rev. D 45, 4002 (1992). 6. V.D. Burkert, Czech. Journ. of Phys. 46, 627 (1996). 7. S. Capstick, Phys. Rev. D 46, 2864 (1992). 8. F. Close and Z.P. Li, Phys. Rev. D 42, 2194 (1990).
1. 2. 3. 4.
QCD CONFINEMENT A N D MISSING BARYONS P.
GONZALEZ
Dpto. de Fisica Te6rica and IFIC llniversidad de Valencia CSIC, fi-~6100 Burjassot, Valencia, Spain E-mail: pedro.gonzalezOuu.es
-
H. GARCILAZO E.S.F.M., Instituto Politicnico Nacional, Edificio 9, 07738 M k i c o D.F., Mexico E-mail:
[email protected]
J. VIJANDE, A. VALCARCE Grupo de Fisica Nuclear Universidad de Salamanca, E-37008 Salarnanca, Spain E-mail:
[email protected], valcarceOmozart.usal.es We show that in a quark model scheme the use of a screened confining potential: suggested by lattice and QCD non-perturbative calculations: instead of an infinitely rising one with the interquark distance may give rise to a one-teone correspondence between the predicted three-quark bound states and the observed baryon resonances. This points out to the use of the baryon spectrum as a quite stringent test of the long-range confining potential.
Constituent quark models of baryon structure are based on the assump tion of effective quark degrees of freedom so that a baryon is a three-quark color singlet bound state. Quarks are bound by means of a quark-quark (44) potential which tries to mimic QCD at the baryon energy scale. The potential may incorporate directly derived perturbative QCD contributions in the form of a one-gluon exchange (OGE) interaction and non-perturbative terms arising from multigluon quark interaction processes. Among them, confinement is usually taken for granted. The form of confinement is attached to the behavior of the running coupling, a,,at low momentum transfer (low Q 2or large distances). In lowest-order QCD a, reads: 4T
where A is the QCD scale parameter and Po = 11 - $ N j , being N j the number of flavors. As Q + A, diverges what is interpreted as a signal of strict confinement. Taking into account lattice simulations for heavy quarks in the
494
495 so-called quenched approximation (considering only valence quarks) a qq confining potential linearly rising with the interquark distance is proposed '. The consideration of this confining force altogether with OGE and/or one-meson exchange or other effective interactions turns out to be fruitful in the construction of quark potential models that provide with a precise description of baryon spectroscopy 2.3.4.5. However all the models predict a proliferation of bound states in the baryon spectrum at excitation energies above 1 GeV which are not experimentally observed as resonances. This difference between the quark model prediction and the data about the number of physical resonances is known as the missing resonance problem. An explanation for such a discrepancy was given by realizing that most of the missing states could be too inelastic to be easily observed6e7. To test experimentally this idea, in order to clarify the issue: is a current objective of the CLAS collaboration in TJNAF'. In this talk we propose as an alternative that there may be a one-to-one correspondence between the predicted bound states and the observed baryon resonances once the confinement dynamics is properly implemented by sea quark contributions. From lattice calculations for the heavy quark sector in the unquenched approximation (including light qq pairs) it has become clear that when increasing the interquark distance creation of light qq pairs out of the vacuum in between the quarks becomes energetically preferable resulting in the complete screening of quark color charges at large distances. Moreover the effective coulomb coupling turns out to be stronger in the presence of sea quarks. In the 80's a specific parametrization of these effects was given in terms of a potentialg. Regarding the confining term it looked like:
This form shows a clear Yukawa screening of the linear potential in terms of a screening length p-' typically around 1fm. u is the string tension with values around 0.16 GeVZ and u / p is the splitting energy of the heavy quark pair. These features can also be inferred from a non-perturbative QCD calculation of as.From an approximate solution of the Schwinger-Dyson equation asreadslo:
(Q2+4m2
(%)I
where Mi(Q2) = mi [In A2 s) / In is a dynamical gluon mass: and m g = 300 - 700 MeV. Hence a freezing of the infrared coupling at distances around 1 fm comes out supporting the view of a screened confinement.
496
-%
I .5z~
u, W
Figure 1: Relative energy nucleon and delta spectrum for the screened confining potential with p = 1.54 f m - ' ~ c = 512.5 MeV, R = R~ = 105.23 MeV fm, ro=0.55 fm, and mu = rnd = 337 MeV. The shaded regions represent the experimental data with their uncertainty. Lines marked with a cross correspond to experimental data for which no uncertainty is available.
To examine the consequences derived from such a screening for the light baryon spectrum we shall assume that the same form of the screening is applicable to light quarks and we shall complement the screened confinement potential with the minimal OGE interaction (coulomb plus spin-spin terms). The same model but with a linear confinement has been applied to the meson and baryon spectrum in the past 11:127 providing a reliable description except for the energies of the first radial excitations and the aforementioned proliferation of missing states. The qq potential is then written as:
where we have assumed the usual color structure for confinement (the A % are In the spirit the Gell-Mann SU(3) matrices) and c should be identified with of quark model calculations c and p should be taken as effective parameters. To get the light baryon spectrum we solve the Schrodinger equation through a Faddeev calculation. The complete resulting spectrum, up to J = $: is shown in Fig. 1 where an almost complete parallelism between predicted bound states and cataloged
E.
497
resonances can be observed avoiding the proliferation of missing states. Note that the precise position of the states very close to the (2q bound-1 free 4)state threshold is very sensitive to the particular quark model considered what could be responsible for the few remaining discrepancies. Moreover with the exception of the Roper resonances the calculated spectrum is of significantly good quality. Concerning the values of the fitted confinement parameters ,u-l = 0.65 fm and c = 0.51 GeV (or equivalently D = 0.156 GeV' ) are not far from the heavy quark case. In conclusion although our calculation is not complete (higher orbital angular momentum excitations should be also calculated and further refinements to understand the energy dependence of LI, should be considered 13) we may conjecture from our results that the confining dynamics in QCD has a clear signature in the baryon spectrum in the form of a one-to-one correspondence between 3q bound states and observed resonances: or inversely that the baryon spectrum tells us about the specific form of the confining mechanism in QCD. Acknowledgments
We thank to V. Vento: S. Noguera: J. Papavassiliou and F. Ferndndez for suggesting discussions. This work has been partially funded by COFAA-IPN (Mexico): by Junta de Castilla y Le6n under Contract No. SA-109/01, and by EC-RTN, Network ESOP, Contract HPRN-CT-2000-00130. References 1. G.S. Bali, Phys. R e p . 343: 1 (2001): and references therein. 2. N. Isgur and G. Karl: Phys. Reo. D 18:4187 (1978). S. Capstick and N. Isgur, Phys. Reo. D 34, 2809 (1986). 3. B. Desplanques e t al: 2. Phys. A 343: 331 (1992). 4. A. Valcarce et nl: Phys. Lett. B 367: 35 (1996). H. Garcilazo et al, Phys. Reo. C 63: 035207 (2001). 5. L.Ya. Glozman and D.O. Riska, Phys. Rep. 268: 263 (1996). 6. R. Koniuk and N. Isgur, Phys. R e v . Lett. 44: 845 (1980). 7. S. Capstick and W. Roberts, Phys. Reo. D 47, 1994 (1993). 8. M. Ripani, Few Body Syst. Supp. 11: 284 (1999). 9. K.D. Born e t al: Phys. Reo. D 40: 1653 (1989). 10. A.C. Aguilar et a( hepph/0109223. J.M. Cornwall and J. Papavassiliou, Phys. Rev. D 40: 3474 (1989); Phy.9. Rev. D 44, 1285 (1991). 11. R.K. Bhaduri et al: Nuovo Cimento A 6 5 : 376 (1981). 12. B. Silvestre-Brac and C. Gignoux: Phys. Reo. D 32: 743 (1985). 13. P. Gonzilez et al: work in progress.
PHOTOPRODUCTION OF THE E HYPERONS J.W. PRICE, J. DUCOTE, AND B.M.K. NEFKENS UCLA Department of Physics and Astronomy, Los Angeles, CA 90095-1547, USA E-mail: priceophysics. ucla.edu
FOR THE CLAS COLLABORATION Very little is known about the doubly-strange B hyperons. s U ( 3 ) ~ symmetry, based on QCD, implies the existence of many B states yet to he found. A complete study of the excited B spectrum can also he used to study other related areas of nuclear physics, such as the s - d quark mass difference and Bp scattering. We will report on a new approach to B physics, using the photoproduction process -p -+ K+K+B-, in which the B is cleanly tagged by the missing mass of the ( K + K + )system. We show the current status of this study with the CLAS detector at Jefferson Laboratory, and discuss how it relates to the above topics. We also comment on the future of this program.
1
Introduction
Quantum chromodynamics (QCD) describes the interactions of the quarks and gluons. An aspect of QCD that is not completely explained is the nature of the hadrons. QCD only permits the existence of color singlet states. The na'ive framework of 444 baryons leads to grouping the baryons in four multiplets: a totally antisymmetric singlet state, the A; two mixed-symmetry octets, made up of N , A, C, and E;and a totally symmetric decuplet, consisting of A, C, E,and R. Inspection of this scheme leads to the conclusion that every N* state has a corresponding octet E state, and that every A state has a corresponding decuplet S. The Review of Particle Properties lists twenty-two N* states and twenty-two A states, implying the existence of forty-four E states. To date, we have only found eleven of these states, only three of which have been fully identified by their mass, width, spin, and parity. Finding these states is of fundamental importance to nuclear physics. One aspect of the E states that will help in this search is their narrower width. As has been pointed out by Risk ', the gross features of the widths of the baryons may be understood as being due to the number of light quarks in the baryon. Since the E has only one light quark while the N* and A have three, we expect the N* and A to be nine times as broad as the S, which is seen to remarkable accuracy. We are further aided in the search for excited E states by the application of flavor symmetry. This symmetry is the consequence of the structure of the
498
499
+ C,
QCD Lagrangian, which we may write as LQCD= LO
where
4
We note that Lo depends only on the quark and gluon fields and their derivatives; Lo is independent of the quark masses. For small mq, the mass term L, is a correction to LO. To the extent that flavor symmetry is a good symmetry, we expect the mass spectrum of the octet baryons to be related to each other, and similarly for the decuplet baryons. The quality of the comparison between the N* and A states has already been demonstrated '. 2
Experimental Method
We have selected the photoproduction process on the proton, y p + K+K+E:-, to study the 8* spectrum. This has resulted in the first exclusive measurement of photoproduction on the proton, and is currently the only suitable method for studying most of the E* spectrum. We detect the two K+, and infer the E- by its characteristic peak in the missing mass of the (K+K+)system. The two positively-charged kaons in the final state ensure that the missing particle has S = -2, Q = -1, and that it is a baryon. The = is the only possibility, making for a very clean experimental signature. The measurement was carried out with the CLAS detector at the Thomas Jefferson National Accelerator Facility (JLab) The photons were individually tagged, and the range of photon energies used was 3.0 - 5.5 GeV. CLAS is a large acceptance detector with a toroidal magnetic field, oriented such that positively-charged particles are bent away from the beamline.
-_
'.
3
Preliminary Results
Figure 1 shows the missing mass spectrum of the (K+K+)system. There are two strong peaks in the figure, corresponding to the ground state E-(1321) and the first excited state 5-(1530). The positions and widths of the missing mass peaks are consistent with the known masses and widths of the states and the resolution of the CLAS detector. We find our production rate of the ground state 5-, given current CLAS data acquisition capabilities, to be several thousand per day.
500 100
Figure 1. The missing mass spectrum for r p + K+K+X. The two peaks correspond to the ground state C- at 1321 MeV and the first excited 8- at 1530 MeV.
4
Future Plans
There are several possit,,: projects we may pursue in this work, including (but not limited to) searches for higher-mass states, the neutral Eo, measuring J p for the E* states, studying the s - d quark mass difference, and using E p scattering to measure the Z - p scattering length and look for exotic baryon states. We will continue this analysis to search for as many states as our energy and statistics allow. There are several poorly-known states which need confirmation. We will also look for a proposed 5* state at approximately 1870 MeV which decays via the process E* -+Ev,which would belong to a J p = 1/2- octet with the N(1535), the A(1670), and the C(1750). We may use a similar process to study the photoproduction of the neutral Eo.Instead of the process y p + K+KoEo,which is complicated by the indeterminate strangeness of the K t , we will use the process y p + K+K+7r-S0. The loss in acceptance due to the requirement of an additional detected particle should be outweighed by the cleanliness of the signature.
501
By detecting the decay chain E*3 ET 4 A m , we can measure the spins and parities of the excited states 6. This would allow us to fill in many of the gaps in our knowledge of the E* spectrum. Finding more E* states along with their spins and parities will allow us to complete several baryon multiplets. This will allow a test of the Gell-Mann decuplet equal spacing relation and the Gell-Mann-Okubo mass relation, which are in turn related to the mass difference between the s and d quarks. Since the B is a relatively long-lived particle, we may have the opportunity to look for a secondary vertex due to the scattering of the E with a proton in the target. Elastic scattering measurements will allow us to measure the Z p scattering length and coupling constant, while inelastic measurements may point to evidence for the H dibaryon or exotic baryon states ’. 5
Conclusion
We have made the first observation of exclusive E photoproduction on the proton, and have shown that the production rate is sufficient to consider mounting a large program based on the physics of the 5 hyperon. This project is still in its infancy, and much work remains to be done. More data exist, which will allow us to improve our statistical precision, and to search for higher-mass states, as well as to broaden our knowledge of the S spectrum. Acknowledgments This work was carried out with the support of the Department of Energy. References 1. D.E. Groom et al., Eur. Phys. J. C15, 1 (2000) and 2001 off-year partial update for the 2002 edition available on the PDG WWW pages (URL: http://pdg.lbl.gov/) . 2. D.-0. Riska, in N S T A R 2001 Proceedings, Mainz, Germany, 2001, edited by D. Drechsel and L. Tiator (World Scientific, Singapore). 3. B.M.K. Nefkens and J.W. Price, in MENU 6001 Proceedings, edited by H. Haberzettl and W.J. Briscoe, TIV Newsletter 16,9 (2001). 4. W.K. Brooks, Nucl. Phys. A663-664,1077 (2000). 5. S.F. Tuan, Phys. Rev. D 46,4095 (1992). 6. N. Byers and S. Fenster, Phys. Rev. Lett. 11, 52 (1963). 7. E.L. Lomon, in Proceedings of the Conference on Advances in Nuclear Physics and Related Areas, Thessaloniki, July 1997.
OPEN STRANGENESS PRODUCTION IN CLAS G . NICULESCU Ohio University, Athens, OH, USA E-mail:
[email protected] (for the CLAS Collaboration) An extensive program dedicated to the study of open strangeness systems was established in Hall B at Jefferson Lab. This program takes full advantage of the excellent characteristics of the CEBAF accelerator combined with the almost complete angular coverage of the CLAS detector. A general overview of the program is given, as well as results for the angular dependence of the electroproduction of kaon-hyperon final states.
The study of K-hyperon leptoproduction can provide new insights on many of the important issues in nuclear physics. To the lowest order, and as far as there is no significant strangeness content of the nucleon, the elementary kaon-hyperon production process involves the production of a single ss pair which breaks the flux tube (argued to be1, alongside with constituent quarks, non-perturbative bound state solutions of QCD). This is highly relevant if one wants to gain insight in the energy range where the transition between hadronic and quark degrees of freedom occurs. Due to the higher masses involved, the study of kaon production allows one to probe a higher W range (with two-body kinematics) than it is possible using pions. Furthermore, the strangeness sector might be the right place to look for some of the so-called “missing resonances”, predicted (but not (yet) observed experimentally) by some quark models2 - as some of these resonances might couple strongly to both photons and kaons. The A and Co hyperons act as natural isospin filters in the sense that only N * resonances can contribute (in an s-channel picture) t o A whereas both N* and A* resonances can contribute to the Co channel. The availability of polarized electron beams, coupled with the self-analyzing nature of the A hyperon weak decay makes single- and double-polarization observables accessible if the detection of at least one of the decay products of the hyperon is possible. A comprehensive program devoted to the study of strangeness electroproduction (hopefully addressing the issues listed earlier) was established in the experimental Hall B at JLab. This program takes full advantage of the excellent momentum and angular coverage provided by the CLAS spectrometer, as well as its multi particle final state detection capabilities. The study of ground state hyperon production (Experiment E93030) is
502
503
an important part of this program; the rest of this contribution will try to highlight some of the results of this study. The missing mass recoiling against the outgoing electron and the K+ meson in electron proton scattering, as measured in CLAS, is shown in Fig. la. Prominent peaks are observed corresponding to the A and Co hyperons, smaller peaks corresponding to the A1520 and the C1385/A1405 are also observed as well as a certain amount of background (mostly from misidentified kaons). The resolution obtained with the CLAS detector is significantly better than the spacing between the two ground state hyperons ( 4 0 MeV), allowing for a clean separation of the two peaks. At each beam energy, further analysis of the data was carried out by binning the data in Q2 (-Q2 being the 4-momentum squared of the virtual photon), W (the total energy in the hadronic center-of-mass frame), cosO;( (the angle of the k a m relative to the virtual photon direction in the K-hyperon center of mass frame), and 4 (the angle between the leptonic and hadronic production planes). The virtual photon cross-section can be written as:
where EL = &Q2/u2 is the longitudinal polarization of the virtual photon. Given the almost complete angular coverage of the CLAS detector the 4 dependence of Eq. 1 can be measured (at fixed Q 2 , W , and cosO*). Through a simple fitting procedure one can then extract the 4 independent part of the cross-section nu = OT + ELUL, as well as the two interference terms, UTT and O L T . This procedure is illustrated in Fig. l b for the A hyperon and Fig. l c for the Co hyperon for a representative kinematic bin (Q2=0.7 (GeV)2, W=1.9 GeV, and cos0°=-o.3). The vertical error bars shown are statistical only while the horizontal error bars merely show the extent of each 4 bin considered. By carrying out this fitting procedure for all available kinematic bins one can study separately the angular and energy dependence of the nu, UTT and OLT observables. In Fig. 2 the preliminarya cosO* dependence of these three observables is shown, separately for A and Co, for Q2= 0.7 (GeV)' and W = 1.9 GeV. The uncertainties shown are statistical only. The solid lines are predictions of the Regge model described in Ref. while the dashed lines are predictions from the effective Lagrangian model of Ref. There are large qualitative differences between the A and Co production. Most striking, the cos8k dependence of nu is very forward-peaked for the A and more central aAs of this writing this analysis is undergoing the final systematic checks and is expected to be finalized in the near future.
504
Figure 1. a) - Missing mass distribution in K + electroproduction as measured with th CLAS detector. b) and c) - Extraction of the uu,UTT and QLT through a fit of the 4 dependence of the differential crosssection for the A channel (top right) and the Co channel (bottom right). For both cases Q2=0.7 ( G e V ) 2 ,W=1.9 GeV, and c0s6~=-0.3.
for the Co. This points to a t*hannel domination of the A production in the forward direction, whereas this mechanism appears to be suppressed for Co. The size, and forward peaking of QLT for A production strengthens the above argument. Neither one of the two models shown is very successful in describing the data other than in its more general features. The models seem to fare worse in explaining the Co data than they do for the A data. In conclusion, the electroproduction of the ground state A and Ca was studied using the CLAS detector at JLab. The hermeticity of the detector allowed the separation of the nu, QTT, and ULT observables. Significant differences between the two hyperons are observed, pointing to different reaction mechanisms, especially in the forward direction. The interference terms are larger in the A than in the Co channel. The discrepancies between the model predictions and the experimental data warrant a revision of the basic assumptions and parameters entering the theoretical models. This work was supported in part by the National Science Foundation under Grant No. PHY-007226.
505
"ijdl
/I -
0.3 0.2
:
0.1 h
h
.r? 0.9
5 W
-0
G d , -0.1 D
d -0.2 -83 -0 -0.1
-0.2 -0.3
cos( O K )
cos( O K )
Figure 2. (TU,(TTT and (TLT observables shown as a function of the cos 8' angle (left panels) and Co hyperons (right panels). From top to bottom the three rows of panels correspond to (TU,@ T T , and OLT respectively. Theoretical predictions obtained with a Regge model (solid lines) as well as an effective Lagrangian model (dashed lines) are shown.
References
1. 2. 3. 4.
N. Isgur, JLAB-THY4O-20, (2000). S. Capstick and W. Roberts, Phys. Rev. D58, 1 (1998). M. Guidal, private communication, (2000). T. Mart, private communication, (2000).
K+ PHOTOPRODUCTION AT LEPS/SPRING-8. R.G.T. ZEGERS FOR THE LEPS COLLABORATION RCNP, Osaka Uniuersity, 10-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan At the LEPS beam line at Spring-8, K+ photoproduction off the proton is studied for 1.9 GeV < W < 2.3 GeV and O0 < O,,(K+) < 6C0. Since data are taken with transversely polarized photons, the photon-polarization assymetry can be measured. In contrast to the cross section, this observable is very sensitive to the details of the reaction process, such as the possible contribution from so-called 'missing' resonances and thus provides a good way to distinguish between various theoretical descriptions. In the paper, the current status of the analysis and expected impact of the results are discussed.
1
Introduction
The study of strangeness photoproduction on the nucleon is a potentially powerful tool t o deepen the insight into baryon structures, because of the strangeness degree of freedom involved. The p ( y ,K+)A and p ( y ,K+)Co reactions are good candidates for such studies, since they provide a way to access a rather large part of the rich excitation spectrum of the nucleon. For a number of these nucleon resonances, the branching into strange channels is well known. On the other hand, a large number of resonances predicted in quark models have so far been undiscovered and are hence referred to as 'missing resonances'. It has been prepositioned that some of these missing resonances could couple strongly to the K A and KC channels. Although the above-mentioned reaction channels had been under investigation for an extensive period of time, data taken at SAPHIR' has resulted in renewed interest. This is largely due t o the fact that structure in the total cross section spectrum of the p ( y ,K + ) A reaction near W=1900 MeV was revealed. Mart and Bennhold2 showed that this structure can be explained if an additional 0 1 3 (1895) resonance is included in the calculations. Alternatively, if from the set of possible candidates in this mass range a P13 (1950) resonance is chosen, the data is equally well3 described. Unfortunately, it is difficult to draw strong conclusions based on cross section measurements only because of ambiguities in the theoretical descriptions. In the region W < 2.5 GeV, most calculations are performed in a tree-level effective-Lagrangian approach. Ambiguities arise from the choice of included resonances, the values of the coupling constants (depending on the magnitude of SU(3)-symmetry breaking) and the choice of hadronic form factors. Further
506
507
complications are due to coupled-channel contributions4 and off-shell effects5. Moreover, different methods to suppress the strength due to the Born terms only, lead to equally good descriptions of the available data3. It can, therefore, be concluded that at present we are left with an unacceptable level of model dependence in the theoretical description of experimental results. Improvement in this situation on the theoretical side is possible by changing approaches as to reduce the number of parameters and limit the model dependencies, for example by using a consituent-quark approach5. On the experimental side, one strives to increase the amount of available data, especially by measuring previously unprobed observables. Inclusion or exclusion of certain resonances2 as well as the use of different model ingredients3 have large effects on the predictions for (double) polarization observables. Therefore, at various places in the world (GRAAL, JLAB, ELSA, MAMI, LEGS and Spring-8) experimental programs are in progress to measure these observables. It has been shown that the photon-polarization asymmetry (the asymmetry measured in the comparison between data taken with different polarizations for the incoming photon) in particular contains large sensitivities. Mart and Bennhold2 predict a sign change for the photon polarization asymmetry if the missing &(1895) resonance is present. Janssen et aL3 showed that various methods to suppress the strength of the Born terms, as well as the choice of form factor also changes the photon polarization asymmetry significantly. 2
K f photoproduction at LEPS/SPring-8
Investigation of the p ( y , K + ) A and p ( y , K + ) C o reactions at the LaserElectron-Photon beam h e at Spring-@ (LEPS) can contribute strongly to the field, because kinematical regions are probed that are not accesible elsewhere. Moreover, since the photons are produced by Compton backscattering of laser photons off electrons, polarization is automatically obtained by polarizing the laser light. Between December 2000 and June 2001, photo-production data was taken with a liquid Hydrogen target7. The photon energy range was between 1.5 GeV and 2.4 GeV (i.e. 1.9 GeV < W < 2.3 GeV) and for these energies the transverse polarization (horizontal or vertical) varies between 50% and 95%, respectively. By comparing the azimuthal dependence of cross sections for horizontally and vertically polarized photons, the photonpolarization asymmetry can be determined via the relation:
508 *
L
v)
5 4500 F 0 " 4000 ? 3500
5
3000 2500
2000 1500 1000
500 0
1
1.5
K* Missing Mass (GeV) Figure 1. Kf missing mass spectrum taken at LEPS.
where C is the photon-polarization asymmetry, P the averaged degree of polarization for the horizontal and vertical polarized data, 4 the azimuthal angle of the K+ and Nh(N,) the measured azimuthal distributions for horizontal (vertical) polarized data. In this relation, detector acceptances are divided out. Only foward K+ production angles (Oo < O,,(K+) < 60') can be probed at the LEPS facility, but with a high accuracy and good statistics. This angular range is especially important to distinguish K and K* contributions, since the former peaks and the latter vanishes at Oo. K+ particles can cleanly be selected7 from the reconstructed mass spectrum. In figure 1 the missing mass spectrum for the p ( y , K + ) is shown for about 50% of the available data. The h ( l l l 6 ) , C0(1193), A(1520) and a combined peak due to the h(1405) and CO(1385) can clearly be distinguished. In figure 2, photon-polarization asymmetries are shown for the A(1116) and C0(11Y3), for two different choices of photon energy (1.7 and 2.2 GeV). No correction for photon polarization has been applied and the plots are scattering-angle integrated. From this figures it is clear that at LEPS the photon polarization asymmetry for the K + , h and K f , C o can be accurately determined. Since the photon polarization asymmetry is expected to fluctuate rather quickly as a function of photon energy in the resonance region, it is important to determine asymmetries for as narrow energy bins as possible. It is envisioned that with the current statistics a binning of 100 MeV in E-, (corresponding to ap-
509 ,0.6
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i
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++O. 4
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Figure 2. Scattering-angle and photon-energy integrated asymmetry curves for the A( 1116) (left) and CO(1193) (right). Open data points/dashed fits are for 1.6 < E, < 1.8 GeV and full data points/solid fits are for 2.1 < E , < 2.3 GeV.
proximately 50 MeV in W )can be achieved for 4 different values o f t between 0 and -0.6 (GeV/c)2.
3
Status and outlook
At present, acceptances and efficiencies for the LEPS detector are being studies. These include Monte-Carlo simulations to determine the geometrical acceptance accurately as well as detailed studies of the separate parts of the detector system, photon-beam properties and tracking errors. With the various details understood, results for the photon polarization asymmetry and the differential cross section are expected to come out in the course of 2002. References
1. M.Q. Tran et al., Phys. Lett. B 445,20 (1998). 2. T. Mart and C. Bennhold, Phys. Rev. C 61 (R) 012201 (2000). 3. S. Janssen et al., Phys. Rev. C 65,015201 (2001). 4. Wen-Tai Chiang it et al., nucl-th/0104052, 2001. 5. B. Saghai, nucl-th/0105001, 2001. 6. T. Nakano et al., Nucl. Phys. A684,71c (2001). 7. T. Nakano et al., these proceedings.
KAONPHOTOPRODUCTI0N:BACKGROUND CONTRIBUTIONS AND MISSING RESONANCES STIJN JANSSEN AND JAN RYCKEBUSCH Department for Subatomic and Radiation Physics, Ghent University, Proeftuinstraat 86, 9000 Gent, Belgium E-mail:
[email protected]. be Kaon photoproduction off the proton is studied in an effective Lagrangian approach. The dominant resonance contributions in the reaction dynamics are identified, including a search for signals of “missing” resonances. SpeciaI attention is paid t o the issue of the elusive role played by background contributions.
1
Formalism
Since long, it has been known that pion production and pion induced reactions may be too restrictive to explore the complexity of the nucleon spectrum. Therefore, the study of other meson production reactions is essential to gain access to excited nucleon states which remain unobserved in pionic reactions but which are predicted by (constituent) quark-model calculations. Reactions of this type are the strangeness production processes p(y, K ) Y , where Y = A or C. Here, we present results of p(y, K ) Y calculations which adopt an effective Lagrangian approach starting from hadronic degrees-of-freedom’ . The effective Lagrangians provide the mathematical structure of the interaction vertices and the propagators of the intermediate fields. In order to account for the short-range physics of the inter-baryon interaction, form factors are introduced at the hadronic vertices. The cutoff mass of those hadronic form factors sets the typical length scale of the hidden short-range dynamics. The. reaction amplitude contains the usual Born terms and the exchange of the vector meson K* in the t-channel (also the K1 is taken into account in the case of K+A production). Apart from the lLbackgroundllcontributions, there is common agreement2 that the three nucleon resonances ,911(165O), P11(1710) and P13(1720) play a substantial role in the p(y, K ) Y reaction dynamics. Due to isospin considerations, contributions of the I = A* resonances are excluded in the K+A channel. For the KC processes, we have identified the 5’31 (1900) and P31(1910) resonances as likely candidates for intermediate A* states. Finally, we have implemented predicted “missing” resonances and investigated whether their inclusion considerably improved the overall description of the data.
4
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4.04
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Figure 1. The extracted coupling constants for the s11(1650), p11(1710), P13(1720) and D l ~ ( 1 8 9 5 s-channel ) resonances in the p ( y , K f ) h process, using three different models for dealing with the background terms. The circles are for model A, the squares for model B and the triangles for model C.
2
Background Contributions
Assuming a moderate breaking of SU(3)-flavor symmetry, one can put forward some ranges for the g K + A p and gK+COp coupling constants starting from the value of gr". Adopting a realistic breaking of sU(S)-flavor symmetry at the 20% level, though, one finds that the predicted contribution from the Born terms largely overshoots the measured p(y, K ) Y cross sections. This observation clearly illustrates that the treatment of the background diagrams poses a serious difficulty when modeling open strangeness photoproduction reactions. We have suggested three schemes which accomplish to reduce the Born strength to realistic levels. In model A, soft hadronic form factors with a cutoff value of the order of the kaon mass (= 0.5 GeV) are introduced. Despite our reservations against the use of soft hadronic form factors, it emerges that they are absolutely necessary in order to reduce the Born strength to an acceptable level when no other ingredients are introduced in the model. Alternatively, we showed that the introduction of u-channel hyperon resonances is able to reduce the Born strength through the mechanism of destructive interferences'. This method is adopted in model B. Finally, in model C the constraints imposed by a moderate breaking of SU(3) symmetry are simply ignored and g K + A p and gK+COp are treated as free parameters. In such an approach, the optimum values for the two coupling constants correspond with a completely broken SU(3)-flavor symmetry. All three schemes succeed in providing a satisfactory description of the SAPHIR3>4data which consists of total and differential cross sections as well
512
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Figure 2. Model calculations for the total p ( y , K + ) hcross section. The solid curve includes the missing D13, the dashed curve includes a Pi3 resonance.
as recoil polarization asymmetries. Despite the fair agreement of the three models with the data, it has to be stressed that in some cases a substantial amount of model dependence is introduced in the extracted resonance parameters. This is made clear in Fig. 1 where the extracted coupling constants of the nucleon resonances for the p(y, K + ) Aprocess are plotted for the three different background models. For the KC counterpart, the extracted resonance coupling constants are less dramatic affected by the model dependences in the background diagrams. The model dependence in the extracted resonance couplings is rather unfortunate, given that this information can bridge the gap between the p(y, K ) Y measurements and the quark-model calculations for baryons. The same variations are also observed in the predictions of the photon beam asymmetry and other polarization observables. Here also, the KC results seem to be more stable than the K + h ones with regard to variations in the parameterization of the background diagrams.
3
Missing Resonances
With the release of the SAPHIR data back in 1998, it became clear that the energy dependence of the total p(y, K + ) h cross section exhibits a peculiar structure about 1.5 GeV photon lab energy. It was suggested by the George Washington group2 that this structure could be theoretically accounted for by the inclusion of a “missing” &(1895) resonance. Such a resonance has never been observed in pionic reactions but its existence was predicted by con-
513 stituent quark-model calculations5. As such, it appears as a good candidate for a “missing” resonance. Our calculations confirm that the description of the p ( y ,Kf)A data is significantly improved after the inclusion of this new 0 1 3 resonance and that the calculations can account for the observed structure in the energy dependence of the total cross section. With respect to the classification of the quantum numbers of this additional resonance, it should be stressed that the data can equally well be described by adding other resonant states. For example, as is made clear in Fig. 2, the inclusion of a “missing” Pl3 resonance can also produce the structure in the energy dependence of the total cross section. In the other isospin channels, p ( y ,K+)Co and p(y, Ko)CC,the quality of agreement between the model calculations and the SAPHIR data only marginally improved after the inclusion of the missing resonance. 4
Conclusion
Model calculations for the p ( y ,K+)Y observables are presented. Special attention is paid to the issue of the background contributions. It turns out that different schemes for dealing with the background can account for the available data but produce significant model dependences in the extracted resonance parameters and in the predictions for the unmeasured polarization observables. Whereas the energy dependence of the measured p(y, K + ) A cross section suggests the existence of a previously unobserved resonance, the current data does not enable one to identify unambiguously the quantum numbers of it. Indeed, both a 0 1 3 and a P13 resonance with a mass of about 1.9 GeV are able to improve the description of the p ( y , K + ) A data. There are no convincing signals for a salient role of a such an additional resonance in the p ( y , K)C channels. We are confident, however, that the upcoming data for various polarization observables and electroproduction response functions will allow to further pin down the full reaction dynamics of the strangeness photoproduction processes and remove some of the model dependences which exist to date. References 1. S. Janssen, J. Ryckebusch, D. Debruyne and T. Van Cauteren, Phys. Rev. C 6 5 , 015201 (2002). 2. T. Mart and C. Bennhold, Phys. Rev. C 61, R0112201 (2001). 3. M.Q. Tran et al., Phys. Lett. B 445, 20 (1998). 4. S. Goers et al., Phys. Lett. B 464, 331 (1999). 5. S. Capstick and W. Roberts, Phys. Rev. D 58, 074011 (1998).
DYNAMICAL DESCRIPTION OF NUCLEON COMPTON SCATTERING AT LOW AND INTERMEDIATE ENERGIES: FROM POLARISABILITIES TO SUM RULES S. KONDRATYUK TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C., V 6 T 2A3 Canada E-mail:
[email protected]
0. SCHOLTEN K V I , 9747 AA Groningen, The Netherlands E-mail:
[email protected] Results of the Dressed K-matrix Model are presented for nucleon Compton scattering, nucleon polarisabilities and related sum rules. Effects of the meson loop dressing on the A resonance are shown.
1
Compton scattering at low and intermediate energies
The Dressed K-matrix Model has been developed to describe pion- and photon-induced reactions on the nucleon at both low and intermediate energies. In this model effects of the meson cloud around the nucleon are included by dressing the nucleon propagator and 7rNN vertices up to infinite order while obeying essential constraints from unitarity, crossing and analyticity. In what follows we will be comparing the fully dressed and the bare calculations. The latter corresponds to the traditional K-matrix models 2 , where analyticity is badly broken since the real parts of the meson loops are not included at all. Fig. 1 shows calculated differential cross sections for proton Compton scattering. Comparing this calculation as well as pion-nucleon and pion photoproduction phase shifts with data, we fixed all parameters of the model. Thus we can do a parameter-free calculation of the nucleon polarisabilities, which are found to be in a reasonable agreement with experiment. 2
Compatibility of the low-energy and sum-rule evaluations of nucleon polarisabilities
Since the present model is applicable in both intermediate and low-energy regions, it allows us to calculate nucleon polarisabilities in two distinct ways 5 , namely: 1)directly from the low-energy expansion of the scattering amplitude, and 2) by integrating calculated total cross sections in sum rules corresponding
514
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Figure 1. Dependence of the Compton cross section on the photon lab energy at fixed angles. The fully dressed and bare calculations are compared with the data.
to coefficients in the low-energy expansion. Such a comparison is important because the sum rules rest on only few fundamental requirements 6 : gaugeinvariance, crossing symmetry, unitarity and analyticity, the latter being of special significance. As can be seen from Table 1, the level of agreement between the low-energy calculation (method 1))and the sum-rule calculation (method 2)) is quite good at the two leading orders in the photon energy: at w,corresponding to the anomalous magnetic moment n of the proton, and at w 2 , corresponding to the sum Q ,@of the electric and magnetic polarisabilities. This means that the model obeys the essential symmetry constraints at these orders. The dressed calculation shows a closer agreement
- -
+
516
since it fulfills analyticity constraints much better than the bare calculation. However, a discrepancy shows up for the forward spin polarisability yo,i. e. at
-
w3.
Table 1. Comparison between the proton polarisabilities as computed directly from the low-energy expansion of the amplitude (LE) and as computed from the sum rules (SR).
-
n LE Bare 1.79 Dressed 11.79
O(w)
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Q
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SR 14.5 13.8
LE 17.2 14.5
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3 Dressing the 7rNA vertex with an infinite number of loops An exploratory calculation indicated that the disagreement between the low-energy and sum-rule evaluations of yo is due to the fact that, unlike the nucleon self-energy, the self-energy of the A resonance was computed only up to one T N loop. The first step in extending the dressing procedure is to dress the A on the same footing with the nucleon in the purely hadronic sector, i. e. for pion-nucleon scattering. In particular, the T N A vertex gets dressed with an infinite number of meson loops. This improves the P33 phase shift at higher energies, as is shown in Fig. 2 (the other phase shifts are not affected). The dressing of the y N A vertex with an infinite number of loops is currently under way.
180 - P33
FULL with: Dressed 7rNA . BarerNA 1
0
200
,
I
I
400
I
600
PION ENERGY (MeV)
Figure 2. The calculated P33 phase shift is improved by the consistent dressing of the A resonance up to infinite order. The data points are from the analysis.
517
References 1. S. Kondratyuk and 0. Scholten, Phys. Rev. C 59, 1999 (1070); ibid., Nucl. Phys. A 677,2000 (396); ibid., Phys. Rev. C 62, 2000 (025203). 2. P.F.A. Goudsmit et al., Nucl. Phys. A 575,1994 (673); T . Feuster and U. Mosel, Phys. Rev. C 58, 1998 (457); ibid., Phys. Rev. C 59, 1999 (460); A. Yu. Korchin, 0. Scholten, and R.G.E. Timmermans., Phys. Lett. B 438,1998 (1). 3. S. Kondratyuk and 0. Scholten, Phys. Rev. C 64,2001 (024005). 4. G. Galler et al., Phys. Lett. B 503,245 (2001); A. Hunger et al., Nucl. Phys. A 62,385 (1997). 5. S. Kondratyuk and 0. Scholten, Phys. Rev. C 65,2002 (038201). 6. A.M. Baldin, Nucl. Phys. 18,1960 (310); L.I. Lapidus, Sov. Phys. JETP 16,1963 (964); S.B. Gerasimov, Sow. J. Nucl. Phys. 2, 1966 (430); S.D. Drell and A.C. Hearn, Phys. Rev. Lett. 16,1966 (908). Phys. Rev. D 63,114010 (2001). 7. R.A. Arndt et al., Phys. Rev. C 52,2120 (1995).
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Session on Hadrons in the Nuclear Medium Convenors N. Bianchi M. Sargsian
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NUCLEAR SHADOWING AND IN-MEDIUM PROPERTIES OF THE po * T. FALTER, S. LEUPOLD AND U. MOSEL Institut fuer Thwretische Physik Universitaet Giessen 0-35392 Giessen, Germany We explain the early onset of shadowing in nuclear photoabsorption within a mu]tiple scattering approach and discuss its relation to in-medium modifications of the p o .
The nuclear photoabsorption cross section is known to be shadowed at large energies, i.e. O,A < Au,N. This was at first interpreted as a confirmation of the vector meson dominance (VMD) model, which assumes that the photon might fluctuate into vector meson states with a probability of order aem. To give rise to shadowing, these hadronic fluctuations must travel a t least a distance ZV that is larger than their mean free path inside the nucleus. This so called coherence length ZV can be estimated from the uncertainty principle
where k, and kv denote the momentum of the photon and the vector meson respectively and mv is the vector meson mass. Recent photoabsorption data1i2 indicate an early onset of shadowing at E, ~1 GeV. From (1) one sees that the lightest vector meson, e.g. the po, has the largest coherence length and therefore its properties determine the onset of the shadowing effect. This lead to the interpretation3 of the low energy onset of shadowing as a signature of a decreasing po mass in medium since a decrease of m, increases the coherence length I,. A quantitative description of the shadowing effect is possible within the Glauber model". The nuclear photoabsorption cross section can be related via the optical theorem to the nuclear forward scattering amplitude. In order a,, one finds the two contributions shown in Fig. 1. The left amplitude stems from forward scattering of the photon from one nucleon inside the nucleus. Summing over all nucleons this amplitude alone leads to the unshadowed cross section U,A = Au,N. Shadowing arises from the interference with the *WORK SUPPORTED BY DFG AND BMBF.
521
522
Figure 1. The two amplitudes that contribute to the nuclear forward scattering amplitude in order aem.
second amplitude in order aem.Here the photon produces some hadron X I on one nucleon inside the nucleus. This hadron then scatters through the nucleus and finally into the outgoing photon which has the same momentum and energy as the incoming photon. Since we are dealing with the forward scattering amplitude and the nucleus has to be in its ground state after the last scattering event one usually assumes that it stays in its ground state during the whole multiple scattering process (multiple scattering approximation). One sees that, in principle, shadowing can be explained without the usage of VMD . In the simple Glauber model one makes use of the eikonal approximation, assuming that all scattering events at high energies go predominantly into the forward direction. This limits the intermediate states X i to hadrons which have the quantum numbers of the photon, e.g. the vector mesons. Neglecting off-diagonal scattering ( V N -+V ' N with V # V ' ) and neglecting the widths of the vector mesons one gets for the total photon nucleus cross section
Here n ( 3 denotes the nucleon number density and frv and fv are the vector meson photoproduction and V N forward scattering amplitudes respectively. In our calculation5 we also account for two-body correlations between the nucleons. In the derivation of (2) one has made an error of order A-' by summing up infinitely many multiple scattering terms for the intermediate vector meson. This is equivalent5 to the propagation of the vector meson in an optical potential, giving rise to an effective in-medium mass and width. The momentum transfer qv = k - kv in the phase factor arises from putting the vector meson on its mass shell. A large momentum transfer qv causes a rapidly oscillating term in the integrand of (2) and reduces the shadowing
523
effect. Note that qv is just the inverse of the coherence length lv as can be seen from (1). We now relate the amplitudes frv and f v using VMD: e
f,v = fvr = -fv. sv
(3)
The pN forward scattering amplitude f, is taken from dispersion theoretical a n a l y ~ e & ~In. the energy region that we are considering the real part of f, is negative and of the same order of magnitude as the imaginary part, leading to an increase of the effective po mass in medium. Within VMD the negative real part also enters the photoproduction amplitude via (3). This enhances the shadowing effect and compensates the suppression due to the larger in-medium mass. In total one gets an increase of shadowing even with a positive mass shift of the po in medium. This can be seen from the left side of Fig. 2 where we show our results for the ratio crA/Aa,N. The calculation that includes the negative real part (solid lines) is in perfect agreement with the data. When the real part of f v is neglected, as done in most other calculations, one gets the result represented by the dotted curves and clearly underestimates the shadowing effect for all nuclei. One even gets anti-shadowing below 2 GeV for P b and 1 GeV for C. In an improved model', we explicitly sum over multiple scattering amplitudes where 1, 2, ... A nucleons participate in the scattering process. This avoids the error of order A-' that occurs in the large A limit as described above. We also take the widths of the vector mesons into account and find that the main contribution to shadowing at low energies stem from light po mesons with masses well below the pole mass. These are favored by the nuclear formfactor because their production is connected with a small momentum transfer. This is in agreement with our qualitative understanding of shadowing, since light fluctuations have a larger coherence length. We also do not hold on to the eikonal approximation any longer. Dropping this restriction leads to a new contribution to the shadowing effect due to no mesons as intermediate states. Since these cannot be produced in the forward direction without excitation of the nucleus they do not contribute to shadowing at high energies. In the shadowing onset region, however, they give rise to 30% of the total shadowing effect in the case of C and 10% in the case of P b as can be seen from the solid lines on the right side of Fig. 2. The dashed lines show the contribution from intermediate p , w and 4 mesons. In total one again gets a good description of the shadowing effect. We have presented a theoretical explanation for the early onset of shadowing as observed in nuclear photoabsorption. It can be explained by taking the negative real part of the pN forward scattering amplitude into account.
524
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*.O
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Figure 2. Calculated ratio cryA/AuyN plotted versus the photon energy E7. The left side shows the result of the simple Glauber model: with real part of fp (solid lines), Refp = 0 (dotted lines). The right side shows the result of our improved model: contributions from p , w and 4 (dashed lines), including the contribution from intermediate r0 (solid lines).
This corresponds to an increase of the effective po mass in nuclear medium, in agreement with dispersion theoretical analyses. The major contribution to shadowing stems from light po with masses much smaller than the pole mass. In addition we find contributions from intermediate xo to shadowing in the onset region. References
N. Bianchi et al., Phys. Rev. C 54, 1688 (1996). V. Muccifora et al., Phys. Rev. C 60, 064616 (1999). N. Bianchi et al., Phys. Rev. C 60, 064617 (1999). T. H. Bauer et al., Rev. Mod. Phys. 50, 261 (1978). T. Falter, S. Leupold and U. Mosel, Phys. Rev. C 62, 031602 (2000). V. L. Eletsky and B. L. Ioffe, Phys. Rev. Lett. 78,1010 (1997). 7. L. A. Kondratyuk et al., Phys. Rev. C 58, 1078 (1998). 8. T. Falter, S. Leupold and U. Mosel, Phys. Rev. C 64, 024608 (2001).
1. 2. 3. 4. 5. 6.
SCALAR- AND VECTOR-MESON PRODUCTION IN HADRON-NUCLEUS REACTIONS W. CASSING’ Institut fiir Theoretische Physik, H. -Bu#-Ring 16, 35392 Giessen, Germany E-mail: Wolfgang.CassingOtheo.physik.uni-giessen.d e The production and decay of vector mesons ( p , w) in p A reactions at COSY energies is studied with particular emphasis on their in-medium spectral functions. It is explored within transport calculations, if hadronic in-medium decays like a+aor a07 might provide complementary information to their dilepton (e+e-) decays. Whereas the &a- signal from the pmeson is found to be strongly distorted by pion rescattering, the w-meson Dalitz decay to a0y appears promising even for more heavy nuclei. The perspectives of scalar meson ( f o , a o ) production in p p reactions are investigated within a boson-exchange model indicating that the fomeson is hard to detected in these collisions in the K K or m~decay channels whereas the channels p p + pna; and p p + da$ look very promising.
1
Introduction
The modification of the vector meson properties in nuclear matter has become a challenging subject in dilepton physics from T - A , p A and A A collisions. Here the dilepton (e+e-) radiation from p’s and w’s propagating in finite density nuclear matter is directly proportional to their spectral function which becomes distorted in the medium due to the interactions with nucleons. Apart from the vacuum width ;?I (V = p, w ) these modifications are described by the real and imaginary part of the retarded self energies C V , where the real part %Ev yields a shift of the meson mass pole and the additional imaginary part 9 C v (half) the collisional broadening of the vector meson in the medium. We recall that the meson self energy in the t - p approximation is proportional t o the complex forward V N scattering amplitude fvN(P,0) and the nuclear density p(X), i.e. C v ( P ,X) = -4np(X)fv~(P,O). The scattering amplitude itself, furthermore, obeys dispersion relations between the real and imaginary parts3 while the imaginary part can be determined from the total V N cross section according to the optical theorem. Thus the vector *IN COLLABORATION WITH E. L. BRATKOVSKAYA, M. BUSCHER, YE. s. GOLUBEVA, V. GRISHINA, V. HEJNY, V. METAG, J . MESSCHENDORP, G. I. LYKASOV, L. A:. KONDRATYUK, M. V. RZJANIN, S. SCHADMAND, A. A. SIBIRTSEV, H. STROHER
525
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meson spectral function
can be constructed once the V N elastic and inelastic cross sections are known. Note that in ( 1 ) all quantities depend on space-time X and 4-momentum P. 2
Production and decay of vector mesons at finite density
As mentioned before, the in-medium vector meson spectral functions can be measured directly by the leptonic decay V+e+e- (cf. ref^.^^^^^), the strong decay po + 7rr+n-- or the Dalitz decay w+7roy, respectively. The vector meson production in p A collisions can be considered as a natural way4y6 to study the p and w-properties at normal nuclear density under rather well controlled conditions. The transport calculations have been performed for p+A collisions at 2.42.6 GeV by introducing a real and imaginary part of the vector meson self energy and width as
in the t-papproximation. Here MO and denote the bare mass and width of the vector meson in vacuum while p ( X ) is the local baryon density and p0=0.16 fm-3. The parameter ,BY-0.16 was adopted from the models in The predictions for the w-meson collisional width rcollat density po range from 20 t o 50 MeV7- depending on the number of wN final channels taken into account - while the collisional width of the pmeson should be about 100 - 120 MeV at po due to the strong coupling to baryon resonances (cf. Fig. 6 of Ref.3). In Ref.8 it has been found that the 7r+7r- decay mode of the po in nuclei is not well suited to reconstruct the in-medium po spectral function except for very light nuclei due to the strong 7r* final state interactions (cf. also Ref.g). The situation changes for the in-medium w-meson Dalitz decay since here only a single pion might rescatter whereas the photon escapes practically without reinteraction. In this case it is foundlo that most of the w-mesons from a 12C target decay in the vacuum (92%) and consequently w decays in the medium as well as no rescattering are rather scarce. The situation changes for a Cu target where 7roy coincidences from finite density are more frequent (19% w's decay inside the target), however, also 7ro rescattering gives a substantial background. The latter can - in the invariant mass range 0.6
527
< M 5 0.9 GeV of interest - be suppressed effectively by kinematical cuts on higher T O energiesll or angular correlations between the photon and the pion12 which provides good perspectives for the n0y decay mode.
3
Scalar meson production
The structure of the lightest scalar mesons a(980) and fo(980) is not yet understood and is one of the most important topics of current hadronic physics. It has been discussed that they could be either ” qq states”, ”Four-quark cryptoexotic states”, KK molecules or vacuum scalars. Moreover, there is a strong mixing between the uncharged ao(980) and the fo(980) due to a coupling t o KK intermediate states. It is, therefore, important to study independently the uncharged and charged components of the ~ ( 9 8 0 because ) the latter are not mixed with the fo(980) and preserve their original quark content. In order t o estimate the cross section of the reactions pp + p p f z , pp + ppag, p p + p a : , p p + d a i at bombarding energies close to threshold which are available at COSY/Julich - an effective Lagrangian approach as well as the Regge pole model have been employed. The amplitudes taken into account are: i) the a,-, coupling to two nucleons through the fl(1285) and Tmeson exchanges; ii) the Q coupling through 77- and 7r-meson exchanges; iii) the production of %-mesons through pion exchange with s- and u- channel nucleon currents. The coupling constants and cut-off parameters Ai for T and 7- meson exchanges are taken from the Bonn potential model; for the a,-,- and f1(1285)-mesons the values from Ref.13 are used while the cut-off A at the nucleon exchange vertex was considered as a free parameter within the interval 1.1-1.3 GeV and fixed approximately by comparison to the LBL data for a0 production14. Within this model the mechanisms i) and ii) are of minor importance and the dominant contribution comes from the nucleon u- and s-channel exchanges. For the deuteron a: final state the two-step model (TSM) described by the triangle diagram is used15J6 employing the deuteron wave function in the parameterization from Ref.17. The results of the calculations show that in p p reactions the ppfo final state is hard to detect due to the nonresonant background from T+T- or K+K-18; a similar statement holds for the ppa: final statelg since the cross section is small due to a destructive interference between s- and u- channel diagrams. However, the p n a i or d a i final states show sizeable cross sections close t o t h r e ~ h o l d ‘which ~ dominate over the nonresonant background channels. We note, that preliminary experimental results for the p p + da: reaction have become available by now and support the calculations performed in Refs.l5~l6.
+
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4
Summary
In this contribution the production and decay of vector mesons (p,w) in p A reactions at COSY energies has been studied with particular emphasis on their in-medium spectral functions. It is found within transport calculations, that hadronic in-medium decays like T + K - or r o y might provide complementary information to their dilepton ( e + e - ) decays. However, the T+T- signal from the pmeson is strongly distorted by pion rescattering on nucleons even for light nuclei like " C . On the other hand, the w-meson Dalitz decay to 7roy appears promising even for more heavy nuclei since only the neutral pion may rescatter and 3-photon events ( K O + yy) have a very small background at high invariant mass. Furthermore, the perspectives of scalar meson (fo,ao) production in pp reactions have been investigated within a boson-exchange approach as well as the Regge pole model indicating that the fo-meson is hard to detect in the K K or T K decay channels in these collisions whereas the final channels pnaof and daof look very promisinglg. References
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
W. Cassing, E.L. Bratkovskaya, Phys. Rept. 308, 65 (1999) R. Rapp, J. Wambach, Adv. Nucl. Phys. 25, l(2000) L. A. Kondratyuk et al., Phys. Rev. C 58, 1078 (1998) Ye. S. Golubeva et al., Eur. Phys. Jour. A 7, 271 (2000) Ye. S. Golubeva et al., Nucl. Phys. A 625, 832 (1997) E. L. Bratkovskaya, NucI. Phys. A 696, 761 (2001) G. I. Lykasov et al., Eur. Phys. Jour. A 6, 71 (1999) A. Sibirtsev, W. Cassing, Nucl. Phys. A 629, 717 (1998) G. M. Huber, these proceedings A. Sibirtsev et al., Phys. Lett. B 483, 405 (2000) J. Messchendorp et al., Eur. Phys. Jour. A 11, 95 (2001) Ye. S. Golubeva et al., Eur. Phys. Jour. A 11, 237 (2001) M. Kirchbach, D. 0. Riska, Nucl. Phys. B 176, 1 (1980) M. A. Abolins et al., Phys. Rev. Lett. 15, 469 (1970) V. Yu. Grishina et al., Eur. Phys. Jour. A 9, 277 (2000) V. Yu. Grishina et al., Phys. Lett. B 521, 217 (2001) M. Lacomb et al., Phys. Lett. B 101, 139 (1981) E. L. Bratkovskayaet al., Eur. Phys. Jour. A 4, 165 (1999) E. L. Bratkovskayaet al., Jour. Phys. G 28, 2423 (2002)
HELICITY SIGNATURES I N SUBTHRESHOLD po PRODUCTION ON NUCLEI G.M. HUBER Department of Physics, University of Regina, Regina, SK S4S OA2, Canada We report a helicity analysis of subthreshold p o production on 2H, 3He h d 12C nuclei at low photoproduction energies. The results are indicative of a large longitudinal p polarization ( I = 1, m = 0 ) and are consistent with a strong helicity-flip mechanism of p production. The analysis supports an in-medium modification of the po spectral function.
Of all particles, the p has received the most attention with regard to medium modifications. Since the po carries the quantum numbers of the conserved vector current, its properties are related to chiral symmetry, and can be investigated with a variety of models. Most models predict a reduction in the renormalized vector meson mass in the nuclear medium. In addition, the in-medium width of the po may be increased by resonant interactions. Experimental evidence for po mass modification has been widespread, but all suffer from significant model uncertainties. The goal of the study reported here is to provide data which can be interpreted in a less model-dependent fashion than those presently available. We have recently published a helicity analysis of our 2Hand natC7r+7rphotoproduction data from TAGX. The most important points of this analysis are: (1) The "s~bthreshold~~ region is chosen to maximize any nuclear interaction effect. Fermi momentum is required to put po on shell, and the po is produced with low boost with respect to the nuclear medium. This choice of photon energy also suppresses diffractive po production. (2) The 7r+7rIT- are detected in the TAGX large solid angle spectrometer. The po + 7rf7r- decay channel has been selected because of its favorable M 100% decay ratio. (3) The p decay angular distribution is reconstructed in the s-channel helicity frame, where the po direction is taken as the quantization axis. 8* is the polar angle of the 7r+ in the po + d 7 r - C.M. system. (4) The geometry of the TAGX spectrometer natually favors 7r+7r- events from po decay, at the expense of the competing background processes. Non-
529
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po background is further suppressed by the requirement that the missing mass
< (mtaTget+125MeV), which eliminates 3n production and n - N inelastic FSI, and by the requirement that the nn opening angle > 120O. As po + ITIT is the only mechanism that emits n+n- back-to-back at a common vertex, this results in a large O,, in the lab frame. Other processes preferentially produce n+x- with smaller lab frame opening angle. These two cuts eliminate > 95% of non-p0 background, and > 90% of n - N elastic scattering FSI following p + nlT+nITdecay. 3He
*H
'*C
500-600MeV
....:.
40 .:.
0
m
W
0
0
600-7W MeV
200
W
7W%W MeV
im
0 1
0
1
-1
0
1
0 -1
0
cos en+ Figure 1. A portion of the data are displayed as a function of cosO:+ in the invariant mass range of 500-800 MeV/c2 in 100 MeV/c2 bins. For each panel, the upper line data have missing mass cuts applied, while the shaded region has in addition an opening angle cut applied, as explained in the text.
Sample data distributions from this analysis are shown in figure 1. The distributions without the O,, cut are featureless, characteristic of the superposition of the many An, N * n , N * , and AA processes dominating x+nproduction in this energy regime. The result of the opening angle cut (shaded distribution) is a dramatic reduction (- 5 : 1) in the number of surviving events in the central regions of the distributions. A pronounced p - wavelike cos20 signature is observed in the 600 5 m,, 700 MeV/c2 region and weaker ones in the 500-600 and 700-800 MeV/c2 m,, bins. This signature is consistent with n+n- production by the decay of a longitudinally polarized po (1 = 1, m = 0). n+n- production from An, N * n and other two-step processes
<
531
are unable to reproduce the observed helicity distributions. Events from undistribution in a uniform manner after polarized po decay populate the the mmiss,&, cuts have been applied. Therefore, we conclude the presence of a strong helicity-flip signature in po photoproduction in the subthreshold region. Such helicity-flip amplitudes may be associated with the excitation of medium-modified ("rhos~bar~') N * (1520) 2 . The ability to isolate the po strength, as presented here, without the uncertainty associated with the deconvolution of K+T- yields originating from many contributing background channels, may be a valuable tool for providing in-medium po spectral shape information. We assume that the physics background surviving the 8,, > 120" cut is reasonably flat in case; and only slowly varying in shape. This assumption is supported by our MC studies, as well as by the featureless shape of the helicity distributions prior to application of the cut. Then we fit the distributions with A + Bcose + Ccos28 and plot the value of the cos28 coefficient versus invariant mass. These are shown in the top panel of figure 2. There is a progressive shift to smaller mp with decreasing A , consistent with the Bianchi et al. photoabsorption analysis 3.
case;,
Data -%
- - 3He - . - . uc
Comparison w i t h W
I
Figure 2. Top panel: Invariant mass distribution of the 1 = 1, m = 0 portion of the data, as described in the text. Each curve is normalized to the same (arbitrary) peak height. Bottom panels: Comparison of top panel data with the free po spectral function, as obtained from + wave analysis. a e+e- + ~ - a partial
532
A comparison to the free p" spectral function in a quasi-free model is made in the bottom panels of figure 2. Here, we use the partial wave analysis of e+e- -+ 7r-7r+ data from 2m, to m,,t '. The spectral function is incorporated into quasi-free models of the p(y, po)p reaction on 2H, and 12C, and MC-simulated p 3 7r+7r- data are tracked through the experimental apparatus, subject to the same cuts as the actual data, and the m,, invariant mass distribution reconstructed. In this manner, experimental acceptance and phase-space restrictions are taken into account, and any deviation from the data may indicate the presence of a medium modification. We note that the PWA model provides an adequate description of the 2H data but underpredicts the low mass tail on 12C,which may indicate an in-medium modification of the spectral function. A more detailed analysis taking into account modified spectral shapes from various theoretical models is underway. In conclusion, 7r+7r- photoproduction on light nuclei in the E-, energy region of 800 to 1120 MeV, which lies mostly below the p" production threshold on the free proton, is reported here with emphasis on helicity information. Significant p -+ 7r7r decay with 1 = 1, m = 0 is observed for 575 5 mTa5 750 MeV on all nuclei, which is consistent with our earlier observations on 3He using a different analysis method. We fit the observed cos13: distributions with A + B c o d + Ccos28 versus m,,. The coefficient C may yield an approximate in-medium p spectral function under the assumption of small and featureless non-p background. The resulting "spectral" distributions are similar for 2H, 3He, 12C, with a systematic shift towards lower mkn with smaller A. The free po spectral function from 7r7r partial-wave analysis, incorporated in quasifree MC simulations were compared with data. The resulting comparison indicates an excess of low mass strength, which may indicate an in-medium modification of the p spectral function. Acknowledgments This work has been partially supported by the Natural Sciences and Engineering Research Council of Canada.
References 1. 2. 3. 4. 5.
G.J. Lolos, et al., Phys. Lett. B 528 (2002) 65. W. Peters, et al., Nucl. Phys. A 632 (1998) 109. N. Bianchi, et al., Phys. Rev. C 60 (1999) 064617. M. Benayoun, et al., Z. Phys. C58 (1993) 31. M. Kagarlis, et al., Phys. Rev. C 60 (1999) 025203.
FROM MESON- AND PHOTON-NUCLEON SCATTERING TO VECTOR MESONS IN NUCLEAR MATTER M.F.M. LUTZt, GY. WOLF* AND B. FRIMANt t GSI and
TU Darmstadt, Planckstr 1, D-6&?91 Dannstadt, Germany RMKI KFKI, Pj. 49, H-1525 Budapest, Hungary
A covariant and unitary approach to pion- and photon-nucleon scattering taking the T N , p N , w N , q N , *A,KA and KC channels into account is presented. It is argued that the s- and d-wave nucleon N(1535), N(1650), N(1520) and N(1700) resonances and as well as the isobar A(1620) and A(1700) resonances should be generated in terms of coupled channel dynamics. A fair description of the experimental data relevant for the properties of slow vector-mesons in nuclear matter is obtained. The p and w-meson spectral functions are evaluated in nuclear matter according to the low-density theorem. They are determined by the vector-meson nucleon scattering amplitudes as obtained in the coupled channel analysis.
The in-medium properties of hadrons is a topic of high current interest. The decay of vector mesons into e+e- and ,LL+,LL- pairs offers a unique tool to explore the properties of dense and hot matter in nuclear collisions. The lepton pairs provide virtually undistorted information on the current-current correlation function (j&) in the medium At invariant masses in the range 500 - 1000 MeV, the correlation function is sensitive to in-medium modifications of the mass distribution of the light vector mesons p and w. There is a longstanding and controversial discussion about the vector meson properties in dense nuclear matter To leading order in the baryon density, modifications of the mass distribution are determined by the vector-meson nucleon scattering amplitudes. Since these amplitudes are not directly constrained by data, the predictions for the vector-meson spectral densities in nuclear matter are strongly model dependent. This work is an attempt to overcome this problem by using the constraints from data on pion- and photon-nucleon scattering considering in particular the w- and pmeson production data in a systematic way. We construct a coupled-channel scheme for meson-baryon scattering, including the T N , pN, wN, ITA,v N , K h and K C channels. In such a scheme the amplitudes for experimentally non-accessible processes like pN and wN scattering are constrained by the data on elastic ITNscattering and inelastic reactions like the pion- and photon-induced production of vector mesons. The goal is to determine the vector-meson nucleon scattering amplitudes close to threshold. Consequently we concentrate on the energy window 1.4 GeV < fi < 1.8 GeV. It is sufficient to consider only s-wave scattering in the pN and wN
'.
2,3,41516.
533
534 channels. This implies that in the T N and T A channels we need only sand d-waves. In order to systematically derive the momentum dependence of the vector-meson self energy, vector-meson nucleon scattering also in higher partial waves would have to be considered. The general form of the interaction kernel may be obtained from a meson exchange model or more systematically from the chiral Lagrangian. In Ref. we construct an effective field theory for meson-nucleon scattering in the resonance region. The philosophy of this approach is to approximate the interaction kernel but to treat rescattering in the s-channel explicitly. We assume that the interaction kernel is slowly varying in energy in the relevant window 1.4 GeV< & < 1.8 GeV. This implies that the s- and d-wave baryon resonances N(1535), N(1650), N(1520) and N(1700) and as well as A(1620) and A( 1700) must be generated by the coupled channel dynamics of the BetheSalpeter scattering equation. The motivation for this assumption follows from the observation that the A( 1405) resonance is a member of the very same largeN, multiplet to which all nucleon and isobar resonances considered in this work belong to. Since the A(1405) resonance was shown to arise as a K N bound state within chiral coupled channel calculations %ln,’’ it is natural to insist on analogous dynamical assumptions for the remaining states of this multiplet. We construct an effective Lagrangian with quasi-local four-point meson-baryon contact interactions, which are adjusted as to approximate the interaction kernel for 1.4 GeV< fi < 1.8 GeV. Details can be found in Ref. ’. Within this framework, the Bethe-Salpeter equation for the coupled-channel system reduces to a matrix equation. The model parameters are constrained by data from meson- and photonnucleon reactions. For the latter we employ a gauge invariant generalization of the phenomenologically successful vector-meson dominance (VMD) model. In the original VMD formulation of Sakurai 1 2 , the vector meson is converted into a photon via the interaction terms A f ’ p f )and Af’w,. Since these terms violate gauge invariance, we use a modified vector-meson dominance assumption, where the strength of the yN -+ X vertex is related to the p @ ) N -+ X and wN + X vertices via a transverse transition tensor. For the latter the most general ansatz compatible with gauge invariance is allowed. By construction the transition tensor is independent on the final state X = K N ,w N ,p N , .... The model is in spirit close to the picture that emerges in the hidden local symmetry approach 13. In contrast to previous coupled channel calculations, we find a fairly weak coupling of the N(1520) to the pN channel. The extraction of the coupling of the N ( 1520) to the pN channel from hadronic reactions alone is model depenT differ by large factors 14915. dent. Different analyses of the K N --t N ~ data
535 25
8 -
20
T
2
-
15
2 h
3
3
W
w 10
np
n3
E -
-
I
E5 I
n 0.4
0.6
0.8
o [Gev]
1.0
1.2
0.4
0.6
0.8
1.0
1.2
o [Gev]
Figure 1. Imaginary parts of the p and w propagators in nuclear matter at p = po and 2p0, compared t o those of the free-space propagators.
To remove this ambiguity was an important motivation for considering the additional constraints provided by the multipole amplitudes for the reaction y N -+ 7rN within the generalized vector meson dominance model. Data on the dilepton production process 7r-p -+ n e+ e- are expected to provide further constraints on the vector-meson coupling strengths to the subthreshold baryon resonances ". Any microscopic theory of the in-medium properties of vector mesons requires the information encoded in the pN and wN scattering amplitudes as input. We use the vector-meson scattering amplitudes as they arise in the coupled channel analysis described above to compute the propagation of the p and w mesons in nuclear matter. According to low-density theorem the self energy of a vector meson in nuclear matter is expressed in terms of the s-wave scattering amplitude averaged over spin and isospin ". In Fig. 1 we show the vector meson spectral functions at the saturation density of nuclear matter, po = 0.17 fmP3 and at p = 2 p o . For the p meson we note an enhancement of the width, and a downward shift in energy, due to the mixing with the baryon resonances at & = 1.5 - 1.6 GeV. At p = po the center-of-gravity of
536
the spectral function is shifted down in energy by about 3 %. The in-medium propagator of the w meson exhibits two distinct quasiparticles, an w like mode, which is shifted up somewhat in energy, and a resonance-hole like mode at low energies. The low-lying modes carry about 15 % on the energy-weighted sum rule. The center-of-gravity is shifted down by about 4 %. However, we stress that the structure of the in-medium w-meson spectral function clearly cannot be characterized by this number alone. On a quantitative level, the spectral functions may change when higher order terms in the density expansion are included. For instance, we expect that the in-medium properties of the baryon resonances depend sensitively on the meson spectral functions. If this is the case, a self consistent calculation, which corresponds to a partial summation of terms in the density expansion, would have to be performed 18.
References
1. 2. 3. 4. 5. 6. 7.
8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
18.
R. Rapp and J. Wambach, Adv. Nucl. Phys. 25, 1 (2000). T. Hatsuda and S.H. Lee, Phys. Rev. C 46, R34 (1992). G.E. Brown and M. Rho, Phys. Rev. Lett. 66, 2720 (1991). M. Herrmann, B. F'riman and W. Norenberg, Nucl. Phys. A 560, 411 (1993). G. Chanfray, R. Rapp and J. Wambach, Phys. Rev. Lett. 76,368 (1996). S. Leupold, W. Peters and U. Mosel, Nucl. Phys. A 628, 311 (1998). M.F.M. Lutz, Gy. Wolf, B. F'rirnan, nucl-th/0112052, Nucl. Phys. A, in print. C.L. Schatt, J.L. Goity and N.N. Scoccola, Phys. Rev. Lett. 88, 102002 (2002). N. Kaiser, P.B. Siege1 and W. Weise, Nucl. Phys. A 594, 325 (1995). E. Oset and A. Ramos, Nucl. Phys. A 635, 99 (1998). M.F.M. Lutz, E.E. Kolomeitsev, Nucl. Phys. A 700, 193 (2002). J.J. Sakurai, Currents and Mesons (University of Chicago Press, 1969). M. Bando, T. Kugo, K. Yamawaki, Phys. Rep. 164, 217 (1988). A.D. Brody et al., Phys. Rev. D 4, 2693 (1971). D.M. Manley and E.M. Saleski, Phys. Rev. D 45, 4002 (1992); Phys. Rev. D 30, 904 (1984). M. Soyeur, M.F.M. Lutz and B. F'riman, nucLth/0202049. W. Lenz, Z. Phys. 56 (1929) 778; C.D. Dover, J. Hufner and R.H. Lemmer, Ann. Phys. 66, 248 (1971); M. Lutz, A. Steiner and W . Weise, Nucl. Phys. A 574, 755 (1994). M.F.M. Lutz and C. Korpa, Nucl. Phys. A 700, 309 (2002).
POLARIZATION TRANSFER IN THE 4HE(l?,E ’ 9 ) 3 H REACTION S. STRAUCH Center for Nuclear Studies, Dept. of Physics, The George Washington University Polarization transfer in the 4He(Z,e ’ g 3 H reaction was measured in Jefferson Lab experiment 93-049. The ratio of the polarization transfer coefficients, (PA/P:)H~, is on average significantly reduced as compared to the same ratio in elastic Zp scattering. This is so far unaccounted for by relativistic DWIA calculations, and favors the inclusion of a predicted medium modification of the proton form factor.
1
Introduction
Whether nucleons undergo considerable change of their internal structure when bound in the nuclear medium is a long standing issue in nuclear physics. Recent calculations by D.H. Lu et al.’ and M.R. Frank et d.’ are consistent with present constraints on possible medium modifications and suggest measurable effects in polarization transfer experiments. The sensitivity of polarization transfer observables to the nucleon form factors is motivated by the relation3
which holds for free electron-nucleon scattering, and directly links the ratio of the electric to magnetic Sachs form factors, GEIGM,to the transverse and longitudinal transferred polarizations, PL and PL; the other quantities are the nucleon mass, M , the incident and final electron energies, Ei and E f , and the scattering angle, 8,. Proper interpretation of experimental results for quasielastic scattering requires accounting for reaction mechanism effects in the framework of some model. A variety of calculations, however, indicates polarization observables for the 4He(Z,e’g3H reaction have minimal influence from bound state wave functions, final state interactions (FSI) and meson exchange currents (MEC). It is precisely these effects that have so far prevented a clean determination of nucleon medium modifications from unpolarized response functions in ( e ,e’p) experiments, see e.g. Ref.4. 2
Experiment
Jefferson Lab experiment 93-04g5measured the polarization transfer in the 4He(Z,e’f13H reaction at four different four-momentum transfers of Q 2= 0.5,
537
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1.0, 1.6, and 2.6 (GeV/c)2. The data were taken in quasielastic, parallel kinematics at low missing momentum. The target 4He was selected for study since its relative simplicity allows for realistic microscopic calculations and since its high density enhances any possible medium effects. The experiment was designed to detect differences between the in-medium polarizations compared to the free values. Thus, additional elastic Zp scattering data were taken. The experiment was performed in Hall-A employing the two high resolution spectrometers, one of which was equipped with a focal plane polarimeter (FPP). The polarization transfer observables, PL and Pi, were extracted by means of the maximum likelihood technique, utilizing the azimuthal distribution of protons scattered off the graphite analyzer in the FPP.
3 Results The results of the measurement are expressed in terms of the polarization transfer double ratio, R = (P;/P~)H~/(PL/P~)H. This ratio is sensitive to differences in the scattering from bound and free protons, and has the additional advantage that systematic errors due to uncertainties in the spin transport partly cancel. Figure 1 shows the preliminary results for R at Q2 = 1.0 (GeV/c)2 as a function of missing momentum. The four data points correI
"
"
I Q2
"
"
I
'
"
'
I
"
"
1
= 1.0 (GeV/c)*
preliminary
a \. a
1.0
W
\ D
I n
N
a \. 0.8
a W
T
.....
RPWlA
Y
1
Figure 1. Preliminary polarization transfer double ratio at Q2 = 1.0 (GeV/c)2 as a function of missing momentum. The data are compared to calculations by Udias et aL6 ; see text.
539
spond to four bins in the acceptance within the one experimental setting. The data are compared to different relativistic calculations by Udias et aL6. The calculations shown are using the Coulomb gauge and the current operator7 ccl; they were averaged over the experimental acceptance. The dotted line is a result of a plane wave calculation (RPWIA); the dashed curve shows the distorted wave calculation (RDWIA). The latter gives a smaller value of R but still overpredicts the data. Calculations with the cc2 operator give results similar in shape but slightly larger in R. The main difference in the results between this full calculation and the RPWIA is due to the enhancement of the negative energy components of the relativistic bound and scattered proton wave functions. This can be demonstrated by projecting the wave functions over positive-energy states (dash-dotted curve) resulting in essentially the same polarization transfer ratio as given by RPWIA. The RDWIA results are brought into excellent agreement with the data by substituting in the current operator the free nucleon form factor with a density dependent, medium modified form factor based on a quark-meson coupling model (QMC) as predicted by Lu et al.' (solid curve). I
1.1 9
B E
(r
Mainz 0 JLab €93-049, preliminary - - Udias RDWlA -Udias RDWlA (OMC) - . - Laget full + 2 Body
-
1.0 ........ +-+-- _---
.......
T T
\
B
I
A
0.9
(r
0.8 0
2
1
Q2 (GeV2/c2) Figure 2. Preliminary polarization transfer double ratios for 4He(Z,e ' d 3 H as a function of Q2. RPWIA calculations serve as baseline.
An overview over the experimental polarization double ratios, RExp,for all four settings of the JLab experiment is given in Fig. 2; Udias'RPWIA calculation serves as baseline, RRPW1*.Our result at Q2 = 0.5 (GeV/c)2 is con-
540
sistent with the findings of a similar Mainz experimenL8 In addition to some of the calculations mentioned before, results of a calculation by Lagetg including two-body currents are shown at low momentum transfer. All calculations are acceptance averaged (diamond symbols) for the experimental 4He and 'H settings and are linearly connected. Udias' calculations at 2.6 (GeV/c)2 use large energy extrapolations of the optical potentials. The full calculation by Udias, which includes the QMC predicted in-medium form factor modifications, is the only result consistent with the data. In summary, the polarization transfer double ratio measured in experiment 93-049 is on average significantly reduced as compared to RPWIA predictions. This reduction is partially explained in the framework of RDWIA by spinor distortions. Using free proton form factors, the present models are not able to account for our data even when various alternative choices for optical potential, current operator and bound state wave function are made. Incorporation of medium modified form factors results in substantially better agreement. These provocative results demand further experimental and theoretical investigation. Acknowledgments
This work was supported in part by the U.S. National Science Foundation and by US.Dept. of Energy contract DE-AC05-84ER40150 under which the Southeastern Universities Research Association (SURA) operates Jefferson Lab. Support was also provided by DOE research grant DE-FG02-95ER40901. References
1. D.H. Lu, K. Tsushima, A.W. Thomas, A.G. Williams and K. Saito, Phys. Lett. B417, 217 (1998) and Phys. Rev. C 60,068201 (1999). 2. M.R. Frank, B.K. Jennings, G.A. Miller, Phys. Rev. C 54, 920 (1996). 3. A.I. Akhiezer, M.P. Rekalo, Sov. J . Part. Nucl. 4, 277 (1974); R. Arnold, C. Carlson, F. Gross, Phys. Rev. C 23, 363 (1981). 4. T.D. Cohen, J.W. Van Orden and A. Picklesimer, Phys. Rev. Lett. 59, 1267 (1987). 5. Jefferson Lab Experiment 93-049, R. Ent and P. Ulmer, spokespersons. 6. J.M. Udias e t al., Phys. Rev. Lett. 83, 5451 (1991); J.A. Caballero et al., Nucl. Phys. A632, 323 (1998). 7. T. de Forest, Jr., Nucl. Phys. A392, 232 (1983). 8. S. Dieterich et al., Phys. Lett. B500, 47 (2001). 9. J.M. Laget, Nucl. Phys. A579, 333 (1994).
sii(1535) RESONANCE IN NUCLEI STUDIED WITH THE C(y,r ] ) REACTION H. YAMAZAKI, T. KINOSHITA, K. KINO, T. NAKABAYASHI, T. KATSUYAMA, A. KATOH, T. TERASAWA, H. SHIMIZU, J. KASAGI Laboratory of Nuclear Science, Tohoku University, Milcamine, Taihah-ku, Sendai 982-0826, JAPAN T. TAKAHASHI, H. KANDA, K. MAEDA Department of Physics, Tohoku University, Sendai 980-8578, JAPAN Y. TAJIMA, H. Y. YOSHIDA, T. NOMA, Y . ARUGA, A. IIJIMA, Y. ITO, T. FUJINOYA Department of Physics, Yamagata University, Yamagata 990-8560, JAPAN T. YORITA, K. HIROTA Japan Synchrotron Radiation Research Institute, Hyogo 679-5198, JAPAN 0. KONNO Ichinoseki National College of Technology, Iwate 021-8511, JAPAN The total cross sections of the (7, a) reaction on C have been measured for photon energies between 620 and 1100 MeV at Tohoku University, in order t o study the property of the S11(1535) resonance in the nuclear medium. Model calculations based on the quantum molecular dynamics (QMD) have been performed. The comparison between the calculation and the experimental data suggests that the resonance property of S ii(1535) might be changed in nuclear interior.
1
Introduction
The S11(1535) resonance is one of the strongest candidates of the negative parity nucleon. Recent theoretical studies predict that the mass and the coupling of the positive and negative nucleons will change in the nuclear medium under the framework of the chiral symmetry 1,293.The study of the property of positive and negative parity nucleons in nuclear medium makes it possible to obtain new information about the chiral structure of nucleons. The s11(1535) resonance strongly couples with Nr] and decays to the Nr] channel with the branching ratio of 45 55 %. Because of this unique property, one can excite only the S11 resonance by using (y, r ] ) reactions with GeV tagged photons. Thus we have measured the total (7,r ] ) cross sections on C at KEKTanashi using 1.3 GeV electron synchrotron to investigate the property of
-
541
542 the s11(1535) resonance in nuclei 4,5. The conclusion of our experiment was that the (y, 7 ) reaction cross section can be basically explained by the known effects. But there was some discrepancy around cross section maximum between the experimental data and the calculation. This discrepancy suggested that the resonance width of S11 might be changed in the nuclear medium; more than 60 MeV increased. Thus, more detailed studies were performed at Laboratory of Nuclear Science (LNS), Tohoku University, Sendai.
2
Experiment
The experiment was carried out using a tagged photon beam line extracted tangentially from the 1.2 GeV electron synchrotron called STretcher-Boosterring (STB) at Laboratory of Nuclear Science, Tohoku University. Quasimonochromatic photons were produced from the photon tagging system, which consists of the internal radiator made of a 11 pm carbon fiber and the tagging hodoscope installed in a bending magnet of STB. The energy of the photon was determined by the momentum measurement of the recoil electron. Tagging detectors are made of the plastic scintillators; 50 main counters and 12 backup counters. Energy ranges of the tagged photon beams are from 0.8 to 1.1 GeV and from 0.63 to 0.85 GeV for the electron energies of 1.2 and 0.93 GeV, respectively. The typical photon intensity was about 3 x lo6 tagged photons par one second. The tagging efficiency was over 90 %. The tagged photon beam bombarded the carbon target and produced meson. Two decaying photons from the 17 mesons were detected by the photon detector called SCISSORS (Sendai CsI Scintillator System On Radiation Search), which consists of 6 sets of pure CsI calorimeters with thin plastic scintillators for charged particle veto. They cover about 1.4 sr. of solid angle. The energy resolution is about 2.5 % at 1 GeV incident photon energy and the position resolution is about 3 cm. The invariant mass spectra were calculated for the bins of 24 MeV, 10 degree and 100 MeV/c, respectively, for the incident photon energy, angle and momentum of q mesons. The invariant mass resolution is about 24 MeV/c2. The yield of the r] mesons in each spectrum was deduced subtracting the background as the exponential function. Detection efficiencies were calculated by the simulation in which the quasi free production process was assumed. The double differential cross sections were deduced from the yields of 77 mesons and the detection efficiencies. The total cross section of 7 photoproduction on carbon was deduced by integrating the double differential cross sections with the emission angle and the momentum.
543
m
LNS tohoku (present result)
- r,
____
= 150 MeV rR=230MeV
coupling constant x 1.25
20
goo
I
Y
600
700
,
800
,
,
,
,
,
900
,
,
,
,
,
1000
,
,
,
1 10
Figure 1. Total cross sections of ( 7 , ~reactions ) on C (closed circles) with the QMD calculations (thin dotted line) for the resonance width of 230 MeV, calculation on C for the width of 150 MeV (solid line) and multiplied by 1.25 (thick dotted line). Triangles and squares show the results on C measured in Mainz and KEK(Tanashi), respectively.
3
Results and discussion
In Figure 1,the total q photoproduction cross sections are shown as a function of incident photon energy. Closed circles show the present results of the (y,q ) reaction cross section on C. Closed triangles and closed squares correspond to the total cross section of the (y,q) reaction on C measured in Mainz and KEK(Tanashi) respectively. It should be noticed that present cross sections have a similar dependence on the incident photon energy to the previous data and better statistics above 800 MeV. The cross section shows the maximum value at around 900 MeV and the width of the resonance structure is about 300 MeV. We have performed the calculation based on the Quantum Molecular Dynamics(QMD) to take into account the known nuclear medium effect; Fermi motion, Pauli blocking, q absorption and collision broadening of the N*. QMD was originally developed to describe the high energy heavy ion reactions 7. Details of the photoreaction in QMD calculation are described in roforonro 4
Tho
rocnnanro naramotorc cot y r r i t h n r r t
+Lo rncnnnnrn m n r l i f i r n t ; r \ n
544
are 1540 MeV, 150 MeV and 0.55 for the resonance energy, the width at the resonance pole and the branching ratio of the r]-N channel, respectively. These values were determined so as to reproduce the H(y, r ] ) cross section in references The r] absorption cross section, which was incorporated in the calculation, was deduced from the detailed balance analysis of the r - p 4 qn cross section. The collision broadening of the s11(1535) in a nucleus have been also considered; the cross section given in ref. l 1 is used. The results of the QMD calculation is plotted in Figure 1 as a solid line. As can be seen in Figure 1, solid line failed to reproduce the measured cross section on C above 800 MeV of incident photon energy. Although the QMD calculation dose not include the coherent eta production on nuclei, the contribution from the coherent eta production on carbon can be neglected because this process requires the iso-scalar component of the reaction amplitude. The measurement of the momentum distribution of the D(y, r ] ) reaction strongly indicates that the S1l photoexcitation is dominated by the iso-vector amplitude 12. In order to reproduce the experiment, 230 MeV of the resonance width is needed. The thin dotted line in Figure 1 indicates the result with 230 MeV. The thick dotted line corresponds to the values of the solid line multiplied by 1.25. These two dotted lines cannot be distinguished each other. Increasing helicity amplitude by 12 % or S11 -+ Nv branching ratio by 25 % might cause this 25 % enhancement of the cross section. In conclusion, some properties of the ,311 (1535) resonance might be changed in nuclear medium; the width, the helicity amplitude or decay branch. 879,10.
References 1. DeTar and T. Kunihiro, Phys. Rev. D 39,2805 (1989). 2. Hungchong Kim et al., Nucl. Phys. A 640,77 (1998) 3. D. Jido et al., Nucl. Phys. A 671,471 (2000). 4. T. Yorita et al., Phys. Lett. B 476,226 (2000). 5. H. Yamazaki et al., Nucl. Phys. A 670,202 (2000). 6. M. Robig-Landau et al., Phys. Lett. B 373,45 (1996). 7. K. Niita et al., Phys. Rev. C 52,2620 (1995). 8. B. Krusche et al., Phys. Rev. Lett. 74,3736 (1995). 9. B.H. Schoch, Prog. Part. Nucl. Phys. 34,43 (1995). 10. S. Homma et al., J. Phys. SOC.Jpn. 57,828 (1988). 11. M. Effenberger et al., Nucl. Phys. A 613,353 (1997). 12. B. Krusche et al., Phys. Lett. B 358,40 (1995).
DOUBLE-PION PRODUCTION IN ?+A REACTIONS J.G. MESSCHENDORP, FOR THE TAPS AND A2 COLLABORATIONS 11 Physikalisches Institut, 0-35392 Giessen, Germany, E-mail:
[email protected]
+
Preliminary differential cross sections of the reactions A(y, T O T O ) and A(y, 7 r 0 d nor-) with A='H,12C, and natPb are presented. A significant nuclear-mass dependence of the 7rn invariant-mass distribution is found in the nono channel. The dependence is not observed in the non* channel. It is consistent with an in~ in the I=J=O channel, changing width medium modification of the 7 r interaction and pole position of a TT resonant state.
1
Introduction
One of the challenges in nuclear physics is to study the properties of hadrons embedded in a nuclear many-body system. This contribution reports on the photoproduction of correlated pion pairs on nuclei in the scalar-isoscalar J=I=O channel, also known as the u meson. In Ref. the meson is identified as the fo(400-1200). The large natural width in free space of F=400-500 MeV makes it doubtful that this particle is a mesonic qij state. Alternatively, the u meson can be considered to be a resonant state of two pions In vacuum, the m r system is mildly attractive. However, in the nuclear medium the T W interaction strength could increase, thereby changing width and pole position of the resonant state. Experimental data on correlated m r pairs in dense nuclear matter can clarify the nature of the u meson. The first measurement of the in-medium mr mass was obtained by a pioninduced experiment by the CHAOS collaboration '. A rising accumulation of strength at low T+T- mass was observed with increasing nuclear mass whereas such an enhancement was not seen in the r+r+-rnass distributions. This effect was interpreted as a signature for an in-medium modification of the mr interaction in the I=J=O channel. A similar effect was found by a pioninduced experiment of the Crystal Ball collaboration where a nuclear-mass dependence of the ro7ro-mass distribution was observed. For the interpretation of the pion-induced measurements the strong interaction of the initial-state pion with the medium has to be taken into account. As a result, only the surface of the nucleus is probed, leading to a small effective nuclear density. It was therefore proposed to produce in-medium m r pairs with electromagnetic probes, which illuminate the complete nucleus, and lead to a larger effective density. 374.
545
546
In this contribution, measurements of A(y, 7ro7ro) and A(y, T O T * ) for A=lH, 12C, and natPb are presented. These measurements allow to study the different mr-isospin states at average effective densities of 35% (12C) to 65% ("'Pb) of the interior nuclear density of 0.17 fm-3. Data are presented for an incident-photon energy of E7=400-460 MeV. The energy was chosen to be small to minimize the effect of final-state interactions of the two pions with the medium and to prevent background from the q + 37r0 channel. 2
Experiment and Analysis
The experiment was performed at the photon-beam facility at MAMI-B. Tagged photons were produced with energies between 200 and 820 MeV. The beam intensity in the energy range of interest, E7=400-460 MeV, was lo7 s-l with a photon-energy resolution of about 2 MeV. A series of measurements were carried out using liquid-hydrogen, carbon, and lead targets. The angles and energies of the pions were measured using the TAPS photon spectrometer consisting of 510 hexagonal BaF2 scintillators. The complete setup covered ~ 4 0 % of the total solid angle. Photons and charged pions were identified by exploiting the time-of-flight information of each detector. A 5 mm thick plastic scintillator was placed in front of each crystal to differentiate between neutral and charged particles. Neutral pions were identified by an invariant-mass analysis of the two decay photons. For the identification of the A(?, T O T O ) reaction, all four finalstate photons were registered in the detector. Charged pions from A(?, T O & ) were selected by exploiting the information on the time-of-flight of the charged pion relative to the one of the photons of the decay and its deposited energy in the BaF2 crystals lo. Since the TAPS detector does not include a magnetic field, positively charged particles can not be discriminated from negatively charged particles.
3
Results and Discussion
The measured M,o,o-mass distributions for incident-photon energies of E,=400-460 MeV are shown in the left panel of Fig. 1. A strong increase in strength towards small M,o,o with increasing A is observed. The dotted curves in Fig. 1 indicate phase-space distributions. The experimentally observed peak position for A=lH (a) lies higher than the phase-space prediction whereas for A=12C (b) the measured mass distribution is compatible with phase space. For A=natPb (c), most of the observed strength lies below the peak of the phase-space distribution. The experimentally determined angular
547
M,IMeVI
M,IMeVl
Figure 1. Preliminary differential cross sections of the reaction A(y, noro)(left panel) and A(y, nor+-) (right panel) for incident photons in the energy range of 400-460 MeV (solid circles). Error bars denote statistical uncertainties and the curves are explained in the text.
distributions in the A(?, 7 r 0 7 r o ) reaction of the 7r07ro center-of-mass system are found to be isotropic lo and are compatible with J=O, supporting the conclusion that a significant A dependence is found in the 7r7r I= J=O channel in photon-induced reactions. The right panel of Fig. 1 depicts the preliminary results of the reactions A(?, T O T * ) . The data do not show an A dependence in shape as was observed in the corresponding distributions. For all targets, the data follow the phase-space distributions depicted as dotted curves, indicating that significant in-medium effects in the isospin 1=1channel are not observed. Furthermore, this observation indicates that the in-medium modification in the 7r07ro channel cannot be explained by final-state interactions of the individual pions with the medium. The solid curves in Fig. 1 are predictions by Roca et al. 4,7. Here, the meson-meson interaction in the scalar-isoscalar channel is studied in the framework of a chiral-unitary approach at finite baryonic density. The model dynamically generates the (T resonance, reproducing the meson-meson phase shifts in vacuum and accounts for the absorption of the pions in the nucleus. It qualitatively predicts a mass shift as observed in the 7ro7ro data. The basic IMnoT0
548
ingredient driving this shift is the p-wave interaction of the pion with the baryons in the medium, resulting in an in-medium modification of the 7r7r interaction. Since the u resonance does not couple to nor*, the model shows no significant change in the shape of the mass distributions between A=12C and A=natPb, which agrees with the experimental observation as shown in the right panel of Fig. 1.
4
Conclusion
An effect consistent with a significant in-medium modification in the A(?, T O T ’ ) (I= J=O) channel has been observed. With increasing A , the strength in the mr-mass distributions is shifting towards smaller invariant masses. The distortion of these distributions due to final-state interactions of the individual pions with the constituents of the nucleus has been studied by measuring the T O T * mass distribution concurrently. A significant in-medium effect was not observed. According to Roca et al. 4 , a dominant part of the modification observed in the 7r07ro-mass distributions can be attributed to a change of the m r interaction. The comparison with the experimental data hints at the nature of the u meson as a ITIT resonance.
Acknowledgments The author acknowledges E. Oset, M.J. Vicente Vacas, and L. Roca for making their calculations available to us prior to publication. The presented data are part of the dissertations of S. Janssen and M.J. Kotulla.
References 1. D.E. Groom et al., Eur. Phys. J. C15, 1 (2000). 2. J.A. Oller et al., Phys. Rev. Lett. 80, 3452 (1998). 3. E. Oset et al., nucl-th/0112033, 2001. 4. L. Roca et al., Phys. Lett. B541, 77 (2002). 5. F. Bonutti et al., Phys. Rev. Lett. 77,603 (1996). 6. A. Starostin et al., Phys. Rev. Lett. 85, 5539 (2000). 7. L. Roca, E. Oset, and M.J. Vicente Vacas, private communications. 8. I. Anthony et al., Nucl. Inst. Meth. A301, 230 (1991). 9. A.R. Gabler et al., Nucl. Instr. and Meth. A346, 168 (1994). 10. S. Janssen, dissertation University of Giefien (2002).
549
Jssam Qattam, John Arrington, and Frank Dohrmann
~
Bertrand Desplanques and Sid Coon
QUARK-HADRON DUALITY IN INCLUSIVE ELECTRON-NUCLEUS SCATTERING
'
J. ARRINGTON', J. CROWDER', R. ENT3, C. KEPPEL334,I. NICULESCU3 Argonne National Laboratory, Argonne, ZL, USA; Juniata College, Huntington, PA, USA; Jefferson Lab, Newport News, VA, USA; Hampton University, Hampton, VA, USA Recent inclusive electron-nucleus scattering data have been utilized for precision tests of quark-hadron duality. The data are in the resonance and quasielastic regions and cover a range in Q2 from 0.5 to 7 (GeV/c)2. The Q2 dependence of the moments of the Fz structure function were investigated and indicate that duality holds for nuclei, even at low Q2.
Inclusive electron scattering is a firmly-established tool for investigation of the quark distributions in a nucleon or nucleus. At large enough values of invariant mass, W and four-momentum transfer, Q 2 , the logarithmic Q2 dependence of the nucleon structure function FJ can be rigorously described in the framework of Quantum Chromodynamics (QCD). At lower momentum transfer however, the data can no longer be described in terms of single parton densities with simple logarithmic Q2 dependence. Inverse power violations in Q 2 ,representing initial and final state interactions between the struck quark and the spectator quarks (higher twist effects), become important. While a smooth scaling curve is not observed for the proton structure functions in the resonance region, it was observed that the F2 structure function in the resonance and the DIS regions can still be related l . Bloom and Gilman showed that, when the structure function was taken as a function of w' = 1 W 2 / Q 2and averaged over the resonance region, the result was identical to the DIS structure function averaged over the same region in w'. Recent data taken at Jefferson Lab dramatically verified this scaling in the resonance-averaged structure function. These data were analyzed in terms of the Nachtmann variable [ = 2z/[1+ 4m2z2/Q2],which has been shown to be the correct variable for studies of scaling violations 3. The new data show that the scaling-like behavior extends beyond the DIS and well into the resonance region, all the way down to Q2 x 0.5 (GeV/c)2. Experiments at SLAC and Jefferson Lab measured inclusive electronnucleus scattering cross section in the resonance and quasielastic (z > 1) regions. The structure function in nuclei is averaged by the Fermi-motion of the nucleons and the resonant structure is no longer visible. Figure 1 shows the structure function per nucleon for deuterium as a function of Q2 at several
+
dl +
550
551 8;
i
'
"
'
I
'
'
~
'
I
"
'
'
I
'
"
I
"
'
'
(:::O.tiO
lo-'
Figure 1. Structure function vs. Q2 for deuterium at fixed values of (. Dashed lines are dlnF2/dlnQ2 fit to higher Q2 data. Solid lines denote fixed W 2 . Errors are statistical only.
values of 5. Even though the Fermi momentum is small in deuterium, the data in the resonance region do not show significant deviations from scaling (dashed lines) even down to W 2 = 2.0 GeV2. At extremely low Q2, the structure function deviates from the scaling curve only as we approach the quasielastic peak. It appears that, in nuclei, the Fermi motion serves to kinematically average over the resonances, creating a smooth duality-type scaling curve in the resonance region. An analysis of the resonance region in terms of QCD was first presented in ref. ', where Bloom and Gilman's approach was reinterpreted, and the integrals of the average scaling curves were equated to the n = 2 QCD moments of I;>. These moments can be expanded, according to the operator product expansion (OPE), in powers of l/Q2, and the fall of the resonances along a smooth scaling curve with incresing Q2 was explained in terms of this QCD twist expansion. Duality is expected to hold so long as the higher twist effects (terms in (1/Q2)" in the OPE expansion) are small. In the present analysis, the Cornwal-Norton moments for nuclear structure function were calculated: M Z N ( Q 2 )= dx F:(x,Q2) x n - 2 . The structure function data used were obtained in experiments at SLAC l 1 p 4 , CERN ', Fermilab lo and JLab 5 . The quasielastic and elastic contributions, important for low Q 2 , were added to the moments. The moments for iron can be constructed (assuming that nuclear effects axe small) by adding the proton and neutron contributions, extracted from
s,"
552
0
1
3
2
Q2
4
5
6
7
(GeV/c)’
Figure 2. The second moment of F2 for proton (stars), deuteron (full circles), iron (squares), and neutron (empty circles), The neutron data are obtained as the difference between the deuterium and proton moments. The solid lines are obtained by fitting the data for proton and deuteron, and using the procedure described in the text for iron.
+
proton and deuteron data: M ( F e ) = 2 x M ( p ) ( A - 2 ) x M ( n ) , where M ( n ) is taken to be M ( d ) - M ( p ) and is shown in Fig. 2 (empty circles). The differences between the moments calculated this way, and those actually measured on iron, and measured moments are smaller than 5% for Q2 above 2 (GeV/c)2, and between 5 and 10% for Q2 between 0.1 and 2 (GeV/c)2. We next examine the nuclear dependence of the EMC effect in the resonance region, and compare this to precise measurements made in the DIS regime. For this analysis, we take the cross section ratio of iron to deuterium in the resonance region for Q2 4 (GeV/c)2, requiring W 2 > 1.3 GeV2 to exclude the region very close to the quasielastic peak where the scaling violations become significant. Figure 3 shows this ratio for the SLAC measurement and for the JLab resonance region data. The resonance region measurement is consistent with the DIS measurements and is more precise in the high-z region. In conclusion, we utilized inclusive electron-nucleus scattering data for precision tests of quark-hadron duality. Duality is observed to hold for nuclei even in the low Q2 regime of Q2 FZ 0.5 (GeV/c)2, well below the DIS limit. Structure functions extracted in the resonance region appear consistent with the DIS results. In the QCD moment explanation this indicates that higher twist contributions are small or cancelling. Further, the EMC effect on the structure function in the nuclear environment is observed to hold in the resonance region. This work was supported in part by the U S . Department of Energy under Grants No. DEFG02-95ER40901 and W-31-109-ENG-38, and the National Science Foundation under Grants No. HRD-9633750 and MPS-9600208.
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553
Figure 3. Ratio of nuclear to deuterium cross section. The diamonds are the Jefferson lab data for iron (resonance region). The circles are data for iron from SLAC (DIS region).
References
1. E. Bloom and F. Gilman, Phys. Rev. D4, 2901 (1971). 2. I. Niculescu et al, Phys. Rev. Lett. 85, 1186 (2000); I. Niculescu et aZ, Phys. Rev. Lett. 85, 1182 (2000). 3. H. Georgi and H. D. Politzer, Phys. Rev. D14, 1829 (1976). 4. B. W. Filippone et al, Phys. RRv. C45, 1582 (1992). 5. J. Arrington et al, Phys. Rev. C64, 014602 (2001); J. Arrington et aZ, Phys. Rev. Lett. 82, 2056 (1999). 6. J. Gomez et al, Phys. Rev. D49, 4348 (1994). 7. M. Arneodo et aZ, Phys. Lett. B364:107, (1995). 8. A. DeRujula, H. Georgi and H. D. Politzer, Ann. Phys. 103,315 (1977). 9. J. J. Aubert et al, Nucl. Phys. B272, 158, (1986); Berge et al, Zeit. Phys. C49, 187, (1991). 10. Oltman. Nevis Report 270, (1989); Adams et aZ, Phys. Rev. D54, 3006, (1996). 11. S. Dasu et al, Phys. Rev. D49, 5641, (1994).
NEUTRON STRUCTURE FUNCTION AND INCLUSIVE D I S FROM 3 H AND 3 H E TARGETS AT LARGE BJORKEN-X M.M. SARGSIAN Depnrtment of Physics, Florida International University, Miami FL 33199, USA
S. SIMULA I N F N , Sezione R o m a III, V i a della Vasca Navale 84, I-00146 Roma, Italy
M.I. STRIKMAN Department of Physics, Pennsylvania State University, University Park PA 16802, USA A detailed study of inclusive deep inelastic scattering from mirror A = 3 nuclei at large values of x ~ j is ~presented. ~ k The ~ ~main purpose is to estimate the theoretical uncertainties on the extraction of FT from such measurements. Within the convolution approach we confirm the cancellation of nuclear effects at the level of = 1%for x <, 0.75 in overall agreement with previous findings. However, within models in which modifications of the bound nucleon structure functions are accounted for to describe the E M C effect in nuclei, we find that the nuclear effects may be canceled at a level of % 3% only, leading to an accuracy of zz 12% in the extraction of FF/F: at x z 0.7 + 0.8. Another consequence of bound nucleon modifications is that the iteration procedure does not improve the accuracy of the extraction of F F / F l .
1
Introduction
The investigation of deep inelastic scattering ( D I S )of leptons off the nucleon is an important tool t o get fundamental information on the structure of quark distributions in the nucleon. At large values of the Bjorken variable z the ratio dlu, or equivalently the ratio FFIF;, is known t o have a high degree of theoretical significance However, our present knowledge of the large-z n / p ratio is quite poor, mainly because its extraction from inclusive deuteron D I S data is inherently model dependent. This fact has led to the suggestion of new strategies. One of them is to try to exploit the mirror symmetry of A = 3 nuclei; in other words, thanks to nuclear charge symmetry, one expects that the magnitude of the E M C effect
’.
554
555
is very similar in 3 H e and 3 H and hence the so called super-ratio
should be very close t o unity regardless of the size of the E M C ratiFs 2 , 3 . In this case the n / p ratio could be extracted directly from the ratio F2 He/F;H without significant nuclear modifications. However we observe that, even if nuclear charge symmetry were exact, the motion of protons and neutrons in a non isosinglet nucleus (say 3 H e ) is somewhat different due to the spin-flavor dependence of the nuclear force. We have therefore performed a detailed study of inclusive D I S from mirror A = 3 nuclei at large x with the aim of estimating the theoretical uncertainties on the extraction of the n / p ratio from such measurements. To this end we have considered a variety of E M C models both with and without modifications of the nucleon structure function in the medium. 2
E M C models with no modification of bound nucleon
We have explored in greater details the E M C model used in 2 , 3 , which is based on the Virtual Nucleon Convolution ( V N C ) approach with no modification of the nucleon structure function in the medium. We have analyzed the effects of i) charge symmetry breaking terms in the nucleon-nucleon ( N N ) interaction; ii) finite Q2 effects in the impulse approximation; iii) the role of different prescriptions for the nucleon Spectral Function normalization providing baryon number conservation; and iv) the role of different parton distribution function sets. Additionally we have also compared the predictions of the V N C model with the ones obtained within the light-cone ( L C ) formalism. Within the V N C model, in which no modification of the bound nucleon is considered] the deviation of the super-ratio (2) from unity is found to stay within 1% only for x <, 0.75 in agreement with in which the effects of (i)-(iv) have not been considered. 213
3
E M C models with FF modifications in the medium
However the above estimations are not complete, since V N C and LC models are just two of the many models of the E M C effect and, moreover, they underestimate significantly the E M C data at large x for a variety of nuclei. In particular] the convolution approach is not able t o reproduce the minimum of the E M C ratio around x M 0.7 as well as the subsequent sharp rise at
556
larger x (see 4). Thus in order to draw final conclusions about the size of the deviation of the super-ratio S R E M Cfrom unity one should investigate effects beyond those predicted by the convolution approach. Furthermore, it is very important to asses any isospin dependence of the E M C effect in order to extract F; from 3 H e and 3 H data in a reliable way. An isospin dependence of the E M C effect is naturally expected from the differences in the relative motion of p n and nn (pp)pairs in 3 H ( 3 H e ) . Since the interaction of a p n pair is more attractive than the one of a nn pair, the overlapping probability to find a N N pair with T N N 5 1 f m, may be 40% larger for a p n pair than for a nn pair (see ’). This is a very important isospin effect in mirror A = 3 nuclei, which can lead to deviations of the super-ratio (2) from unity depending on the size of the E M C effect itself. It is worth noting that the nuclear charge symmetry will not limit such deviations. Hence we have carried out a detailed analysis of the super-ratio within a broad range of models of the E M C effect, which take into account possible modifications of the bound nucleons in nuclei, like: i) a change in the quark confinement size (including swelling); ii) the possible presence of clusters of six quarks; and iii) the suppression of point-like configurations due to color screening. Our main result is that one cannot exclude the possibility that the cancellation of the nuclear effects in the super-ratio may occur only at a level of M 3%, resulting in a significant uncertainty (up to M 12% for x M 0.7 t 0.8) in the extraction of the free n / p ratio from the ratio of the measurements of the 3He and 3 H D I S structure functions (see Fig. 1). In it was suggested that, once the ratio F i H e / F ; H is measured, one can employ an iterative procedure to extract the n l p ratio which can almost eliminate the effects of the dependence of the super-ratio SREMCon the largex behavior of the specific structure function input. Namely, after extracting the n l p ratio assuming a particular calculation of S R E M Cone , can use the extracted F; to get a new estimate of S R E M Cwhich , can then be employed for a further extraction of the n l p ratio. Such a procedure can be iterated until convergence is achieved and self-consistent solutions for the extracted F;/Fi and the super-ratio SREMCare obtained. In a good convergence was achieved for x up to = 0.8. However this result depends on the assumed validity of the convolution approach at large x. Within the E M C models considered above we have found that: i) the consistency between the n l p ratio used as an input and the extracted one is not guaranteed; ii) the iteration diverges already at values of x (= 0.7) smaller than the ones obtained in 3; moreover, below x N 0.7 the iteration procedure converges to a value of the n l p ratio which differs from the input one exactly by the amount of the E M C effect implemented in the calculation of F:He/F;H.
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Figure 1. The expected accuracy for the extraction of F T / F i vs. x at Q2 = 10 (GeV/c)’. The lower and upper shaded areas correspond to the CTEQ and modified CTEQ parameterizations as described in 4 . Full dots are N M C data
Thus we conclude that in spite of the presented limitations the measurements with mirror A = 3 nuclei will significantly improve our knowledge of the n / p ratio at large z. However, it will be very important to complement them with the measurements of semi-inclusive processes off the deuteron, in which the momentum of the struck nucleon is tagged by detecting the recoiling one. Imposing the kinematical conditions that the detected momentum is low ( 5150 MeV/c), which means that the nucleons in the deuteron are initially far apart it is possible t o minimize significantly the nuclear effects. Furthermore, all the unwanted nuclear effects can be isolated by using the same reaction for the extraction of the proton structure function by detecting slow recoiling neutrons and comparing the results with existing hydrogen data, as well as by performing tighter cuts on the momentum of the spectator proton and then extrapolating t o the neutron pole. 6y7,
References 1. N. Isgur, Phys. Rev. D 59,034013 (1999) and references therein quoted. 2. I.R. Afnan et al., Phys. Lett. B 493,36 (2000). 3. E. Pace et al., Phys. Rev. C 64,055203 (2001). 4. M.M. Sargsian et al.: Phys. Rev. C 66,024001 (2002). 5. S.C. Pieper et al., Annu. Rev. Nucl. Part. Sci. 51,53 (2001). 6. S. Simula, Phys. Lett. B 387,245 (1996); Nucl. Phys. A 631,602c (1997); e-print nucl-th/9608053. 7. W. Melnitchouk et al., 2. Phys. A 359, 99 (1997); e-print nuclth/9609048. 8. M. Arneodo et al., Phys. Rev. D 50,R1 (1994).
HADRON FORMATION IN NUCLEI IN DEEP-INELASTIC LEPTON SCATTERING E. GARUTTI (FOR THE HERMES COLLABORATION) Nationaal Instituut voor Kernfysica en Hoge-Energiefysica (NIKHEF), P.O. Box 41882, 1009 D B Amsterdam, The Netherlands E-mail:
[email protected] The influence of the nuclear medium on the production of charged hadrons in semi-inclusive deep inelastic scattering (DIS) has been studied by the HERMES experiment at DESY with a 27.5 GeV positron beam. A large reduction of the differential multiplicity of charged hadrons and identified charged pions from krypton relative to that from deuterium is observed. The reduction is larger than that seen in previously published HERMES data on nitrogen. The data are compared to two theoretical models. Both describe well the reduction of the multiplicity ratio at low values of the virtual photon energy v and at high values of the fractional energy transfer z to the hadron. The A dependence of the data is also addressed.
1
Introduction
Hadronization (or fragmentation) is the process by which final-state hadrons are formed from the struck quark in a hard scattering event. When embedded in a nuclear medium, the hadronization process is influenced by quark energy loss through multiple scattering and gluon radiation as the quark propagates through the medium. Though interesting in their own right, these processes need to be understood for the accurate interpretation of ultra-relativistic heavy ion collisions: a modification of hadronic spectra is one of the expected signatures of the transition from cold nuclear matter to the deconfined quarkgluon plasma Semi-inclusive deep inelastic lepton-nucleus scattering provides a clean tool for the study of such quark propagation effects. 2
Experimental results
The HERMES experiment has measured the multiplicity ratio R L of hadrons of type h produced per DIS event on a nuclear target of mass A relative to that from a deuterium target (D):
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'.
Here z = Eh/u is the fraction of the virtual photon energy Y transfered to the hadron. The quantities N,(v)and Nh(z,Y ) are the number of inclusive DIS leptons and of semi-inclusive hadrons of type h recorded in each kinematic bin. The 27.5 GeV HERA positron beam was used in conjunction with D, 14N and 84Kr gas targets with densities of up to 10%ucl/cm2. Both the scattered beam positron and one or more final-state hadrons were observed in the HERMES spectrometer'. The HERMES data for the charged-hadron multiplicity ratio Rk are shown in Fig. 1as a function of Y and z , for Y > 7 GeV. The data are compared with the model of Ref. 2 , where modified fragmentation functions and their evolution were calculated in the framework of multiple parton scattering and induced gluon radiation. The kinematic behavior of the data is reproduced quite well by the model. Also, the observed attenuation of fast hadrons is considerably stronger for 84Krthan for 14N, and roughly agrees with the A2/3 dependence predicted by the model. In the context of this same model, the average parton energy loss in the nuclear medium was evaluated from the 84Kr data 3 . The obtained value of dE/dx M 0.3 GeV/fm for the krypton target is in surprising agreement with dE/dx M 0.25 GeV/fm extracted from recent PHENIX data on Au-Au collisions. However, when corrections are made for the rapid expansion of the dense medium in the heavy ion case, a result of dE/dx x 12 GeV/fm is obtained. This value is 40 times larger than that from the DIS data, and suggests that the gluon density in the PHENIX Au-Au collisions is 40 times higher than in cold nuclear matter. Fig. 2 shows the multiplicity ratio for pions alone. The pions were identified in the momentum range from 4 to 15 GeV using the new HERMES RICH detector for the 84Kr data and a threshold Cerenkov detector for the
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‘.
older I4N data. The data are compared to the gluon bremsstrahlung model of Ref. 4 , which includes effects of hadronic rescattering after the pion is formed. Calculations in this model are only available for leading pions, and so the comparison is restricted to z > 0.5. Both the model calculation and the data agree well with a simple parametrization involving a single time scale 7h = ChV(1 - z ) for pion formation in the laboratory frame. Fits of this type to the model calculation and to the HERMES data produce values of ch = 1.35 fm/GeV and Ch = 1.37 f0.14 fm/GeV respectively. The HERMES data are presented in Fig. 3 as a function of p,”, the transverse momentum squared of the hadrons relative to the virtual photon direction. The nuclear enhancement at high pz is comparable to that seen in p A and AA collisions, where it is known as the Cronin effect. This enhancement is caused by multiple parton scattering in the nuclear medium. In the model of Ref. the observed change in behaviour at the predicted scale of pt 1 - 2 GeV corresponds to a transition from soft to hard rescattering processes. The data also show a pronounced dependence of the effect on nuclear size. The importance of the present result in e A scattering as compared to existing hadronic scattering data is that neither multiple scattering of the incident particle nor the interaction of its constituents complicate the interpretation. Such data can thus provide relatively clean information on quark transport in cold nuclear matter. The results presented so far involve the sum of positive and negative hadrons and pions. Fig. 4 shows the separated multiplicity ratios for the N
561
two charge states, as produced from the 84Kr target. The data for positive and negative pions are shown to agree, while a significant difference in the attenuation is observed for positive and negative hadrons. This observation is in qualitative agreement with that reported for the 14N target '. One possible interpretation is that the formation time for pions and protons is very different: Monte Car10 simulations indicate that the fraction of protons in the positive hadron sample is much larger that the fraction of antiprotons in the negative hadron sample. Alternatively, the data may indicate different modifications of the quark and antiquark fragmentation functions in nuclei To clarify this issue, separate multiplicity ratios for identified pions, kaons, and protons are needed. Such data axe presently under investigation at HERMES.
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0.85 0.8 0.75 0.65 0.6
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References
1. 2. 3. 4. 5. 6. 7. 8. 9.
K. Ackerstaff et al., HERMES coll. NIM A417 (1998) 230. X.F. Guo & X.N. Wang PRL 85 (2000) 3591. X.N. Wang, hep-ph/01111404. B.Kopeliovich et al., hep-ph/9511214. B .Kopeliovich, Private Comunications. K. Adocox et al., PHENIX coll., nucl-ex/0109003. E. Wang and X.N. Wang nucl-th/0104031. A. Airapetian et al., Eur. Phy. J. C, DO1 10.1007/s100520100697 (2001) X.F. Guo & X.N. Wang, hep-ph/0102230.
NUCLEAR TRANSPARENCY FROM QUASIELASTIC A(E,E’P) REACTIONS U P TO Q 2 = 8.1 (GEV/C)2. K. GARROW Department of Physics, Simon Fraser University, Burnaby, British Columbia V6T 2A3, Canada E-mail: [email protected]. de The quasielastic (e,e’p) reaction was studied on targets of deuterium, carbon, and iron up to a value of momentum transfer Q2 of 8.1 (GeV/c)2. A nuclear trans parency was determined by comparing the data to calculations in the Plane-Wave Impulse Approximation. The dependence of the nuclear transparency on Q2 and the mass number A was investigated in a search for the onset of the Color Transparency phenomenon. We find no evidence for the onset of Color Transparency within our range of Q2.
Under certain conditions it is possible to select hadrons which consist of their minimal Fock space components. Large four momentum transfer reactions are expected to select these point-like configurations. Mueller and Brodsky conjectured these small transverse size quark configurations would posses a small color dipole moment and thereby interact weakly with the nuclear medium leading to an increase of the nuclear transparency. This effect has become to be known as Color Tkansparency (CT). A similar phenomenon occurs in QED where an e+e- pair of small size has a small cross section determined by its electric dipole moment ’. In QCD, a qq or qqq system can act as an analogous small color dipole moment Originally the onset of nuclear transparency above that predicted by Glauber calculations, CT, was thought to indicate that one is approaching the asymptotic limit where perturbative QCD calculations become applicable. However it has been demonstrated that a large increase in the pion transparency in nuclei can result from using nonperturbative pion distribution amplitudes. Although the observation of CT can not unambiguously indicate that one is in the perturbative regime it’s observation is required as a necessary but not sufficient condition for the applicability of factorization ‘. Factorization theorems are intrinsically related to the access to Generalized Parton Distributions (GPD’s), introduced by Ji and Radyushkin 5,6. The transparency of the nuclear medium to high energy protons in quasielastic A(p,2p) measured at Brookhaven has shown a rise consistent with CT for Q2 N 3 - 8 (GeV/c)2, but decreases at higher momentum transfer. Two explanations for the surprising behavior were given: Ralston and Pire proposed that the interference between short and long distance amplitudes in the free p p cross section was responsible for these energy oscillations, where
562
563
the nuclear medium acts as a filter for the long distance amplitudes. Brodsky and De Teramond lo argued that the unexpected decrease could be related to the crossing of the open-charm threshold. For the case of the quasielastic A(e,e'p) reaction the cross section is given in the non-relativistic plane-wave impulse approximation (PWIA) as
where dEef,do,, ,dEpt and dRpt are the phase space factors of the electron and proton, K = l ~ p t l Eis p ~a known kinematical factor, and uepis the offshell electron-proton cross section. The spectral function S(Em,flm)is defined as the joint probability of finding a proton of momentum P;, and separation energy Em within the nucleus. The definition of the transparency ratio is the ratio of the cross section measured in a nuclear target to the cross section for (e,e'p) scattering in PWIA. Numerically this ratio can be written as
J" d3~mdEmYezp(Em,Pm) T ( Q 2 )= J" d 3 ~ m d E m Y ~ ~ ~ ~ ( E m 1 P m ) '
(2)
where the integral is over the phase space V defined by the cuts Em < 80 MeV and IP;l < 300 MeV/c, YeZp(Em,Pm) and Y ~ w I A ( E , , ~ ' ,are ) the corresponding experimental and simulation yields. The measured transparency T ( Q 2 )values from this (large solid symbols) and previous work are presented in Fig. 1. The errors shown include statistical and systematic uncertainties, but do not include model-dependent systematic uncertainties in the spectral functions and correlation corrections used in the simulations. This is the same as for the data of Ref. 11 (small solid symbols). Data from previous experiments (represented by open symbols) include the full uncertainty. The present results for carbon and iron are of similarly high precision as those of Ref. 11, and of substantially higher precision than of Refs. 12,13,14. Clearly the new data for deuterium, carbon and iron, for Q2 greater then M 2 (GeV/c)2, show no marked increase in the transparency ratio which could be interpreted as a signal for CT. Excellent constant-value fits can be obtained for the various transparency results above such Q 2 . For deuterium, carbon, and iron fit values are obtained of 0.904 (k 0.013), 0.570 (* 0.008), and 0.403 (4~O.OOS), with x2 per degree of freedom of 0.56, 1.29, and 1.17, respectively. Alternatively one can analyze the A-dependence of the transparency ratio. Figure 2 shows T as a function of A. The curves represent empirical fits of the form T = ,Aa(@), using the deuterium, carbon, and iron data. We find, 12913714
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Figure 1. 'Ikansparency for (e,e'p) quasielastic scattering from D (stars), C (squares), Fe (circles), and Au (triangles). Data from the present work are the large solid stars, squares, and circles, respectively. Previous JLab data (small solid squares, circles, and triangles) are from Ref. 11 . Previous SLAC data (large open symbols) are from Refs. 12,13. Previous Bates data (small open symbols) at the lowest Q2 on C, Ni, and Ta targets, respectively, are from Ref. 14. The errors shown include statistical and systematic ( z t 2.3%) uncertainties, but do not include model-dependent systematic uncertainties on the simulations. The solid curves shown from 0.2 < Q2 < 8.5 (GeV/c)2 are Glauber calculations from Ref. 15. In the case of D, the dashed curve is a Glauber calculation from Ref. 16.
within uncertainties, the constant c to be consistent with unity as expected and the constant CY to exhibit no Q 2 dependence up to Q2 = 8.1 (GeV/c)2. Clearly a discrepancy exist between the A(p,2p) and A(e,e'p) measurements. The proposed explanation of Ralston and Pire ', that the nuclear medium A eliminates the long distance amplitudes in the A(p,2p) case, might resolve the apparent discrepancy between the A(e,e'p) and A(p,2p) results. In light of the ambiguity in the existing proton data it is hoped that an upcoming pion transparency l7 measurement will help our understanding of the transparency of hadrons in nuclei.
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Atomic Number [A] Figure 2. Nuclear Transparency as a function of A at Q2 = 3.3, 6.1, and 8.1 (GeV/c)2 (top to bottom). The curves are fits to the D, C, and Fe data using T = cAa.
References 1. A.H.Mueller, in Proceedings of the Seventeenth Recontre de Moriond Conference on Elementary Particle Physics, Les Arcs, fiance, 1982, edited by 3. R a n Thanh Van (Editions F'rontieres, Gif-sur-Yvette, fiance,1982); S.J.Brodsky, in Proceedings of the Thirteenth International Symposium on Multiparticle Dynamics, Volendam, The Netherlands, 1982, edited by W. Kittel et al. (World Scientific, Singapore, 1983). 2. D. Perkins, Phil. Mag. 46, 1146 (1955). 3. B. Kundu, J. Samuelsson, P. Jain, and J.P. Ralston, Phys. Rev. D 62, 113009 (2000).
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4. M. Strikman, Nucl. Phys. A663&A664, 64c (2000). 5. X. Ji, Phys. Rev. Lett. 78,610 (1997); Phys. Rev. D 55, 7114 (1997). 6. A.V. Radyushkin, Phys. Lett. B380, 417 (1996); Phys. Rev. D 56, 5524 (199 7). 7. AS. Carroll e t al., Phys. Rev. Lett. 61,1698 (1988). 8. Y. Mardor e t al., Phys. Rev. Lett. 81,5085 (1998); 9. J.P. Ralston and B. Pire, Phys. Rev. Lett. 61,1823 (1988). 10. S.J. Brodsky and G.F. de Teramond, Phys. Rev. Lett. 60,1924 (1988). 11. D. Abbott et al., Phys. Rev. Lett. 80, 5072 (1998). 12. N.C.R. Makins et al., Phys. Rev. Lett. 72,1986 (1994). 13. T.G. O'Neill et al., Phys. Lett. 351,87 (1995). 14. G. Garino e t al., Phys. Rev. C 45,780 (1992). 15. H. Gao, V.R. Pandharipande, and S.C. Pieper (private communication); V.R. Pandharipande and S.C. Pieper, Phys. Rev. C 45,791 (1992). 16. L.L. Frankfurt, W.R. Greenberg, G.A. Miller, M.M. Sargsian, and M.I. Strikman, Z. Phys. A 352,97 (1995). 17. R. Ent and K. Garrow, spokepersons, Jefferson Lab experiment E01-107.
NUCLEON MOMENTUM DISTRIBUTIONS FROM A MODIFIED SCALING ANALYSIS OF INCLUSIVE ELECTRON-NUCLEUS SCATTERING J. ARRINGTON Argonne National Laboratory, Argonne, IL, USA Inclusive electron scattering from nuclei a t low momentum transfer (corresponding to 2 2 1) and moderate Q 2 is dominated by quasifree scattering from nucleons. In the impulse approximation, the cross section can be directly connected to the nucleon momentum distribution via the scaling function F(y). The breakdown of the y-scaling assumptions in certain kinematic regions have prevented extraction of nucleon momentum distributions from such a scaling analysis. With a slight modification to the y-scaling assumptions, it is found that scaling functions can be extracted which are consistent with the expectations for the nucleon momentum distributions.
Quasielastic (QE) electron scattering can provide important information about the distribution of nucleons in nuclei. With simple assumptions about the reaction mechanism, functions can be deduced that should scale (ie. become independent of momentum transfer), and which are directly related to the nucleon momentum distribution. The concept of y-scaling of the quasielastic response was first proposed' in 1975. It was shown that in the plane wave impulse approximation (PWIA) a scaling function, F ( y ) , could be extracted from the inclusive cross section which was related to the nucleon momentum distribution. In the simplest approximation, the scaling variable y is the initial momentum of the struck nucleon along the direction of the virtual photon. We determine y from energy conservation assuming a spectator model of the interaction and neglecting the transverse momentum of the struck nucleon: v +MA =
Jw+ Jm,
(1)
where M A is the mass of the target nucleus and MA-^ is the ground state mass of the A - 1 nucleus (assumed to be in an unexcited state). Measurements of inclusive electron-nucleus scattering from deuterium and heavy nuclei at x > 1 have been performed2 at JLab up to Q2 w 7 GeV2. At low Q2 values the scaling function depends strongly on Q2 due to final state interactions (FSIs). As these FSIs become small the extracted scaling function becomes nearly independent of Q2 and depends only on y, as predicted in the y-scaling picture. However, while the data show scaling in y, this by itself does not ensure that the scaling function is connected to the momentum
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Figure 1. Scaling function F(y) for deuterium from E89-008 for scattering angles between 15 and 55 degrees, after subtracting a model of the inelastic contributions (large for y > 0, generally negligible for y < 0). Errors shown are statistical only. The solid line represents the expected F ( y ) based on a calculation of the deuteron momentum distribution using the Av14 NN potential.
distribution. We present here an attempt to test the assumptions of the scaling analysis and the extraction of the nucleon momentum distributions. Figure 1 shows F(y) for deuterium, as extracted from the cross sections measured in E89-0082. As the momentum distribution is related to the derivative of F ( y ) , the lack of high precision data on deuterium at large IyI makes it difficult to directly extract the momentum distribution from this data. We can, however, compare the scaling function to what we expect based on a calculation of the deuteron momentum distribution. The solid line is a calculation of F ( y ) using a momentum distribution calculated from the Argonne-vl4 N-N potential. The normalization of the scaling function extracted from the data is consistent with unity (as it must be if it is related to the momentum distribution) and the distribution is in generally good agreement with the calculation. In particular, they are in very good agreement at very large values of the nucleon momentum, (y). This region is especially important because these high momentum components are generated by short range interactions of the nucleons. It has been suggested that final state interactions in this region, where the nucleons are close together, may not disappear as Q2 increases. If there were large final state interactions that were nearly independent of Q 2 ,
569
one might see scaling but the scaling function would not yield the proper momentum distribution in the tails. The data from deuterium indicate that such Q2-independent FSIs are small or absent, although higher precision data at high Q2 and large IyI would allow a much stronger limit to be set. While the y-scaling analysis of the deuterium data appears to yield the correct deuteron momentum distribution, this is not the case for the heavier nuclei. The momentum distribution extracted from F(y) for heavy nuclei falls off much more rapidly at large y, indicating that the high momentum components in heavy nuclei are much smaller than in deuterium, which is the opposite of what one might expect. In addition, the normalizations of the scaling functions for heavy nuclei are -20-30% lower than they should be if F ( y ) is related to the nucleon momentum distribution. These problems indicate that there is a failure of some kind in the scaling analysis for heavy nuclei. The breakdown for A > 2 nuclei comes from the assumption that the residual ( A - 1) nucleus remains in an unexcited state. This is a reasonable approximation when removing a single nucleon from a shell at low missing energy. However, the high momentum nucleons are predominantly generated by short range correlations, meaning that the momentum of the struck nucleon is mostly balanced by a single nucleon, leaving a high momentum nucleon in the residual nucleus. In the following analysis, we take this into account by assuming a simple three-body breakup of the nucleus, where the struck nucleon is assumed to be one of a correlated pair of nucleons moving within the residual ( A - 2 ) nucleus. The scaling variable in this case is y* = k K2N/2, where y* is the total momentum of the struck nucleon, coming from the relative momentum of the two correlated nucleons, k , and the momentum of the pair within the residual nucleus, K ~ N . Figure 2 shows F ( y * ) from iron, along with the fit to the deuterium scaling function (note that for deuterium there is no ( A- 2 ) residual nucleus, so y* = y). The high momentum behavior is identical for deuterium and heavy nuclei (carbon, iron, and gold), indicating that the two-nucleon correlations that dominate in deuterium are the main source of high momentum components in heavy nuclei. Using the modified scaling variable, the normalization of F ( y * ) is also consistent with unity, as it should be if the scaling function is related to the nucleon momentum distribution. While this data indicates that the modified scaling analysis is valid and allows extraction of the nuclear momentum distributions, the data at large nucleon momentum is somewhat limited, especially for few-body nuclei where the extracted distributions can be compared to essentially exact calculations of nuclear structure. Future measurements are planned with 6 GeV beam3 which will significantly increase the amount of data in the scaling region at
+
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Y* [GeVl Figure 2. Scaling function F ( y * ) for iron from E89-008, after subtracting a model of the inelastic contributions which dominate for y > 0. The solid line is a fit to the measured F ( y * ) for deuterium. The dashed line is the tail of the deuteron fit, scaled up by a factor of six.
large nucleon momenta. This data will significantly improve the data at large IyI and Q 2 , and will include measurement on 3He and 4He. We can then use this to extract information on the momentum distributions in heavy nuclei, and study in more detail the nature of their short range correlations. This work is supported (in part) by the U.S. DOE, Nuclear Physics Division, under contract W-31-109-ENG-38. References
1. G. B. West, Phys. Rep. 18, 263 (1975) ; Y. Kawazoe, G. Takeda and H. Matsuzaki, Prog. Theo. Phys. 54, 1394 (1975). 2. J. Arrington et al., Phys. Rev. Lett. 82, 2056 (1999). 3. Jefferson Lab experiment e02-019, J. Arrington, D. B. Day, B. W. Filippone, A. Lung, spokespersons.
MEDIUM EFFECTS IN A(,??,E‘P) REACTIONS AT HIGH Q2 D. DEBRUYNE AND J. RYCKEBUSCH Ghent University, Proeftuinstraat 86, B-9000 Gent, Belgium E-mail: [email protected]. be Medium dependencies of bound nucleons are studied in a fully relativistic and unfactorized framework for the description of exclusive A(S, e’fi processes. The theoretical framework, which is based on the eikonal approximation, can accommodate both optical potential and Glauber approaches for the treatment of final state interactions. It is discussed how both approaches compare to one another. Calculations for 12C(e,e’p) nuclear transparencies are presented. The issue of measuring the predicted medium modifications for the bound nucleon’s electromagnetic form factors is addressed by presenting 4He(S, e’fi results.
Exclusive A(Z,e’p3 reactions at high Q2 [Q2 >_ 1 ( G ~ V / C )are ~ ] a tool to study several aspects of nuclear and nucleon structure in a region where one expects that both hadronic and partonic degrees-of-freedom may play a role. Amongst the physics issues which can be investigated with electromagnetically induced proton knockout reactions is the short-range structure of nuclei. Here, one wants to find out if there are any hadronic components in the nucleus that carry large momenta, or whether the high momentum components in the nuclear wavefunction are entirely governed by the partonic degrees-of-freedom. Exclusive A(<, e’p3 reactions can also provide stringent tests of constituentquark models. Hereby, one is primarily addressing the question to what extent nucleons are modified in the medium. Closely related to this topic is the study of the nuclear transparency, where one searches for signatures for the onset of the predicted color transparency phenomenon. The extraction of physical information from measured A(Z, e’p3 observables involves some theoretical modeling of which the major ingredients are : the initial state of the struck nucleon, the electromagnetic electron-proton coupling, and the scattering state of the ejected nucleon. To model A(Z, e‘p3 processes we use a relativistic description with initial (bound state) wave functions from a mean-field approximation to the Walecka model. The scattering state is computed in the eikonal approximation which is based on the observation that high energy nucleon-nucleon elastic scattering occurs predominantly in a small cone centered about the incoming nucleon’s momentum. For A(e, e’p) processes, the relevance of the small-angle approximation requires that the incoming momentum transfer_is much larger than the proton’s initial momentum in the nucleus, 141 >> Ikil. Solving the relevant Dirac
571
572
equation with scalar and vector potentials in this approach, leaves us with a wave function that ressembles a relativistic plane wave,
but for two extra ingredients. First, there is the dynamical enhancement of the lower component through the presence of the scalar (Vs)and vector (Vv) potentials, and, second, there is the extra phase factor zS(g, z). At higher energies the highly inelastic nature of p p and p n collisions makes that a potential based description of FSI effects appears no longer feasible and one can make use of the Glauber approach, which is a multiple-scattering extension of the eikonal approximation. In the Glauber model one assumes that the struck proton undergoes subsequent collisions with the spectator nucleons, and each of these collisions is then treated in the eikonal approximation. One assumes that spectator nucleons are frozen, and that only elastic or mildly inelastic collisions occur. The Glauber wave function can be formally written as
with 8 the Glauber phase shift function. The reader is referred to Refs.lp2 for more details. Within the context of exclusive A(Z, el$ reactions, color transparency stands for the suggestion that at sufficiently high values of Q2 the struck proton may interact in an anomalously weak manner with the spectator nucleons in the target nucleus. The Q2 and A dependence of the nuclear transparency can provide information about the non-hadronic, small-sized components in the nucleon, and is thus a direct measure for the occurence of color transparency. The nuclear transparency basically expresses the likelihood that a nucleon, after absorption of a virtual photon, escapes the nucleus. Results of relativistic calculations for the nuclear transparency in the 12C(e,e'p) reaction are shown in Fig. 1. Neither the data nor the model calculations give any evidence for the predicted onset of color transparency. At high Q2 the nuclear transparency saturates at a value of 50-60 %. A recent re-analysis of the world's 12C(e,e'p) database5 resulted in spectroscopic factors of the order of 50-60% of the sum rule value for Q2 values below 0.8 (GeV/c)2. At higher values of Q2, spectroscopic factors approaching the sum rule value were extracted. It should be stressed, though, that at low Q 2 an analysis based on optical potentials was used, whereas at high Q2 a Glauber method was adopted. In view of the apparent discrepancy
573
05 0.6 0.7 0.809 I
3
4
5
6
1
8
Qz [(&V/c)’]
Figure 1. Nuclear transparency for 12C(e,e’p) as a function of Q2. The curves are from relativistic calculations within the optical model eikonal approximation (OMEA) and the relativistic multiple-scattering Glauber approach (RMSGA) with or without short-range correlations (SRC). All calculations use the CC1 current operator in the Coulomb gauge. The displayed curves assume full occupancy of the single-particle levels. The data are from ref^.^,^
between the extracted spectroscopic factors at low and high Q2, one may wonder whether a typical optical potential and Glauber approach actually lead to comparable spectroscopic factors when applied to the same l 2C ( e ,e’p) data set. The summed spectroscopic factors for the s (SlS) and p (5’1,) shell can be deduced from the transparency results of Fig. 1 through the following formula : SIZC z (251, 4$,)/6 N Tezp/Ttheo.From Fig. 1 one observes that at moderate values of Q2 the optical potential calculations and correlated Glauber calculations produce similar nuclear transparencies, and, hence, similar summed spectroscopic factors. From this observation one may conclude that in the kinematical regime where both the Glauber and optical potential approach are plausible descriptions of FSI effects, there is a reasonably smooth transition from the low to the high Q2 regime. The steady rise of the spectroscopic factors as a function of increasing Q2, manifesting itself as an overshoot of the data at low values of Q 2 , can also b e inferred from this figure. Recently, it has been suggested that the electric and magnetic form factors of a bound nucleon may deviate considerably from those of the free nucleon6. Double polarization experiments of the A(Z, e’p3 type provide excellent opportunities to probe these effects. We have compared our model calculations for the 4He(Z,e’p3 double polarization ratio at Q2 M 0.4 (GeV/c)2 with data collected at Mainz. From the results displayed in Fig. 2 it can be seen that
+
574
the inclusion of medium modified form factors has a considerable impact on the double ratio results. Implementing the effect of short-range correlations (SRC) only marginally affects the results. A study of the Q2 dependence of this ratio, performed recently at JLab, confirms these findings’. 4
He(e,e’p) at Q2 = 0.38 (GeV/c)2
.
RMSGA
X
RMSGA + QMC
A
0.81, 0
, , , , 1
2
3
4
I
5
RMSGA + QMC + SRC
, , , , , , ,j 6
7
8
9 1 0 1 1 1 2
Theoretical Model Adopted Figure 2. Double polarization ratio for the ‘He(Z, e’p3 reaction. Shown are calculations in the Glauber approach (RMSGA), with and without the effect of medium modification included (QMC), and with or without the inclusion of SRC. Each set of four calculations shows the results for the CC1 current operator, once in the Coulomb gauge, and once in the Weyl gauge, and for the CC2 operator, also in both gauges. Data are from Ref.7
References
1. D. Debruyne and J . Ryckebusch, NPA 699, 65c (2002). 2. D. Debruyne, J . Ryckebusch, S. Janssen and T. Van Cauteren, PLB 527, 62 (2002). 3. T. O’Neill et al., PLB 351,87 (1995). 4. D. Abbott et al., PRL 80, 5072 (1998). 5. L. Lapikas, G. van der Steenhoven, L. Frankfurt, M. Strikman and M. Zhalov, PRC 61, 064325 (2000). 6. A.W. Thomas, contribution to this conference. 7. S. Dieterich et al., PLB 500, 47 (2001). 8. S. Strauch, contribution t o this conference.
STUDY OF NUCLEON SHORT RANGE CORRELATION IN A(E,E') REACTION AT X , > 1 K. EGIYAN, H. BAGDASARIAN, N. DASHYAN Yerevan Physics Institute, 2 Brother Alikhanyon Street, Yerevan 375036, Armenia E-mail: egiyanajereuanl. yerphi. a m
For the CLAS Collaboration The cross section ratios of inclusive electron scattering from the nuclei 4He, 12C, 56Fe and 3He are measured for the first time. It is shown that these ratios as a function of Q2 and zg are scaled in Q2 > 1.4 (GeV/c) and ZB > 1.5 range. This scaling was predicted within Short Range Correlation (SRC) model. The values of these ratios in the scaling region can be used to derive the probabilities of SRC in heavy nuclei. Our analysis demonstrate that for nuclei with A 2 12 these probabilities are 4.5-5.2times larger than in deuterium, while for 4He it is larger by factor of 2.6-3.3only.
High energy inclusive electron scattering off nuclei can be used for investigation of high momentum component of the nuclear wave functions where contribution of short range correlations (SRC) is dominant. To suppress the contribution from the inelastic events one should study the lower energy transfer ( v ) part of the scattered electron spectra, which corresponds to the condi> 1 Furthermore, from kinematic relation of quasielastic e A tion X B = scattering one can evaluate the X B dependence of the magnitude of minimal missing momentum contributing in the reaction at the given values of Q2 (see Fig.1). As it follows from Fig.1 one can identify a value xg(Q2) such that at X B > 2; the missing momenta involved in the reaction exceed the average Fermi momenta (- 250 M e V / c ) characteristic for uncorrelated nucleons in nuclei. Additionally, to remove nucleons from SRC the energy transferred, v, should exceed the missing energy characteristic to SRC (- 250 - 270 M e V ) 2, therefore, v > 300 M e V . If these conditions are met one can expect that inclusive (e,e') reactions off nuclei will proceed through the interaction of the incoming electron with the correlated nucleon in SRC. In Ref. it was shown that the dominance of SRC contribution in the above mentioned kinematic region can be checked if to study the normalized" ratios of A(e,e')X cross
&
'.
'
~
OHereafter, by the ratio of the cross sections we will mean the ratios normalized by A. We will separately discuss effects due to uep > men which are important for 3He due to Z not equal to N.
575
576
sections defined as follows:
Here ffe.41 and CleA1 are the inclusive cross sections of the electron scattering from nuclei with atomic numbers A1 and A2, respectively. For practical purposes it was chosen A1 > Aa, with A2 = 2,3. The basic prediction of
A0 0.8
0.7 0.6
0s 0.4 0.3 02
0.1 0
02
0.4
OS
0.8
1
12
1.4
1.6
1.8
-
2
X,=Q'I~MV - 1 0.9 0.8 0.7 0.6
0.6 0.4
0.3 0.2
0.1 0
0.2
0.4
0.6
0.8
1
12
Id
1.6
1.8
2
X,=Q2/2Mv
-
Figure 1. The minimum d u e of nucleon Fermi momentum as a function of zg . a) For twonucleon system at several Q2 in (GeV/c)2;b) - For different nuclei at Q2 = 2.0 (GeV/c)2. Horizontal lines indicate the Fermi momentum characteristic to uncorrelated motion of nucleons in nuclei ( w 300 MeV/c).
SRC model for R ( Q 2 , z g )is that they are expected to scale as a function
of 28 > 2; and Q2 > 1. Previously, the predictions for scaling have been checked in using the existing SLAC data for deuterium (as a light nucleus) and heavier nuclei and it was indicated the existence of the scaIing regime at Q2 > 1 and x 2 1.5. However, the data are not purely experimental, since they include the theoretical calculations, and the ratios may have 33475
577
been affected by the fitting and interpolation procedures used. In this talk we present the experimental studies of the cross section ratios of inclusive electron scattering from the 4 H e 12C 56Fe and 3 H e measured for first time.
m3
'.
a
025
2
2
V 01s
m
1
4
0.5 0
0.8
1
12
1.4
1.8
is
Xb=Q2/2mP~ m3
8
024
\o
vr
b2
3
0%
m
1 05 0
0.8
1
12
1.4
1.6
1.8
Figure 2. SRC Model predictions for the normalized inclusive cross section ratio as a function of X B for several values of Q2 (in (GeV/c)2). a) - 12C to 3He, b) - 56Fe to 3He.
We study the ratio:
Using the data from
it is possible to calculate the predictions for the ratio
R i e 3 defined in Eq. (2). The results of these calculations are shown in Fig.2 for 12C and 56Fe nuclei. The primary goal of this work is to check the existence of the scaling for the ratio defined in Eq. (2).
578
The measurement was performed with the CLAS detector in Hall B at Thomas Jefferson Accelerator Facility. The 2.261 GeV and 4.461 GeV electron beam was incident on a cylindrical 1cm diameter 4 cm length target cell filled by the liquid 3 H e or 4 H e and/or 1x1 cm2 plates of 12C(lmm thick) or 5sFe (0.15 mm thick) solid targets. The scattered electron was detected in wide kinematic range. The data were binned in X B and Q2 and the cross sections
g 4 3.5
m
e">1.40
1
2.5
l ' l l
a
I
b)
0.5
0.8
1.2
1.4
1.e
1.8
2
Xb=Q2/2Mv
Figure 3. The ratios Eq. (2) for 12C. a)- circles - Q2= 0 . 7 5 f 0 . 1 ; squares - Q2 = 1 . 0 f 0 . 1 ; triangles - Q2 = 1.20 f 0.1 and at incidant energy 2.261 GeV. b) - circles - Q2 = 1.5 f 0.1 with incident energy 2.261 GeV; squares - Q2 = 1 . 7 f 0.3; triangles - Q2 = 2.30 f 0.3,both with incident energy 4.461 GeV.
were calculated as a function on these variables. We study the ratios of obtained cross section in the 1 < X B < 2 range for H e , 12Cand 56 Fe targets. In Fig.3a,b these ratios are shown for 12Ctarget at several values of Q2. The similar data were obtained for 56Feand 4 H e targets. Based on these data one can draw the following important conclusions: (i) there is a clear Q2 evolution of &),3(XB) shape - at low (< 1.3 (GeV/c)2)Q2, the R$,,(xB) ratios increase with X B in all 1 < X B < 2 range (see Fig.Sa),
579
(ii) as Q2 increases the saturation (scaling) effect is observed (see Fig.3b), (iii) these behaviors do not depend on neither the target-nucleus nor the incident energy. (iiii)there is a good agreement in shapes between the theoretical ) calculations based on pair SRC model and the experimental R i e 3 ( z ~(see Fig.2). Based on the obtained data on R i e 3 ( z 8 ) within , the SRC model of
" ,2.8
;:
03
2.2
*
2 1.8 1.6 1.4
4
1.2 ' 0
10
20
30
40
so
I
A
2; 5 4
+
3 2 1
A Figure 4. a) - A-dependences of ratio R i e 3 (rectangles) and ratio T $ (circles). ~ ~ b) - Adependences of a 2 , A : circles - and rectangles using the experimental and theoretical values of a 2 , ~ ~.respectively; 3 , triangles - data from
'.
Ref. we can calculate the probabilities of 2-Nucleon short range correlations in the scaled region of ZB (see Fig.3b). According to these probabilities are proportional to the a2,A parameters defined as: a 2 , ~ = B +Un PA which
(~!,.tNo),)uD,
represents the ratio of two-nucleon correlation probability in nucleus A to that of the deuteron. To extrac the a2,A values from our data, we put together all data for Q2 > 1.5 (GeV/c)2for each nuclei. ) over this Q2region are shown in Figda The ratios R i e 3 ( z ~averaged with the blue rectangles. Using these values we then evaluate the ratios r i e 3 ( z B ) = a2 A which are shown FigAa by the red circles. One can con-
=
580
clude that the probabilities of pair correlation per nucleon are approximately 2.2-2.5 times larger in “C and 56Fe than in 3 H e , while for 4 H e this ratio is approximately 1.5-1.6 only. The absolute values of a 2 , ~ can be extracted if one knows the a 2 , ~ ~ The 3 . only experimental value of a 2 , ~ is ~ 3 known to be l . 7 f 0.3 from Ref. On the other hand this parameter can be evaluated using the realistic wave functions of the deuteron and 3 H e nucleus. These calculations yield, a 2 , ~ = ~ 32 f 0.1. The our extracted values of a 2 , as ~ well as results from are shown in Fig.4b which demonstrate that for A < 12 nuclei there is a sizeble Adependence of a 2 , parameter, ~ while at A 12 this dependence is very weak. The absolute values of a 2 , parameters ~ for A 12 are in the interval of 4.55.3, while for 4 H e it is in 2.7-3.2 interval. Within the error bars our data are consistent with the results of previous SLAC ( e , e / )data analysis in Ref.
’.
>
>
’.
References
1. L.L. Frankfurt, M.I. Strikman, D.B. Day, M.M. Sargsian, Phys. Rev. C48, 2461, (1993). 2. L.L. Frankfurt and M.I. Strikman, Pys. Rep., 76, 215 (1981); ibd 160, 235 (1988). 3. W.P. Schutz et al., Phys.Rev.Lett., 38, 8259 (1977). 4. S. Rock et al., Phys.Rev.Lett., 49, 1139 (1982). 5. R.G. Arnold et al., Phys.Rev.Lett., 61, 806 (1988). 6. D. Day et al., Phys. Rev. Lett., 59, 427 (1979). B 343, 47 (1995).
N N CORRELATIONS MEASURED IN 3He(e,e’pp)n R. A. NIYAZOV, L. B. WEINSTEIN FOR THE CLAS COLLABORATION Physics Dept., Old Dominion University, Norfolk,
VA 23529, USA E-mail: [email protected]. edu [email protected]. edu We have measured the 3He(e,e’pp)n reaction at 2.2 and 4.4 GeV over a wide kinematic range. The kinetic energy distribution for ’fast’ nucleons ( p > 250 MeV/c) peaks where two nucleons each have 20% or less and the third or ‘leading’ nucleon carries most of the transferred energy. These fast nucleon pairs (both pp and pn) are back-to-back and carry very little momentum along f, indicating that they are spectators. Experimental and theoretical evidence indicates that we might have measured N N correlations in 3He(e,e’pp)n by striking the third nucleon and detecting the spectator correlated pair.
1
Introduction
One signature of correlations is finding two nucleons with large relative momentum and small total momentum in the initial state. Unfortunately, the effects of N N correlations are frequently obscured by the effects of two body currents, such as meson exchange currents (MEC) and isobar configurations (IC) l. In order to disentangle these competing effects, a series of comprehensive measurements are needed. In order to provide this, we measured electron scattering from nuclei, A(e,e’X), using the Jefferson Lab CLAS (CEBAF Large Acceptance Spectrometer), a 47r magnetic spectrometer. These measurements were part of the ’EZ’ run group that took data in Spring 1999. This paper will concentrate on the results from the 3He(e,e’pp)n reaction which exhibit a signature for N N correlations. 2
The 3He(e,e’pp)nMeasurements
We studied electron induced two proton knockout reactions from 3He using the CLAS detector and made a cut on the missing mass M, = to select 3He(e,e’pp)n events. Figure 1 shows the electron acceptance and undetected neutron missing mass resolution for Ebeam= 2.2 GeV. The threshold of the CLAS is approximately 0.25 GeV/c for protons.
581
582 Figure 1. a) Q2 vs w for 3He(e,e'pp)n events. b) Missing mass for 3He(e,e'pp) events. We cut on the peak at M z = M , to isolate (e,e'pp)n events.
0
0.5
1
2
1.5
0.5
3
1.1
Missing Mass (GeVlc') b)
a)
0
1
0.9
Omega (GeV)
1
Iel
-1
-0.5
0
0.5
1
cowp")
b)
Figure 2. a) Kinetic energy balance distribution for 2.2 GeV electrons with cut p , > 250 MeV/c. The boxes correspond to cuts used in later figures. b) Opening angle of the fast p n pairs corresponding to the cut in the upper left and lower right corners of a). The shaded histogram shows the fireball phase space distribution (with arbitrary normalization).
In order to understand the energy sharing in the reaction, we plotted the kinetic energy of the first proton divided by the energy transfer ( T p l / w )versus that of the second proton (Tp2/w)for each event. We eliminated events with p , < 0.25 GeV/c, which are mostly dominated by hard final state rescattering, and focussed on events where all three nucleons are 'active', i.e p~ > 0.25 GeV/c (see Figure 2a). In this case we see three peaks at the three corners of the plot, corresponding to events where two nucleons each have less than 20% of the energy transfer and the third 'leading' nucleon has the remainder. We call the two nucleons 'fast' because p >> p f e r m i . Then we looked at the opening angle of the two fast nucleons. Figure 2b shows fast pn pairs with a leading proton. Note the large peak at 180 degrees (cosOpn x -1). The peak is not due to the cuts, since we do not see it in a fire ball phase space simulation assuming three body absorption of the virtual photon and phase space decay. It is also not due to the CLAS acceptance since we see it both for leading protons and leading neutrons. This back-to-back peak is a strong indication of correlated N N pairs.
583 Figure-3. a) Total momentum of the fast pn pair at 2.2 GeV. b) The same for pair relative momentum.
2 F
<
f
2
1
E:
0
0.2 0.4 0.6 0.8
1
pair low m m n m ( G d k )
0
0.2 0.4 0.6 0.8
a)
3
1
p l r r*.Uw m o m n h M (WVk)
b)
Studying Correlated Pairs
In order to reduce the effects of final state rescattering, we cut on the perpendicular component of the leading nucleon's momentum, p l < 0.3 GeV/c. The resulting fast N N pair opening angle distribution is almost entirely backto-back. These fast nucleons are distributed almost isotropically. Further evidence that the fast N N pair is uninvolved in absorbing the virtual photon comes from the average momentum of the pair along $ This is about 0.07 GeV/c for Ebeam= 2.2 GeV and about 0.1 GeV/c for Eaeam= 4.4 GeV, much less than the average momentum transfers of Q2 = 0.7 and 1.4 (GeV/c)2 respectively. The fast N N pair total (pt,t = If& +&I) and relative ( p T e l = ilpi $21) momentum distributions for fast pn pairs are shown in Figure 3. The distributions are very similar for both p p and pn pairs and for both beam energies. 4
Comparison to Theory
W. Glockle calculated the cross section for 3He(e,e'pp)n where the leading nucleon momentum p" = 4', the fast pair total momentum ptot = 0, 400 5 14 5 600 MeV/c and various values of the relative momentum. He found that a) MEC did not contribute, b) rescattering of the leading nucleon did not contribute and c) the continuum state interaction of the outgoing N N pair decreased the cross section by a factor x 1 0 relative to the PWIA result. We compared our results t o 1) model of pion production on the struck proton followed by pion absorption on the remaining pn pair and 2) a Plane
584
Wave Impulse Approximation (PWIA) calculation by M. Sargsian '. We averaged both models over the CLAS acceptances and cuts using a monte carlo. We did not include radiative corrections to our data. The first model used pion production cross sections from MAID 4 , pion absorption cross sections on deuterium from SAID 5 , and proton initial momentum distributions in 3He from Jans et d.6 . This model does not explain our data in several key respects: a) the average energy transfer was much larger than the data, b) the relative momentum distribution was too large, c) the ratio of the number of fast pn to p p pairs was much lower than the data. The PWIA calculation of Sargsian has Q2 vs w ,N N pair opening angle, and relative momentum distributions that are consistent with the data. It is a factor of 10 larger than the data which is consistent with the expected effects of the N N continuum state interaction calculated by Glockle. It predicts p n / p p = 5 ( 3 for data) and a(2.2 GeV)/a(4.4 GeV)=4 ratios (11for data).
5
Summary
We have studied the 'He(e,e'pp)n reaction, selecting events where one nucleon has most of the kinetic energy and has less than 300 MeV/c of momentum perpendicular t o 4': When we do this, we see isotropic, back-to-back, fast N N pairs with small average momentum along g. We have measured the total and relative momentum distributions of these pairs and found that they do not depend significantly on isospin ( p p vs pn pairs) or on momentum transfer. We have selected, for the first time, kinematics where NN correlations appear to be directly measured. The various momentum and angular distributions are consistent with a simple PWIA treatment. However, we have to wait for a more quantitative estimate of higher order mechanisms for a definite conclusion. References
1. S. Janssen et a]., Nucl. Phys. A672,285 (2000). 2. W. Glockle e t al., Acta Phys. Polon. B32,3053 (2001) 3. M. Sargsian, private communication. 4. D. Drechsel et al., Nucl. Phys. A645 (1999) 5. C.H.Oh, R.A. Arndt, 1.1. Strakovsky, R.L. Workman, Phys. Rev. C 56, 635 (1997) 6. E. Jans, et al., Nucl. Phys. A475,687 (1987).
ELECTROPRODUCTION OF STRANGENESS ON LIGHT NUCLEI F. DOHRMANN~",D. ABBOTT~,A. AH MID OUCH^'^, P. AMBROZEWICZ~, C.S. ARM STRONG^^, J. ARRINGTON"', R. ASATURYAN~, K. ASSAMAGAN', S. AVERY', K. BAILEY', O.K. BAKERf, S. BEEDOEd, H. BITAO', H. BREUERk, D.S. BROWNk, R. CARLINIb, J . CHA', N. CHANTk, E. CHRISTY', A. COCHRAN', L. COLE', G. COLLINSk, C. COTHRAN', J. CROWDER", W.J. CUMMINGS', S. DANAGOULIANdb, F . DUNCANk, J. D U N N E ~ D. , DUTTAO, T. EDEN', M. ELAASARP, R. E N T ~ L. , EWELL~, H. FENKERb, H.T. FORTUNEq, Y. FUJII', L. GANfflH. GAO', K. GARROWb, D.F. GEESAMAN', P. GUEYE', K. GUSTAFSSON~,K. HAFIDI', J.O. HANSEN', W. HINTON', H.E. JACKSON', H. JUENGST', C. KEPPELf, A. KLEIN*, D. KOLTENUKq, Y. LIANG", J.H. LIU', A. LUNGb, D. MACKb, R. MADEYfe, P. MARXOWITZab, C.J. MARTOFFg, D. MEEKINSb, J . MITCHELLb, T. MIYOSHI', H. MKRTCHYANj, R. MOHRINGk, S.K. MTINGWAd, B. MUELLER', T.G. O'NEILL', G. NICULESCU", I. NICULESCU'", D. POTTERVELD', J.W. PRICE", B.A. RAUE'", P.E. REIMER', J. REIN HOLD"^^, J. ROC HE^, P. R O O S ~M. , SARSOURY, Y. SATO', G. SAVAGE', R. SAWAFTAd, R.E. SEGELO, A.YU. SEMENOVe, S. STEPANYANj, V. TADEVOSIANj, S. TAJIMA", L. TANGf, B. TERBURG+, A. UZZLE', S. WOODb, H. YAMAGUCHI', C. YANlb, C. YANze, L. W A N ' , M. ZEIER', B. ZEIDMAN', AND B. ZIHLMANN' 'Florida International University, Thomas Jefferson National Accelerator Laboratory, 'Argonne National Laboratory, N C A b T State University, University of North Carolina at Wilrnington, K e n t State University, Harnpton University, g Temple University, College of William and Mary, California Institute of Technology, j Yerevan Physics Institute, University of Maryland, University of Virginia, Juniata College, "Forschungszentrum Rossendorf, O Northwestern University, PSouthern University at New Orleans, University of Pennsylvania, Tohoku University, 'University of Minnesota, Old Dominion University, American University, Ohio University, The George Washington University, Rensselaer Polytechnic Institute, University of Houston, ' D u k e University, + University of Illinois
'
'
The A ( e ,e ' K f ) Y X reaction has been investigated in Hall C at Jefferson Laboratory for 6 different targets. Data were taken for Q2 M 0.35 and 0.5 GeV2 at a beam energy of 3.245 GeV for 1H,2H,3He,4He,C and A1 targets. The missing mass spectra are fitted with Monte Carlo simulations taking into account the production of A and Co hyperon production off the proton, and C- off the neutron. Models for quasifree production are compared to the data, excess yields close to threshold are attributed to FSI. Evidence for A-hypernuclear bound states is seen for 3 y 4 ~ etargets.
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1
Introduction
The advent of high intensity CW electron beams at the Thomas Jefferson National Accelerator Facility provides the feasibility to study with high precision the electroproduction of strangeness as a complementary Ansatz to experiments with pion and kaon beams Jefferson Lab experiment E91016 measured the A(e, e'K+)YX for 1H,2H,3He,4He, C and A1 targets. Angular distributions of K+ were measured at forward angles with respect to the virtual photon, y*. Data for ' H and 2 H targets have been presented p r e v i ~ u s l y so ~ ~that ~ ~ ~the , data on Helium targets will be the focus of the present paper; the results are still preliminary.
'.
2
Experiment
The experiment was performed in summer 1996 and fall 1999. The scattered electrons, e', were detected in the High Momentum Spectrometer (HMS) in coincidence with the electroproduced K+, detected in the Short Orbit Spectrometer (SOS) in Hall C of Jefferson Lab. For a description of the experimental method see '. During the experiment the spectrometer angle for detecting the e' was kept fixed; the K+ arm was varied. For A = 1,2,3,4 three different angle settings between the y* and the ejected K+ were studied, = O", N 6", and N 12". Since special high density cryogenic targets were used, the background, consisting of random coincidences as well as contributions from the aluminum walls of the targets cells were subtracted to obtain charge normalized yields.
OF'
3
Results and Discussion
The missing mass distribution for ' H ( e ,e'K+)Y shows two clearly resolved peaks corresponding to the A and Co hyperons3v4. The two spectrometer coincidence acceptance as well as radiative processes are computed by Monte Car10 simulations. A parametrization of the y*N cross section has been derived by fitting the kinematic dependences of the l H ( e ,e'K+)Y cross section over the acceptance 4; the same parametrization has been used for A _> 2. For A 2 2 we do not resolve separated Co,C- hyperon peaks, which are produced off the proton and the neutron, respectively. Moreover, for nuclear targets, the Fermi momentum and energy of the target nucleons have to be taken into account. Using the impulse approximation, we obtain momentum and in-medium energy of the struck nucleon in the nucleus from full spectral functions for the various targets, as provided by Benhar '. Excess yields close
587 'He
'He
j 2000 1000 1000 500 0
2.95 2.975
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3.025
3.05 3.075
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3.125 3.15
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M M (GeV)
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M M (GeV)
3.9
3.925 3.95
3.975
4
4.025 4.05
Mm (GeV)
4.075
4.1
MM (GeVJ
Figure 1. Missing mass distributions for 394He(e,e'Kf) at B$b,K = O0,6O,1 2 O . The solid line represents a Monte Carlo simulation of the qf contributions for A, Co, C- production off a nucleon in 334He. FSI corrections have been applied and the coherent production of 394He(e,e'K+)24Hhas been added as well. The dot-dashed vertical lines depict the threshold for quasifree A, C o and C- production for A = 3 and 4.
to the respective An and C N thresholds are attributed to FSI; for A = 2 a more extensive study has been described in '. For A = 3 , 4 we employ a simple effective range model of the FSI as described in '. For A = 3 and 4 the agreement comparison between simulation and data is shown in Fig. 1. The separation of the two peaks for quasifree (qf) A and C production becomes less and less pronounced with increasing A. The foundation of the analysis for 314Heis described in '. In the regions of the qf A-thresholds for A = 3 and 4, Fig. 1 exhibits relatively narrow enhancements that we attribute to the i H and i H bound states. For both targets the structure is independent of the angle and is centered, within the resolution of the experiment, right at the correct binding energy. While barely discernible for 3He at = O", the structure becomes more evident for = 6", 12". It is clearly visible for
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all three measured angles for 4He. The resolution of the experiment does not allow for a separation of the ground and first excited states of i H , although the reaction mechanism favours the excited state. The preliminary analysis yields a cross section for the H state of a few nb/sr and roughly 20 nb/sr for the i H state. Further quantitative statements are expected after completing the analysis of the data. 4
Summary
The measurements on ' H ( e ,e'K+)Y established the basic high precision data to extend the experiments on associated hyperon production to nuclear targets. For A 2 targets a full spectral function is used t o describe the struck nucleon in the nucleus. In each case the kinematic model derived from hydrogen is used in impulse approximation to describe the qf production of hyperons off nuclear targets. Moreover, for A = 3,4, we observe clear evidence for the X H , i H bound states produced in electroproduction. After completing the analysis, we expect to obtain quantitative measurements of the electroproduction cross section for all of the targets studied: ' H , 2 H , 3He, 4He, C, and
>
Al. 5
Acknowledgements
This work was supported in part by the US. Department of Energy and the National Science Foundation. Support from Argonne National Laboratory and the U.S. Dept. of Energy under contract No. W-31-109-Eng-38 is gratefully ackowledged. The support of the staff of the Accelerator and Physics Division of Jefferson Lab is gratefully acknowledged. F. Dohrmann acknowledges the support by the the A.v.Humboldt Foundation through a Feodor Lynen Research Fellowship as well as the support by Argonne National Laboratory as the host institution for this research. References 1. J.-M. Laget Nucl. Phys. A 691, l l c (2001) 2. D. Abbott et al, Nucl. Phys. A 639, 197c (1998). 3. B. Zeidman et al, Nucl. Phys. A 691, 37c (2001). 4. J. Cha, PhD thesis, Hampton University, 2000.
5. 0. Benhar et al, Nucl. Phys. A 579,493 (1994). 6 . D. Gaskell et al, Phys. Rev. Lett. 87, 202301 (2001). 7. A. Uzzle , PhD thesis, Hampton University 2002.
HYPERNUCLEAR SPECTROSCOPY OF i 2 B IN THE (E,E'K+) REACTION J. REINHOLD Florida International University, Miami, FL 331 99 E-mail: reinhold0jiu. edu for the Jefferson Lab E89-009 Collaboration
T. MIYOSHI', M. SARSOUR3, L. YUAN', X. ZHU', A. AHMIDOUCH4, P. AMBROZEWICZ5, D. ANDROIC', T. ANGELESCU7, R. ASATURYAN', S. AVERY', O.K. BAKER', I. BERTOVIC', H. BREUER', R. CARLINI", J. CHA', R. CHRIEN", M. CHRISTY', L. COLE', S. DANAGOULIAN4, D. DEHNHARD", M. ELAASARI3, A. EMPLI4, R. ENT", H. FENKER", Y. FUJII', M. FURIC', L. GAN', K. GARROW", A. GASPARIAN', P. GUEYE', M. HARVEY', 0. HASHIMOTO*, W. HINTON', B. HU', E. HUNGERFORD3, C. JACKSON', K. JOHNSTON", H. JUENGST", C. KEPPEL', K. LAN3, Y. LIANG', V.P. LIKHACHEV", J.H. LIU", D. MACK", K. MAEDA', A. MARGARYAN', P. MARKOWITZ17, J. MARTOFF5, H. MKRTCHYAN', T. PETKOVIC', J. REINHOLD", J. ROCHE'', Y. SATO'72, R. SAWAFTA4, N. SIMICEVIC'5, G. SMITH", S. STEPANYAN', V. TADEVOSYAN', T. TAKAHASHI', H. TAMURA', L. TANG'?'', K. TANIDA", M. UKAI', A. UZZLE', W. VULCAN'', S. WELLS", S. WOOD", G. XU3, Y. YAMAGUCHI', AND C. YAN" Hampton University, Hampton, VA 23668 Tohoku University, Sendai 980-8578 University of Houston, Houston, T X 77204 4 N ~ r t hCarolina A & T State University, Greensboro, N C 27.4 11 Temple University, Philadelphia, PA 19122 University of Zagreb, Croatia University of Bucharest, Romania Yerevan Physics Institute, Armenia University of Maryland, College Park, MD 20742 Thomas Jefferson National Accelerator Facility, Newport News, VA 23606 " Brookhaven National Laboratory, Upton, N Y 11973 l 2 University of Minnesota, Minneapolis, MN 55455 13Southern University at New Orleans, New Orleans, L A 70126 l 4Rensselaer Polytechnic Institute, R o y , N Y 12180 15Louisiana Tech University, Ruston, L A 71272 l6 University of Sao Paulo, Brazil 17Florida International University, Miami, FL 331 99 College of Williams and Mary, Williamsburg, VA 23187 University of Tokyo, Tokyo 113-0033
' ''
'
'
''
''
T he first A-hypernuclear spectroscopy study using an electron beam has been carried out a t Jefferson Lab. T h e hypernuclear spectrometer system (HNSS) was used t o measure spectra from the " C ( e , e 'K + ) i'B reaction with close t o 1 MeV resolution, the best energy resolution obtained so far in hypernuclear spectroscopy with magnetic spectrometers. This paper describes the HNSS and preliminary results for the i 2 B system. A program of hypernuclear physics experiments is planned for the future with much higher yield and even better energy resolution.
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1
Introduction
Hypernuclear spectroscopy allows the investigation of features of the nuclear many-body system that are not accessible by conventional methods. It has been shown, e.g., that A-particles because distinguishable from nucleons can occupy any of the nuclear shells. An intrinsic width in the order of a few 100 keV is expected even for highly excited A single-particle states above the nucleon emission threshold1. This allows observation of A single-particle excitations over a range of more than 20 MeV. Further, due to the lack of suitable hyperon beams the low momentum hyperon nucleon interaction and particularly its spin dependent components can only be studied in hypernuclear structure. The basic features have long been established, mainly by means of reaction spectroscopy in ( K - , T ) and (n,K + ) reactions (see for a review and for recent activities). The best achieved resolution of roughly 1.5 MeV does not yet allow to fully explore the potential of hypernuclear spectroscopy. Coincident y spectroscopy, undoubtedly, will provide the most accurate information, however, it will most likely be limited to lighter nuclei with low excitation energies. The high quality of electron beams and the recent availability of a high-duty factor accelerator at Jefferson Lab now should allow to achieve sub-MeV resolution for reaction spectroscopy. The ( e ,e’K+) reaction converts a proton in the target nucleus into a A hyperon exciting proton-hole lambda-particle states. This is in contrast to meson reactions which populate neutron-hole lambda-particle states. In addition, the ( e ,e’K+) reaction carries significant spin-flip amplitudes therefore exciting multiplet states complementary to those favored in meson reactions. 2
Experiment & Results
The underlying elementary p ( e , e’K+)A reaction mechanism and optimum conditions for hypernucleus formation require detection of both scattered electrons and produced kaons at angles near zero degree. This has been realized in the HNSS setup of Jefferson Lab experiment E89-009. A 12C target was irradiated by 0.6 pA electron beams at energies of 1.7 and 1.8 GeV. Scattered electrons and kaons in the very forward angles were deflected by a splitter magnet in opposite directions and then momentum analyzed by separate spectrometers. The scattered electrons in the energy range from 200-300 MeV were measured at 0 degrees by the ENGE split pole spectrometer, while kaons were detected by the SOS spectrometer which covered an angular range from -2 to + 5 degrees and a momentum range of 1.2 GeV/c. Hypernuclear missing mass spectra were obtained from the momenta of kaons and electrons. The
59 1 240
Surmnmed 12-B-Lambda Spectrum
-. 12C(e,e7K+)',28
HhTSS-LAB
220 -
200
~ 1 8 0
L?
.
8160
x 9140
120
I00
80
Figure 1. Reconstructed A binding energy for A2B. The shaded area shows the background which is mainly due to accidental coincidences.
mass scale was calibrated to an accuracy of 125 keV with the known A and Co masses in the ' H ( e , e ' K + ) reaction from a CH2 target. An upper limit of 820-keV (FWHM) for the resolving power was obtained by investigating triple coincidences for pair production in the A ( e ,e'e+e-)A reaction. A more detailed description of the experimental procedure has been given elsewhere4. A preliminary spectrum for the A binding energy for i 2 B is shown in Fig. 1. Only specific hypernuclear states are expected to have significant strength in the (e,e'K+) reaction The peak located at BA M -11.5 MeV is from the transition to the unresolved (1-, 2-) ground state doublet of A2B;a A in the s shell coupled to the ground state of l 1B. The 2- state can be reached only by spin-flip and is thus expected to be more strongly excited by the ( e ,e'K+) reaction. Theory predicts a spacing between the two states (resulting from spin-dependent parts of the interaction) of roughly 100 keV, too close to be resolved in this experiment. Near breakup threshold, between BA = -2 and +1 MeV, several states arising from coupling a A in the p3/2 shell to the 3/2g.s. of " B are expected. A 3+ state is predicted to be most strongly excited, but, as with the ground state doublet cannot be resolved from the other states 536.
592
with the current resolution. Therefore, the observed width of roughly 1 MeV is consistent with having achieved sub-MeV resolution. 3
Summary & Outlook
The first experiment using the HNSS at Jefferson Lab achieved the so far best resolution in any hypernuclear reaction spectroscopy, therefore providing new opportunities for future hypernuclear studies. Some shortcomings of the existing setup, however, have been recognized. Therefore, an improved system has been proposed to and approved by Jefferson Lab '. A new high-resolution and short-path-length kaon spectrometer (HKS) is currently under construction. It will improve the kaon arm momentum resolution by a factor of two and its solid angle acceptance by a factor of about 3. The electron arm will be placed at an angle with respect to the floor plane such as to reduce background from bremsstrahlung. This new geometry allows a luminosity increase of more than a factor of 200. Overall, the yield is expected to increase by a factor of about 50 and the energy resolution may reach 350 keV (FWHM). The goal of the new experiment is to carry out high precision and high statistics studies on medium mass hypernuclei, e.g. ;*A1 and ;'Ti.
Acknowledgments The authors acknowledge the support of the staff of the Accelerator and Physics Division of Jefferson Lab. This work is supported in part by DOE and NSF. SURA operates JLab under DOE contract DE-AC05- 84ER40150. Construction of the HKS spectrometer is funded as specially promoted research by a Grant-in-Aid for Scientific Research from Monka-sho, Japan.
References 1. H. Bando, T . Motoba, Y. Yamamoto, Phys. Rev. C 31, 265 (1985). 2. B. F. Gibson and E. V. Hungerford, Phys. Rept. 257, 349 (1995). 3. Proc. 7th Int. Conf. on Hypernuclear and Strange Particle Physics, Torino (Italy), 23 October 2000, Nucl. Phys. A 691, 1-530 (2001). 4. L. Tang, et al., Proc. 8th Conf. on Mesons and Light Nuclei, Prague, Czech Repulic, July, 2001, AIP Conference Proc. 603 (2001) 173-185. 5. T . Motoba, M. Stone, K. Itonaga, Progress of Theoretical Physics Supplement No. 117, 123 (1994) & M. Sotona and S. Frullani, ibid, p. 151. 6. D.J. Millener, private communication. 7. 0. Hashimoto, L. Tang, and J . Reinhold, JLab E01-011 proposal, (2001).
Session on Chiral Physics Convenors A. M. Bernstein U. van Kolck U. G. Meifher
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GOLDSTONE BOSON DYNAMICS: INTRODUCTION TO THE CHIRAL PHYSICS SESSION A.M. BERNSTEIN PHYSICS DEP.4RTMENT AND LABORATORY FOR NUCLEAR SCIENCE M.I.T., CAMBRIDGE MASS., USA
The study of the chiral structure of matter is an active and fundamental field1. The relevant phenomena are the properties of the Goldstone Bosons, their interactions, production and decay amplitudes; these are linked to QCD by an effective (low energy) field theory, chiral perturbation theory (ChPT)2. In QCD, when the light quark masses are set to zero (the chiral limit), the Lagrangian exhibits chiral symmetry. This is observed to be spontaneously broken (hidden) since degenerate parity doublets are not seen. The symmetry is not lost but appears in the form of massless, pseudoscalar, Goldstone Bosons. Spontaneous symmetry breaking is well-known in condensed matter physics, e.g. magnetic domains in iron which breaks the rotational symmetry of the Coulomb interaction. In this case the Goldstone Bosons are spin waves or magnons. In QCD the small non-zero light quark masses explicitly break the chiral symmetry of the Lagrangian with the result that the pion, eta, and kaon have finite masses. Nevertheless there is a mass gap and these eight pseudoscalar mesons are the lightest hadrons. The pion best approximates the ideal Goldstone Boson. Ideally, it would not interact with hadrons at very low energies (i.e. the s wave scattering lengths would vanish). The small, but nonzero, low energy interactions are due to finite quark (meson) masses. They are important to measure since they are an explicit effect of chiral symmetry breaking and have been calculated by ChPT. At this point it has become traditional to express the hope that in the future lattice gauge theory will make accurate predictions. An insightful example of quark mass effects is the 7r -hadron scattering length calculated pre QCD by Weinberg, using current algebra/PCAC3. The result for the s wave scattering length, a ( w , h) can be written as :
where f = I; +& is the total isospin,I,, and Ih are the isospin of the pion and hadron, and the chiral symmetry breaking energy scale A, N 47rf, N 1GeV (where f, N 92MeV is the pion decay constant). Thus a N l / A , N O.lfm Which is much smaller than for a “typical” strong interaction (without a low lying resonance) where a N l/m, N l f m . From Eq. 1 it is seen that a -+ 0 in the chiral limit (i.e. where the light quark masses and m, -+ 0). Since this
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formula works in the long wavelength limit it is physically reasonable that the structure of the projectile and target do not matter, only their isospin. In addition, this formula can be used for the other Goldstone Bosons if the appropriate isospin and mass are used. The current algebra calculation is now understood as the lowest order ChPT calculation2. The scattering lengths are a power series in ( ~ n , / h , )The ~ . PCAC result presented in Eq. 1is the lowest order n= 1 term with the chiral corrections4 starting at n = 2. Since the occurrence of the quasi Goldstone Bosons signify spontaneous chiral symmetry breaking in QCD, their low energy interactions with other hadrons, their electromagnetic production and decay amplitudes as well as their internal properties (e.g. radii, polarizabilities, decay) will serve as fundamental tests of the chiral structure of matter. These measurements represent timely physics issues and a technical challenge for experimental physics. In the past five years there has been rapid progress in such measurements. The recently completed K14 experiment at Brookhaven has accurately measured the low energy m r phase shifts and found the A - A scattering length5 t o be in agreement with ChPT calculations to two loops. This suggests that the magnitude of the chiral condensate is not small, as had been conjectured6. Beautiful experiments on pionic hydrogen and deuterium at PSI have measured the s wave I ~ N scattering lengths7. They have the anticipated magnitude and are in good agreement with ChPT calculations4. On the same "chiral footing" the amplitude for the threshold s wave neutral pion photoand electro production amplitudes vanish in the chiral limit. Photoproduction datag for this small magnitude are in reasonable agreement with ChPT calculations, but some discrepancies in electroproduction lo at Q2 = 0.05GeV2need to be resolved. Overall, these pion scattering and production experiments verify our underlying concept of the pion as a quasi Goldstone Boson reflecting spontaneous chiral symmetry breaking in QCD. Not all of the chiral predictions have been properly tested. The long standing prediction of Weinberg that the mass difference of the up and down quarks leads to isospin breaking in 7rN ~cattering"?~ is of special interest in this field. The accuracy of the completed experiments7 and of the model extractions from the deuteron pionic atom12, does not yet permit a test of this fundamental prediction. An interesting possibility is the use of the pion photoproduction reaction with polarized targets to measure the isospin breaking predictions of low energy RON scattering14, which is related to the isospin breaking quantity -N 30%. This is an unusual experimental opportunity since the general order of magnitude of the predicted isospin breaking4 is md-mu N 2%. There have been claims of observing isospin breakAQCD ing in medium energy AN scattering experiments at a level several times this
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magnitude13, which need independent testing. If these results are correct this would represent a serious discrepancy with the predicted quark mass effects at medium energies. The experimental magnitude of the C term in K N scattering15 is still uncertain[StahovIa. This fundamental quantity vanishes in the chiral limit and gives a measure of the strange quark contribution to the nucleon mass. Accurate experiments in low energy pion-nucleon scattering and charge exchange are presently being performed and are also in the planning stage. Another unsolved problem is a contradictory experimental situation for the pion polarizabilities?. Uncertainty about this fundamental pion property needs to be resolved; the performance of these difficult experiments should have high priority. Experiments on q and K production and scattering' are in their infancy. They require both the high quality of existing beams and experiments cleverly designed to reduce the resonance contributions. Measurements of the N and K N interactions would provide important tests of the quasi Goldstone Boson nature of these heavier pseudoscalar mesons. In this case the decay modes of the kaon are in better experimental shape and are in general agreement with chiral predictions'. Some fundamental nucleon properties ( e g electromagnetic polarizabilities) are part of the overall picture since they diverge in the chiral limit, indicating that they are pion dominated. Measuring these with real and virtual photons allows us t o make a detailed map of their spatial distributions. The study of the non-spherical amplitudes in the nucleon and A wave functions also reflect significant non-spherical pion field contributions, as expected from Goldstone's theorem. A profound example of symmetry breaking in QCD is the axial anomaly. The classical U(l) symmetry of the QCD Lagrangian is absent in the quantum theory presumably due t o quantum fluctuations of the quark and gluon fields. The physical consequences are the non-zero mass of the q' meson in the chiral limit and the 2 photon decays of the pseudoscalar mesons. There is an absolute prediction of the -+ yy decay rate in agreement with the measured value. At present the accuracy of the experiments is approximately 15%. An effort to reduce this by an order of magnitude is in progress[Gasparian]. In parallel there is a theoretical effort to calculate the chiral corrections to the decay rate[Goity]. These involve mixing of the no with the q and (. This involves isospin breaking and is proportional to md-mu. There are also other reactions for which the axial anomaly is the dominant mechanism such as y7r -+ m. areferences to talks in this conference will be indicated in square brackets
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Experimental work on these reactions is also in progress[Miskimen]. This brief survey has presented a snapshot of some of the important activities in the study of the chiral structure of matter. References
1. For an introduction and review see Chiral Dynamics 2000: Theory and Experiment, A. M. Bernstein, J. Goity, and U. G. MeiBner editors, Proceedings From the Institute of Nuclear Theory-Vol. 11, World Scientific, Singapore(2001). 2. S.Weinberg, Physica A96,327(1979). J.Gasser and H.Leutwyler, Ann. Phys.(N.Y.) 158,142(1984), Nucl.Phy-s. B250, 465 and 517(1985). 3. S.Weinberg, Phys. Rev. Lett. 17,168(1966). 4. N. Fettes and U.G.Meiher, Nucl. Phys. A693,693(2001) and Phys. Rev. C63,045201(2001) 5. S. Pislak et al., Phys.Rev.Lett.87:221(2001) 6. G. Colangelo, J. Gasser, H. Leutwyler, Phys.Rev.Lett.86,5008(2001) 7. H.-Ch. Schroder et al., Phys. Lett. B469,25(1999), Eur .Phys .J .C21:473(2001) 8. V.Bernard, N.Kaiser, and U.G.MeiBner, Eur.Phys.J.A11:209,20Oland Nucl.Phys.A607:379,1996, Erratum-ibid.A633:695,1998 9. A. Schmidt et al., Phys. Rev. Lett. 87, 232501(2001). 10. H. Merkel et al., Phys.Rev, Lett. 87, 012301(2002), and invited talk at Barons. 11. S.Weinberg,Transactions of the N.Y.Academy of Science Series I1 38 (1.I.Rabi Festschrift),l85(1977). 12. S.Ft.Beane, V. Bernard, T-.S.H.Lee, U.G. MeiBner, Phys. Rev. C57,424( 1998). 13. W.R.Gibbs, Li Ali, and W.B.Kaufmann, Phys. Rev. Lett .,74,3740(1995). E. Matsinos, Phys. Rev. C58,3014(1997). 14. A.M.Bernstein,Phys.Lett. B442,20(1998); nN Newsletter 15,1(1999). 15. For an introduction t o the C term see the article by J. Gasser and M. Sainio and the report of Working Group I1 on Goldstone-Boson Nucleon in'. 16. D. Babusci et al., Phys. Lett. B277,158(1992).
v’ ELECTROPRODUCTION OFF NUCLEONS B. BORASOY Physik Department, Technische Universitat Munchen, 0-85747 Garching, Germany E-mail: [email protected] T h e electroproduction of the 7’meson on nucleons is investigated within a relativistic chiral unitary approach based on coupled channels. The s wave potentials for electroproduction and meson-baryon scattering are derived from a chiral effective Lagrangian which includes the 7’ as an explicit degree of freedom and incorporates important features of the underlying QCD Lagrangian such as the axial U(1) anomaly. The effective potentials are iterated in a Bethe-Salpeter equation and cross sections of 9’ electroproduction from nucleons are obtained. The investigation of the ?‘-nucleon system may offer new insights into the role of gluons in chiral dynamics.
1
Motivation
Photoproduction of mesons is a tool to study baryon resonances and the investigation of transitions between these states provides a crucial test for hadron models. Because of their hadronic decay modes nucleon resonances have large overlapping widths, which makes it difficult to study individual states, but selection rules in certain decay channels can reduce the number of possible resonances. The isoscalars 77 and 77’ are such examples since, due to isospin conservation, only the isospin-i excited states decay into the 7 N and TIN channels. Electroproduction experiments are even more sensitive to the structures of the nucleon due to the longitudinal coupling of the virtual photon to the nucleon spin and might in addition yield some insight into a possible onset of perturbative QCD. In this work, we restrict ourselves to the low-energy region where nonperturbative QCD dominates. Chiral symmetry is believed to govern interactions among hadrons at low energies where the relevant degrees of freedom are not the quark and gluon fields of the QCD Lagrangian, but composite hadrons. In order to make contact with experiment one must resort to non-perturbative methods such as chiral perturbation theory (ChPT) which incorporates the symmetries and symmetry breaking patterns of underlying QCD and is written in terms of the active degrees of freedom. A systematic loop expansion can be carried out which inherently involves a characteristic scale A, = 47rF, M 1.2 GeV at which the chiral series is expected to break down. The limitation to very low-energy processes is even enhanced in
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the vicinity of resonances. The appearance of resonances in certain channels constitutes a major problem to the loopwise expansion of ChPT since their contribution cannot be reproduced at any given order of the chiral series. Recently, considerable effort has been undertaken to combine the chiral effective Lagrangian approach with the Bethe-Salpeter equation making it possible to go to energies beyond A, and to generate the resonances dynamica1ly.l Two prominent examples of resonances in the baryonic sector are the A( 1405) and the 511(1535). The experimental data for 77’ photoproduction from ELSA suggested the coherent excitation of two resonances Sll(1897) and Pll(1986). In this work we will restrict ourselves to s waves and therefore the comparison with data should only be valid in the near threshold region. One of the purposes of this work is to shed some light on the s wave resonance Sll(1897). Our results must be compared to the cross section reported in and will also deliver predictions for 77’ electroproduction. The 77’ is closely related to the axial U (1) anomaly. The QCD Lagrangian ~ symmetry which with massless quarks exhibits an s U ( 3 ) ~x s U ( 3 ) chiral is broken down spontaneously to S U ( 3 ) ” , giving rise to a Goldstone boson octet of pseudoscalar mesons which become massless in the chiral limit of zero quark masses. On the other hand, the axial U (1) symmetry of the QCD Lagrangian is broken by the anomaly. The corresponding pseudoscalar singlet would otherwise have a mass comparable to the pion mass. Such a particle is missing in the spectrum and the lightest candidate would be the 77‘ with a mass of 958 MeV which is considerably heavier than the octet states. 2
Sketch of the calculation
We start by including the 77’ in a chiral effective Lagrangian with the ground state octet baryons in a systematic fashion as outlined in Within this framework the 7’ is combined with the Goldstone bosons (T,K,q) into a nonet and the q‘-baryon couplings are constrained by chiral symmetry. First, the s wave potentials V of meson-baryon scattering are extracted from the contact and s-channel Born terms. Unitarity imposes a restriction on the T-matrix
’.
T-l= V-l+ G
(1)
where G is the scalar meson baryon loop integral
G(q2)=
1-!?-
( 2 ~ [(q ) ~ 1)2 - M i
i
+ if][Z2- m$ + if]
60 1
with ImG = ImT-', and we have approximated the remaining real part in Eq. (1) by V-I. Matrix inversion of Eq. (1) yields the Lippmann-Schwinger equation
T = [1+ V . G ] - ' . V
(3)
which is equivalent to the summation of a bubble chain. This approach is readily extended to electroproduction of mesons on baryons. The electric dipole amplitude B: and the longitudinal s wave C$ at the tree level are derived from the contact and Born terms of meson electroproduction and inserted into the meson-baryon bubble chain in order to obtain the full electric dipole amplitude E$ and longitudinal s wave Lof, respectively, E:=[l+V.G]-'.B;,
L,f=[l+V.G]-'.C,f.
(4)
Diagrammatically, Eq. ( 4 ) is illustrated by
Figure 1. Shown is the electroproduction of mesons on baryons. The empty circle denotes electroproduction at the tree level, whereas the full circles are the full meson-baryon scattering and electroproduction amplitudes. Wavy, dashed and solid lines represent the photon, mesons, and baryons, respectively.
The s wave total cross section for the electroproduction of mesons on the nucleon is
with q the three-momentum of the meson in the center-of-mass frame and E L = - 4 ~ s k ~ ( s - M $ + k ~ )where - ~ E and k2 are the virtual photon polarization and momentum transfer, respectively.
3
Results
By fitting a few chiral parameters we are able to obtain reasonable agreement with a large amount of data, such as K , q and q' photoproduction on the proton and meson-baryon scattering proce~ses.~ Once we have determined
602
these parameters, we can predict the total cross section for rf electroproduct i o n which provides a better test for our model. In Fig. (2) we present 77’ electroproduction on the proton for various virtual photon momenta k 2 . The curve we obtain for 77’ photoproduction ( k 2 = 0) corrsponds t o a resonance S11 with mass M = 1.98 f 0.05 GeV and width F = 0.27 f 0.10 GeV.
k2 [ GeV’ ]
I
I
~
2.5
3
3.5
Figure 2. S wave total cross section for 7’ electroproduction on the proton for various virtual photon momenta k 2 and virtual photon polarization 6 = 0.78. The case of 7’ photoproduction is given by k2 = 0.
The results of our investigation indicate that chiral dynamics governs processes up to 2 GeV and that the 7’ can be included systematically in a chiral effective Lagrangian with baryons. However, in order to obtain more rigorous statements in our appraoch, one must include p waves.
Acknowledgements Work supported in part by the Deutsche Forschungsgemeinschaft.
References 1. See, e.g., N. Kaiser, T. Waas, W. Weise, Nucl. Phys. A612 (1997) 297; N. Kaiser, P. B. Siegel, W. Weise, Nucl. Phys. A594 (1995) 325; J. A. Oller, E. Oset, Nucl. Phys. A620 (1997) 438. 2. R. Plotzke et al., Phys. Lett. B444 (1998) 555. 3. B. Borasoy, Phys. Rev. D61 (2000) 014011. 4. B. Borasoy, E. Marco, S. Wetzel, in preparation.
A UNIFIED CHIRAL APPROACH TO MESON-NUCLEON INTERACTION E.E. KOLOMEITSEV~AND M.F.M. L U T Z ~ tECT', Villazzano (Trento), I-38050 Italy, and G.C. I N F N D e n t o Italy GSI and T U D a m s t a d t , Planckstr 1 , 0-64291 D a m s t a d t , Germany A combined chiral and l / N c expansion of the Bethe-Salpeter interaction kernel leads to a good description of the kaon-nucleon, antikaon-nucleon and pion-nucleon scattering data typically up t o laboratory momenta of PI& E 500 MeV. The covariant on-shell reduced coupled channel Bethe-Salpeter equation with the interaction kernel truncated t o chiral order Q3 and t o the leading order in the l/Ncexpansion is evaluated.
We review the recent application of the chiral SU(3) Lagrangian to mesonbaryon scattering'. The acronym 'x-BS(3)' is used as to indicate that the Bethe-Salpeter scattering equation is applied and properly furnished with an interaction kernel constrained by the chiral SU(3) symmetry. In addition we consider the number of colors (N,) in QCD as a large parameter relying on a systematic expansion of the interaction kernel in powers of l/N,. Since the baryon octet and decuplet states are degenerate in the large-N, Iimit of QCD the latter are included as explicit degrees of freedom in our scheme. The coupled-channel Bethe-Salpeter kernel is evaluated in a combined chiral and l / N c expansion including terms of chiral order Q 3 . In contrast t o previous coupled channel appro ache^^?^ that are based on the chiral Lagrangian, particular emphasis is put on the interplay of the regularization and renormalization of the scattering kernel and scattering amplitude. The use of phenomenological form factors or cutoff parameters is avoided. An important ingredient of the X-BS(3) scheme is a systematic and covariant on-shell reduction of the Bethe-Salpeter equation. This is required as to avoid an unphysical and uncontrolled dependence of the scattering amplitudes on the choice of chiral coordinates or the choice of interpolating fields. Given any scheme the on-shell scattering amplitude should not change if a different representation of the chiral Lagrangian is used. In the X-BS(3) scheme the on-shell reduction is implied unambiguously by the existence of a unique and covariant projector algebra which solves the Bethe-Salpeter equation for any choice of quasi-local interaction terms. The covariant projector algebra permits the application of dimensional regularization. In the language of the N/D method introduced by Chew and Mandelstam4 this leads to a strong correlation of the many subtraction constants, which arise when imposing a
603
604
S'~ [MeV]
Figure 1. Left panel: S- and p-wave pion-nucleon phase shifts. The single energy phase shifts are taken from7. Right panel: S- and pwave K+-nucleon phase shifts. The solid lines represent the results of the X-BS(3) approach. The open circles are from the Hyslop analysis8 and the open triangles from the Hashimoto analysisg
dispersion-integral representation for the unitarity loop function of a given partial wave. As compared to the scheme proposed recently by Oller and MeiBner5, which applies the N/D method, a significant parameter reduction is achieved in particular when higher partial wave amplitudes are considered. Approximate crossing symmetry of the amplitudes is guaranteed in the xBS(3) scheme by a renormalization program which leads to the matching of subthreshold amplitudes. For instance, the kaon- and antikaon-nucleon scattering amplitudes are shown to agree below threshold within their respective applicability domains. At subleading order Q2the chiral SU(3) Lagrangian predicts the relevance of 12 basically unknown parameters, which all need to be adjusted to the empirical scattering data. It is important to realize that chiral symmetry is largely predictive in the SU(3) sector in the sense that it reduces the number of parameters beyond the static SU(3) symmetry. For example one should compare the six tensors which result from decomposing 8 €3 8 = 1 @ 8s @ 8~ €I3 10 @ €13 27 into its irreducible components with the subset of sU(3) structures selected by chiral symmetry in a given partial wave. Thus, static SU(3) symmetry alone would predict 18 independent terms for the s-wave and two p-wave channels rather than the 12 chiral Q2 background parameters. The number of parameters was reduced further by insisting on large-Nc sum rules for the symmetry conserving quasi-local two body interaction terms. All together there remain 5 parameters only, all of which are found to have natural size. At chiral order Q3 the number of parameters increases significantly unless further constraints from QCD are imposed. A systematic expansion of the in-
605
Figure 2. Coefficients A1 and Az for the K - p -+ no& K - p + d C * and K - p -+ a°C differential cross sections, where d ' ( ~ ; ~ ~ e ) = An(&) Pn(cos 0). The data are taken from lo. The solid lines are the result of the X-BS(3) approach with inclusion of the d-wave rescnances. The dashed lines show the effect of switching off d-wave contribut ions.
c:=p,,
200
300
400
200
300
400
200
300
400
500
P,,, [MeV1
teraction kernel in powers of l/Nc leads to a much reduced parameter set. For example the l/Nc expansion leads to only four further parameters describing the refined symmetry-conserving two-body interaction vertices. This is to be compared with the ten parameters found to be relevant at order Q3 if largeN , sum rules are not imposed. At order Q3 there are no symmetry-breaking 2-body interaction vertices. To that order the only symmetry-breaking effects result from the refined 3-point vertices. A particularly rich picture emerges. At order Q3 there are 23 parameters describing symmetry-breaking effects in the 3-point meson-baryon vertices. For instance, to that order the baryonoctet states may couple to the pseudo-scalar mesons also via pseudo-scalar vertices rather than only via the leading axial-vector vertices. Out of those 23 parameters 16 contribute at the same time to matrix elements of the axialvector current. Thus, in order to control the symmetry breaking effects, it is mandatory to include constraints from the weak decay widths of the baryon octet states also. A detailed analysis of the 3-point vertices in the l/Nc expansion of QCD reveals that in fact only ten parameters, rather than the 23 parameters, are needed at leading order in that expansion. Since the leading parameters together with the symmetry-breaking parameters describe at the same time the weak decay widths of the baryon octet and decuplet ground states, the number of free parameters does not increase significantly at the Q3 level if the large-N, limit is applied.
606
In the left panel of Fig. 1 we confront the result of our global fit with the empirical 7rN phase shifts. All s- and p-wave phase shifts are well reproduced up to fi e 1300 MeV with the exception of the S11 phase for which our result agrees with the partial-wave analysis less accurately. One should not expect quantitative agreement for fi > m N 2 m, e 1215 MeV where the inelastic pion production process, not included in this work, starts. The missing higher order range terms in the S11 phase are expected to be induced by additional inelastic channels or by the nucleon resonances N(1520) and N(1650). In the right panel of Fig. 1 we confront the s- and p-wave Kf-nucleon phase shifts with the most recent analyses by Hyslop et a1.8 and Hashimoto’. The phase shifts are reasonably close to these single energy phase shifts except the Po3 phase for which we obtain much smaller strength. Note however, that at higher energies the single energy phase shifts of Hashimoto’ are reached smoothly. In Fig. 2 we compare the empirical ratios A1/Ao and A2/Ao of the elastic and inelastic K - p scattering with the results of the X-BS(3) approach. For plab < 300 MeV the empirical ratios with n 2 3 are compatible with zero within their given errors. A large A1/Ao ratio is found only in the K - p + 7roA channel demonstrating the importance of p-wave effects in the isospin one channel. The dashed lines of Fig. 2, which are obtained when switching off d-wave contributions, confirm the importance of the A( 1520) resonance for the angular distributions in the isospin zero channel. The latter resonance is included in the X-BS(3) approach as part of a baryon nonet resonance field. For details we refer to’.
+
References
1. M.F.M. Lutz and E.E. Kolomeitsev, Nucl. Phys. A 700,193 (2002). 2. N. Kaiser, P.B. Siegel, W. Weise, Nucl. Phys. A 594,325 (1995). 3. E. Oset, A. Ramos, Nucl. Phys. A 635,99 (1998). 4. G.F. Chew, S. Mandelstam, Phys. Rev. 119,467 (1960). 5. U.-G. MeiDner, J.A. Oller, Nucl. Phys. A A 673,311 (2000). 6. S. Kondratyuk, A.D. Lahiff, H.W Fearing, Phys. Lett. B 521,204 (2001). 7. R.A. Arndt et al., Phys. Rev. C 52,2120 (1995). 8. J.S. Hyslop et al., Phys. Rev. C 46,961 (1992). 9. K. Hashimoto, Phys. Rev. C 29, 1377 (1984). 10. T.S. Mast et al., Phys. Rev. D 11,3078 (1975); R.O. Bangerter et al., Phys. Rev. D 23, 1484 (1981).
MEASUREMENT OF THE WEAK PION-NUCLEON COUPLING CONSTANT, H:, FROM BACKWARD PION PHOTO-PRODUCTION NEAR THRESHOLD ON THE PROTON R. SULEIMAN Jefferson Lab, MS 12H, 12000 Jefferson Ave, Newport News VA 23606, USA E-mail: [email protected]
The longest range weak pion-nucleon coupling constant, h:, is important for nuclear parity violation. However, after considerable effort in the past two decades, its value is still poorly known largely due to many-body theoretical uncertainties. Prospects of a new measurement of h: in a theoretically clean process are presented. A measurement of the parity-violating asymmetry in pion photoproduction off the proton is related to h: in a low-energy theorem for the photon polarization asymmetry at threshold in the chiral limit. At present two completed experiments - photon circular polarization for 18F and the anapole moment of 133Cs- have been interpreted to give very different values of h i . This experiment will be the first attempt to measure h: in the single nucleon system. A reliable measurement of h i provides a crucial test of the meson-exchange picture of the weak N N interaction. Such a test of the meson-exchange picture will shed light on low energy QCD.
1
Introduction
The nucleon-nucleon ( N N ) weak interaction is the last sector of the weak interaction where the main aspects of the electroweak theory have not been verified. In the presence of the nuclear interaction, the weak N N interaction can be isolated via parity violation. The most comprehensive theoretical treatment t o date t o describe the weak N N interaction is given in a review by Desplanques, Donoghue, and Holstein (DDH) '. Their best guess value of the weak pion-nucleon coupling constant is h i = 4.6 x The determination of hk from experimental measurements in nuclei are discussed in Reference '. There are substantial uncertainties in interpreting most experiments in nuclei because one can not make reliable calculations of the amplitudes of the weak meson-nucleon exchange potential operators. This measurement is free from nuclear structure uncertainties and is a clean measurement of hi.
607
608
---E,
= 160
MeV
E - = 180 MeV
-E, =
230 MeV
Y
0
30
60
90
120
150
180
elLab [degl Figure 1. Asymmetry of the differential cross section for T p pion Lab angle (h; = 4.6 x lo-').
2
+ nn+
as a function of the
Pion Photoproduction at Threshold
The weak interaction induced parity-violating asymmetry in low energy pion photoproduction was calculated by Chen and Ji '. They found that the photon helicity asymmetry:
A T
d o ( & = +1) - d o ( & = -1) = +I) d a ( & = -1)
- d+,
+
(1)
at the first non-vanishing order (NLO) in heavy-baryon chiral perturbation theory (HBxPT) at threshold is:
where fr is the pion decay constant and gA is the neutron decay constant. There is an extended threshold region in which the effective theory description remains effective and, at the same time, the cross section is appreciable. This region is between 180 and 230 MeV in laboratory photon energy. The higherorder corrections are expected to be O ( E T / M ~ )20%.
-
609 Table 1. Experimental conditions for the proposed measurement. Beam Energy Beam Current Beam Polarization
230 MeV 400 pA 80%
Radiator Thickness Photon Energy ( E , ) f (N7INe) Photon Polarization
3% r.l. Cu (0.043 cm) 230-180 MeV 0.006 75%
Target Luminosity (Is) Average Cross Section % ( y p Solid Angle Acceptance
80 cm LH2 0.5 x lo3' cm-2 sec-' 5x cm2/sr 1.0 sr
4
Experimental Asymmetry ( A )
ma+)
1.7x 1 0 - ~
The asymmetry A,(O") in the differential cross section for T p mr+ as a function of the pion Lab angle is shown in Fig. 1. Note the strong dominance of the photon polarization asymmetry at forward and backward angles in the threshold region. Only at angles near 90" and E-, > 200 MeV does the modification from high partial waves become significant.
3 Experimental Considerations
A polarized electron beam will be used to produce a circularly polarized photons by hitting a radiator. The electron beam will be deflected away through a chicane to a beam dump. The photon beam will be incident on a liquid hydrogen target. A toroidal magnet will bend the backward produced pions to a total absorption plastic scintillator detector. The expected counting rate is approximately 250 MHz. The detector will be out of direct view of the target and will operate in current mode. The experimental conditions are listed in Table 1. 1000 hours of beam time are required for 20% statistical accuracy. A high quality electron beam will be used to produce the photon beam with no amplification of any of the helicity correlated differences in beam parameters (energy, angle, and position). The total systematic uncertainty is anticipated to be smaller than the statistical one.
610 15
10
P
Y
5
k
r 0
-5
Figure 2. The projected error bar from this experiment compared to DDH theoretical estimate and other completed and planned experiments.
4
Summary
The weak pion-nucleon coupling constant will be measured in pion photoproduction to a high level of accuracy in a reasonable beam time. Fig. 2 shows values of h i : (from left to right) DDH theoretical estimate, 18Fexperiments 4 , 133Cs experiment 5 , and expected statistical uncertainty from LANSCE experiment (it will achieve this uncertainty in 9 months of data taking). The last value represents the expected statistical uncertainty from this experiment in 1.5 months of data taking. References
1. B. Desplanques, J. Donoghue, and B.R. Holstein, Ann. Phys. 124, 449 (1980). 2. E.G. Adelberger et al, Ann. Rev. Nucl. Part. Sci. 35, 501 (1985). 3. J.W. Chen and X. Ji, Phys. Rev. Lett. 86, 4239 (2001). 4. S.A. Page et al, Phys. Rev. C 35,1119 (1987). 5. C.S. Wood et al, Science 275, 1759 (1997). 6 . J.D. Bowman (Spokesperson) et al, “Measurement of the Parity-Violating Gamma Asymmetry A, in the Capture of Polarized Cold Neutrons by Para-Hydrogen, n’ p -+ d + y”, Proposal for DOE, 17 April 1998.
+
TO
+ yy TO NLO IN CHPT
JOSE L. GOITY Department of Physics, Hampton University, Hampton, VA 23668, and Thomas Jefferson National Accelerator Facility, Newport News, VA 23606. The x o + yy width is determined to next to leading order in the combined chiral and l/Nc expansions. It is shown that corrections driven by chiral symmetry breaking produce am enhancement of about 4.5% with respect to the width calculated in terms of the chiral-limit amplitude leading to rno+-,-,= 8.10 f 0.08 MeV. This theoretical prediction will be tested via T O Primakoff production by the PRIMEX experiment at Jefferson Lab.
1 Introduction
In QCD there are predictions whose character is fundamental: one of them is the 7ro -+ yy decay width. In the limit of exact s U ~ ( 2x) s U ~ ( 2chiral ) symmetry, i.e. when the u- and d-quark masses vanish, the decay amplitude is predicted by the chiral anomaly induced by the EM interaction on the axial current associated with 7ro Goldstone mode. This amplitude results in the width rnO+-,? = = 7.73 eV. Although this prediction agrees well with the world averaged experimental value, this has a generous error of about 7% that prevents the observation of deviations from the chiral limit prediction resulting from explicit chiral symmetry breaking by the quark masses. This situation will change with the PRIMEX experiment at Jefferson Lab that aims at a more precise measurement in the 1 to 2% range '. This talk reports on the theoretical prediction for such deviations including next to leading order corrections in the low energy expansion, and shows that indeed these deviations would be observable in that experiment. As shown in 2 , the non-vanishing u-and d-quark masses induce corrections to the 7ro -+ yy amplitude that can be predicted in the framework outlined below. These corrections are of two types: i) Mixing corrections induced by isospin breaking implying that the physical 7ro is not a pure isospin eigenstate having a projection on the pure U ( 3 ) states associated with the 77 and the 7'. They are controlled by the ratios (mu- md)/ms and N,(m, - m d ) / A , (A, is the chiral expansion scale, and N , the number of colors). ii) corrections controlled by the ratio m / A x , where 7fi = (mu+ m d ) / 2 . Since the first type of corrections turn out to be dominant, it is natural to work in a framework where the q and rf are included as active degrees of freedom. Such a framework is indeed available and consists in chiral pertur-
($-)2(q)3
61 1
612
bation theory (ChPT) with three light flavors supplemented with the l/Nc e x p a n s i ~ n ~In? this ~ . framework, the corrections i) start at leading order (LO), while the corrections ii) are of next-to-leading order (NLO). In this talk the calculation of the rate rrro+y7 including NLO corrections is outlined and the results discussed. 2
The decay amplitude
The two-photon decay amplitudes of the self-conjugate pseudoscalars are obtained from the Ward identity satisfied by the associated axial currents:
where M , is the quark mass matrix, eQ is the electric charge operator, FF = ~ E , , , , ~ ~ Fand ~ ” similarly F ~ ~ , GG = Considering the matrix elements of Eqn.(l) between the vacuum and two-photon states and selecting the pole terms generated by the physical K O , y and y’, it is possible to extract the twophoton transition amplitudes for these states. At NLO these matrix elements require a NLO calculation of the masses and the decay constants, as well as contributions due to excited states and continuum that are of type ii) and thus of NLO. The NLO masses and decay constants are calculated in the mentioned framework of ChPT and l/Nc expansion, while the contributions due to excited states are represented by an U ( p 6 )unnatural parity Lagrangian, the O ( p 6 ) Wess-Zumino (WZ) term. With the low energy counting in which l/Nc is a quantity of order p 2 , the NLO evaluation of masses and decay constants requires the chiral Lagrangian up t o order p4, which with standard notation reads: c = p )+ c(4)+ . . .
+ x t u ) - 21 ~ ; 7 T ; c(4) = Ls(DpUtDpU(xtU+ U t x ) )+ Lg(xUtxUt + h . ~ . ) + $A D , ~ T ~ D , T-~-iFoAz - - ~ T ~ ( x-ux ~ u ) , c(2)=
~F~(D,uD+ ~ u-1F ~ : ( X)U ~ 4
4
2 6
(2)
where only terms relevant for masses and decay constants are kept. Here U is the U (3 )matrix parametrized by the pseudoscalar nonet, where ~ T , Jis the singlet member whose mass in the chiral limit is MO when l/Nc corrections are disregarded. Note that terms such as the L4 and others are not included because they are O(p4 x l/Nc) = O(p6),and thus of NNLO. The terms A1,z represent l/Nc corrections. Since one-loop corrections with L(’)are of order O(p4 x l/Nc) O(p6),they ought to be neglected as well. The masses and decay constants are then extracted by calculating the two-point function of axial currents, and are given by:
613 Fo
where L58
+4L5Bo 3Fo ( m u+ md + 4ms); FOO= Fo(l+ -) + 8L5Bo (mu+ md + ms); 2 3Fo A1
2L8
- L5 and p
+ 2A2 - 8L5-L). FO MZ
-A1
The Oh6)WZ term relevant here is determined in terms of a single low energy constant t l , and reads:
L$Q7 = -i7ratl(X-Q2)FF;
u=
fi,X -
=u t p t
- uxtu.
(4)
The low energy constants are determined by fitting to the masses in the nonet, to F,+ and F K + , and to the two-photon decay widths of the q and q'. Corrections to Dashen's theorem are included for the extraction of isospin breaking by the quark masses. Unfortunately, tl cannot be determined from the fit and its estimate via QCD sum rules is used: t l _N -+(F," +), where m y _N m p . The term 7%
proportional to
T
+Md
involving the excited pion pole is small
and can be neglected.
3 Results and conclusions The two-photon amplitudes of the physical states for N, = 3 finally reads:
(77I R I T = ~ ~-)i o (-CaFG1 1 47r
+ ~ Bo - t i B a e ( { ~ " , M q } Q 2 )(77 ) I F F I O), FO
m,
(5)
where 7rg = 7ro, 7rg = q, and q=j = q', and c3 = 1 , c8 = I / & and CO= 0 is the mixing matrix determined from the mass matrix in the 7ro-71-77' subspace. The decay constant matrix in this subspace is defined by: ( r a , p I A; I 0) = -ippFaa,
614 where 8, = eSbFba,with Fat, the decay constant matrix in the basis of pure u(3) states as given in Eqn.(S). At LO only the first term in Eqn.(5) is left with Fa, = F&,, where 0 is determined from the LO mass formulas. At LO the 7ro width is enhanced as a result of the mixing by 4.5% from 7.73 to 8.08 eV, an effect first noted in Ref. '. The mixings with the 77 and 77' give similar contributions that add up; this is the reason why an analysis where the 77' is explicitly included is important for understanding the effect. The NLO result for the width is almost identical to the LO one: 8.10 eV. This stability is however non-trivial. The mixing matrix 0 is affected in the entries involving the 7ro by corrections of the order of 20%, but at the same time the decay constant matrix in the U(3) basis receives corrections that tend to undo those leaving the relevant decay constant matrix elements FToa almost unchanged. In the abscense of the O@) WZ term these NLO corrections amount to a 0.5% further increase in the width, which is then largely compensated by the estimated cointribution of the said WZ term. There are several sources of theoretical errors. The most important one is the uncertainty in the ratio R = ms/(md - m,) that largely determines the corrections due to mixing; this ratio is determined from MK0 - M K + after removing the EM contribution determined using the corrected Dashen theorem; this leads to R = 3 7 f 5 and an uncertainty in the T O width of 0.6%. Other uncertainties such as EM corrections and NNLO corrections are estimated to be in the 0.2-0.3% range. In all, it is expected that the overall uncertainty is below 1%. In conclusion, the theoretical prediction rTo+rr= 8.10 eV obtained in the framework of ChPT@l/N, indicates a substantial enhancement of about 4.5% over the prediction based on the chiral limit decay amplitude. The magnitude of this enhancement is such that it should be observed in the forthcoming 7ro lifetime measurement by the PRIMEX collaboration at Jefferson Lab where a measurement with a precision better that 2% is expected.
Acknowledgments The work reported here was done in collaboration with A. M. Bernstein and B. R. Holstein, and was in part supported by NSF grant PHY-9733343 and by DOE contract DE-AC05-84ER40150.
References 1. A. Gasparian, these proceedings. 2. J. L. Goity, A. M. Bernstein and B. R. Holstein, JLAB-THY-02-15. 3. P. Herrera-Siklbdy, J. I. Latorre, P. Pascual and J . Taron, Nucl. Phys. B497 (1997) 345, and Phys. Lett. B419 (1998) 326. 4. R. Kaiser and H. Leutwyler, Eur. Phys. J. C17 (2000) 623. 5. B. Moussallam, Phys. Rev. D51 (1995) 4939. 6. Fayyazuddin and Riazuddin, Phys. Rev. D37 (1988) 149.
THE DEPENDENCE OF THE "EXPERIMENTAL" PION NUCLEON SIGMA TERM ON HIGHER PARTIAL WAVES J.STAHOV Abilene Christian University, Abilene, T X , 79699, U S A E-mail: stahov@physics. acu. edu and Unzversity Tuzla, 35000 Tuzla, Bosnaa and Herzegovina A dependence of the value of the pion-nucleon sigma term on higher partial waves is discussed. Two recent predictions of a high value of the sigma term are scrutinized. It has been concluded that tha main reason for obtaining high values of the sigma term are input D waves that are not consistent with analyticity.
1
Introduction
The value of the 7rN sigma term C is given in terms of the D+amplitude (bar indicates that the pseudovector Born term is subtracted) at the Chang-Dashen (CD) point Y = 0, t = 2m:: C = F,2D+(V = 0, t = 2m,), 2 where F,=92.4 MeV is the pion decay constant. For details concerning the 7rN kinematics we refer to reference'. Generally, there are two kinds of methods used to calculate the D+amplitude at the CD point. The first method uses dispersion relations to calculate 2m:) directly. The second method determines the coefficients in the subthreshold expansion of the D+ amplitude:
o+(O,
D+(O,2m2,) = (c7,:o+d&t+Z$2t2+..); C = (c7,~o+Z~'t-t~~~t2+..)F,2 3 CD+AR, where C D denotes contributions from the first two terms, and AR is so a called curvature term that includes contributions of quadratic and higher terms. Obtained values for C range from 60 M e V to 93 MeV. It is of interest to understand which partial waves give important contributions to D+ in each of the above mentioned methods. It is clear that the leading contributions come from the input S and P waves, but earlier evaluations(see reference' and references therein) show that contributions from D and higher partial waves must not be neglected. 2
The role of the higher partial waves
In order to demonstrate the importance of the higher partial waves in determination of the C term, let's briefly describe two methods, that have produced
615
616
dramatically different results in the past few years. Gasser, Leutwyler, Locher, and Sainio(GLLS)2, proposed a method to improve results for Co previously derived from the KH80 solution by taking into account newer, mutually consistent meson factory data below pion lab. momentum k~ = 185 MeV/c. The method is based on six forward dispersion relations for the invariant amplitudes D + , B’, E* e &D’. D waves and higher partial waves are needed as a part of the input below a cutoff momentum ko. Above ko, results from one of the existing PW solutions are used. As a result, GLLS machinery predicts coefficients &o and in the subthreshold expansion. The curvature term was determined using another method3. Several further updates were made by Sainio. In reference4 a value C = 62 MeV was reported. Higher partial waves below cutoff momentum ko were taken from Ka85 solution’. It was pointed out that “results are rather insensitive to the choice of PW solution above the cutoff momentum”. The most recent update w a given in reference6. Results from SpOO solution7, including D waves below ko, were used. Obtained value, C = 93 MeV, is more than 50% higher than previously reported values. One concludes that GLLS machinery is sensitive to the input for D waves and higher partial waves below the cutoff momentum. Starting from the fixed-t dispersion relations for t = 2m:, Olsson’ derived a sum rule in which the value of the Df amplitude at the CD point is expressed in terms of the S, P, D-and higher partial waves threshold parameters. Using Koch’s values for the D-and higher partial wave scattering lengths, Olsson obtained value C = (71 f 9)MeV. Using D-and higher partial waves scattering lengths ,from VPI/GW solution SrnO17, Olsson and Kaufmanng recently obtained significantly higher values ranging from 80 MeV to 88 MeV. Common to both of these high evaluations of the sigma term was the use of the higher partial waves at low energy from the latest VPI/GW solutions. It is important to point out that below the GLLS cutoff momentum ko = 185 MeV/c reliable values for D and higher partial waves can not be obtained from experimental data only. One has to start from first principle in 7rN physics-Mandelstam analyticity and the analytic structure of the 7rN partial waves. Consistency of a given partial wave with analyticity can be tested using one of the methods developed in the past (see referencelo end references therein). In the hyperbolic partial wave relations (HPWR) a given s-channel partial wave is expressed in terms of other s-channel partial waves and the t-channel partial waves, multiplied by corresponding s-channel and t-channel kernels. Kernels, that are explicitly known, reproduce the analytic structure of the T N partial waves. In addition, there is also a contribution from nucleon exchange term that is explicitly known as well. The method is superior compared to
617
_"
0
0.1
0.2
Figure 1. Comparison of F+ :
0.3
0.4
0.5
0.6
form HPWR to input from SpOO
other methods when predicting higher partial waves (D waves and higher) in the low energy region ( k 5 500 MeV/c). In that case, there are two leading contributions-the nucleon exchange and the t-channel contribution. Due to behavior of the t-channel kernels, contributions from higher values of t are strongly suppressed, so that input available today makes it possible to obtain reliable predictions for the higher T N partial waves. For example, the main contribution to the isospin even combinations of D waves, FZ*, comes from the region t< 25m;. Recent calculation" shows that our input from the tchannel in that kinematical region is fairly well known. Results from HPWR for isospin even combinations of reduced partial waves ( F L = qZ/q1+' , see ref.') are shown in Fig.1 and Fig.2. It is evident that D waves from VPI/GW solution SpOO are not consistent with analyticity at low energies. For instance, the isospin even combination F$+ (shown in Fig.1) has the wrong sign.
3
Conclusions
D waves in the VPI/GW SpOO partial wave solution are not consistent with analyticity in the low energy region and are evidently wrong. Methods sensitive to the input D waves produce high values of the pion nucleon sigma term because of the low energy D waves from VPI/GW solutions. A high "experimental value" of the sigma term could be accepted as reliable only if partial waves from the input partial wave solution are consistent with analyticity.
618
loo 80
khan
+
0
0.1
0.2
0.3
0.4
0.5
0.6
Figure 2. Comparison of F$- from HPWR to input from SpOO
I wish to thank Prof. G. Hohler for his continuous support and valuable discussions. This work was supported by DOE project DE-FGO3-94ER40860 References
1. G. Hohler, Landolt-Bornstein, Vol. I/9b2, Pion-nucleon Scattering, Springer 1983. 2. J. Gasser, H. Leutwyler, M. Locher, and M.E. Sainio, Phys. Lett. B213, 85,(1988). 3. J. Gasser, H. Leutwyler, and M.E. Sainio, Phys. Lett. B253, 252(1991). 4. M.E. Sainio, 7rN Newsletter 13, 144(1997). 5. R. Koch, Z. Phys. C 29, 597(1985). 6. M.E. Sainio, Proc. from the Inst. for Nuclear Theory, Vol.l1,346, A.M. Bernstein, J.L. Goity, Ulf-G. Meifher, Editors, World Scientific 2000. 7. SAID 7rN database, http://gwdac.phys.gwu.edu. 8. M.G. Olsson, Phys. Lett. B428, 50 (2000). 9. M.G. Olsson, W.B. Kaufmann, will be published in 7rN Newsletter 16. 10. J. Stahov, will be published in 7rN Newsletter 16. 11. J. Stahov, In preparation.
FIRST BEAM-TARGET DOUBLE-POLARIZATION MEASUREMENTS USING POLARIZED HD AT LEGS A. LEHMANN', K. ARDASHEV', C. BADE', M. BLECHER3, C. CACACE4, A. CARACAPPA4, A. CICHOCKI', C. COMMEAUX', I. DANCHEV7, A. D'ANGELO', A. D'ANGELO', R. DEININGER', J.P. DIDELEZ', R. DI SALVO', C. GIBSON', K. HICKS', S. HOBLIT4, A. HONIG', T. KAGEYA3, M. KHANDAKER", O.C. KISTNER4, A. KUCZEWSK14, F. LINCOLN4, M. LOWRY4, M. LUCAS2, J. MAHON', H. MEYER3, L. MICEL14, D. MORICCIANNI', B. NORUM', B.M. PRJ3EDOM7, T. SAITOH3, A.M. SANDORF14, C. SCHAEdF', C. THORN4, K. WANG5, X. WE14, AND C.S. WHISNANT'. (THE LEGS SPIN COLLABORATION) 'James Madison U.'Ohio U., Virginia Tech., 4Brookhaven National Lab., U. Virginia, U. de' Paris-Sud (Orsay), U. of South Carolina, U. d i Roma 11 and INFN-Sezione di Roma, 'Syracuse U., lo Norfolk St. U
'
'
'
A new polarized target using HD in the solid phase has been developed for studies of the nucleon spin structure at Q 2 = 0 using pion photo-production. In combination with the high quality LEGS photon beam and a large solid angle spectrometer this target allows practically background-free measurements on the proton and on the neutron. The first beam-target double-polarizationdata taken with this target are reported here.
1
Introduction
With the development of the Strongly Polarized Hydrogen deuteride ICE target (SPHICE), LEGS (the Laser Electron Gamma Source) has started a program of double-polarization measurements. This unique target is complemented by the high quality polarized Compton backscattered photon beam at LEGS and the large acceptance Spin ASYmmetry (SASY) detector system built for these experiments. With the combination of SPHICE and SASY at LEGS, we are beginning a detailed study of pion photo-production and nucleon spin structure. The goal of these experiments is the measurement of the Gerasimov-DrellHeard (GDH) and the forward spin polarizability2 sum rules on the proton and on the neutron, from pion threshold to 470 MeV. The dominant contributions to these sum rules are contained in this energy region. In addition, these measurements will allow the extraction of double-polarization asymmetries, putting significantly stricter constraints on the multipole amplitudes of pion photo-production.
619
620
2
Experiment
2.1 LEGS Photon Beam
The photon beam at LEGS is produced by Compton backscattering of laser light from the 2.8 GeV electron beam at the National Synchrotron Light Source (NSLS) at Brookhaven National Laboratory. This electron energy, in combination with a new frequency quadrupled laser and a conventional ArIon laser, permits the production of tagged photons from pion threshold up to 470 MeV. The polarization of the photon beam is determined by the polarization of the incoming laser beam and known to an accuracy of better than 1%. This also allows a “random” flipping through various polarization states, linear and circular ones, by changing the polarization of the laser beam. A complete specification of the laser polarization is obtained by the measurement of the Stokes vector, Sl = (01, Ul, K}. The three components of this vector are Q 1 , the intensity of a 0’ polarized beam, Ul,the intensity of the beam polarized at +45”, and K , the intensity of a right circularly polarized beam. With the known polarization transfer functions, Pli,,,, (E,) or Pcircz,lar (E,), Sl can be transformed into the photon beam Stokes vector, S, ( E T )= {Qr (E,) , U, (E-,),V, (E,)}. The photon polarization is typically 270% throughout the tagging range.
2.2 Strongly Polarized Hydrogen deuteride ICE Target (SPHICE) SPHICE represents a new technology using molecular HD in the solid state3. These targets are very pure, with only 2 protons and 1 neutron per molecule. The sole background reactions stem from the ~ 2 0 % (by weight) of aluminum wires which are needed for cooling purposes. SPHICE is polarized in a low temperature (15-20 mK) and high field (1517 T) environment. The spin-lattice relaxation time TIof HD is long, but by adding a small concentration of ortho-H2 to the HD gas, the H (and D ) in HD can be polarized via spin-spin coupling4. Eventually, with a time constant of a few days, ortho-Hz decays into the magnetically inert para-Hz, and after typically ~ 4 days 0 the spins of HD are “frozen in”. The target used for the experiment reported here was polarized at ~ 1 8 mK and 15 T for 40 days. The TImeasured in-beam (1.25 K/0.65 T) was 13 days for l? and 36 days for 8 . The initial polarization obtained for hydrogen was 71%. However, due to numerous tests and manipulations done on this first target, the hydrogen polarization was 30 f3% when in-beam. This large drop in polarization is the result of, among other things, the equivalent of
621
five transfers of the target between the dilution refrigerator and the in-beam cryostat (IBC), and a detailed mapping of the relaxation time as a function of temperature and field. 2.3 Spin-ASYmrnety Array (SASY)
The Spin-Asymmetry detector array, SASY, determines angle, energy, and particle identity for all reactions induced by photons on hydrogen and deuterium over the entire LEGS energy range. In this way, a simultaneous measurement of the four pion photo-production channels n+n , n - p nop , and ,On is possible. The major detector subsystems are: the crystal box (an array of 432 NaI(T1) crystals), and a forward wall of plastic scintillator :.( 30% neutron efficiency) and Pb-Glass Cerenkov counters. Atomic events are rejected by a gas Cerenkov counter at 0" and an Aerogel detector covering angles out to 30". The space between the IBC and the crystal box is filled with a plastic scintillator, azimuthally segmented in 32 sections, extending the neutron coverage to 90". The pion solid angle coverage of SASY is about 3n.
3
Results
With the specifications of the photon polarization, the most general expression for the cross section on a longitudinally polarized target can be written as
where C (0; E,) is the 0"/90" beam polarization asymmetry on an unpolarized target, G (0; E,) is the f 4 5 " beam polarization asymmetry with longitudinal target polarization, E (0;E,) is the helicity cross section asymmetry, and P, is the longitudinal target polarization. To disentangle these asymmetries from data obtained with beam polarizations less than 100%requires measurement with four linear (OD, go", k45")as well as left and right circular polarizations. This is readily done at LEGS by randomly cycling the laser polarization through all six states. Data collected in this way with a longitudinally polarized target permits the extraction of and E (0; E,) simultaneously. (0; E,), C (0; E,), G (0;
622
With the help of the Eq. (1) asymmetries can be constructed from the beam polarization states Oo/900 linear, f45" linear, and left/right circular. The results are plotted in Figure 1, dependent on the pion azimuthal angle 4. The solid lines are the calculated distributions fitted simultaneously to the data in the three panels, with C,E , and G as the only free parameters.
0
:*
-0.5
+
Figure 1. Inclusive 7 G D + ?yo azimuthal angle dependence of the three asymmetries constructed from the data. The bottom panel shows the Oo/900beam polarization asymmetry, the center panel shows the asymmetry for f45' linear polarization and the top panel contains the left/right circular polarization asymmetry. The curves are simultaneous fits to the data.
As an example, in Figure 2 the results of these fits are shown for the inclusive pion photo-production reactions 9 + f i D + 7 ~ ' and 7 f i D + rTf as a function of the polar angle at E-, = 317 MeV. Both reaction channels were taken in the same data run. Note the quality of the results after a data taking period of only 3.5 days. These are the first simultaneous measurements of the double-polarization observables E and G.
+
623
Figure 2. Pion polar angle dependence for the beam asymmetry C (top) and the doublepolarization asymmetries G (center) and E (bottom) at E , = 317 MeV. The left panel is for the reaction 7 I?D --t T O , the right one for 7 f i D + T * .
+
+
Acknowledgments This work is supported by US Dept. of Energy under contract DE-ACO298CH10886 and by the US National Science Foundation. References
1. S.B. Gerasimov, Sou. J. Nucl. Phys. 2, 430 (1966); S.D. Drell and A.C. Hearn, Phys. Rev. Lett. 16,908 (1966). 2. V. Bernard, N. Kaiser, J. Kambor, and Ulf-G. Meissner, Nucl. Phys. B 38,315 (1992). 3. A. Honig, Q. Fan, X. Wei, A.M. Sandorfi and C.S. Whisnant, Nucl. Instrum. Methods A 356,39 (1995). 4. A. Honig, Phys. Rev. Lett. 19,1009 (1967).
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Session on Lattice QCD and Heavy Quarks Convenors K.-F. Liu S. Ohta
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LATTICE CALCULATION OF BARYON MASSES USING THE CLOVER FERMION ACTION D.G. RICHARDS Jefferson Laboratory, 12000 Jefferson Avenue, Newport News, VA 23606, USA M. GOCKELER, P.E.L. RAKOW Institut fur Theoretische Physik, Universitat Regensburg, 0-93040 Regensburg, Germany R. HORSLEY, C.M. MAYNARD Department of Physics & Astronomy, University of Edinburgh, Edinburgh EH9 SJZ, Scotland, UK
D. PLEITER, G. SCHIERHOLZ Deutsches Elektronen-Synchrotron DESY, John von Neumann Institute for Computing NIC/Deutsches Elektronen-Synchrotron DESY, D-15738 Zeuthen, Germany We present a calculation of the lowest-lying baryon masses in the quenched approximation to QCD. The calculations are performed using a non-perturbatively improved clover fermion action, and a splitting is found between the masses of the nucleon and its parity partner. An analysis of the mass of the first radial excitation of the nucleon finds a value considerably larger than that of the parity partner of the nucleon, and thus little evidence for the Roper resonance as a simple three-quark state.
1
Introduction
The calculation of the excited nucleon spectrum provides a theatre to explore many of the central questions in hadronic physics, including the applicability of the quark model, the r61e of excited glue, and the existence of “molecular” states. Recently, several lattice calculations of the masses of lowest-lying nucleon states have appeared, using a variety of fermion actions. In this talk, I describe a calculation of the mass of the lowest-lying negative-parity state using an O(a)-improved clover fermion action. By using a variety of volumes and lattice spacings, we are able to estimate finite-volume and finitelattice-spacing effects; further details of this calculation are provided in earlier papers. 5 ) 6 For a subset of our lattices, we also determine the mass of the first radial excitation of the nucleon. 1~29374
627
628
2
Calculational Details
There are two interpolating operators that we will consider in our measurement of the low-lying J = 112 nucleon spectrum:
Nii2’
=~ijk(uTCygdj)uk,
Nii2’ = ~ i j k ( u T C d j ) 7 5 ~ k . (1) These operators have an overlap with particles of both positive and negative parity; on a lattice periodic or anti-periodic in time, the best delineation that can be achieved is that of a forward-propagating postive-parity state, and a backward-propagating negative-parity one. The “diquark” piece of Nl couples upper, or large, spinor components whilst that of Nz couples an upper and a lower spinor component and hence vanishes in the non-relativistic limit. Thus we expect N1 to have a better overlap with the positive-parity ground state than N2. The expectation is that N2 couples primarily to the lightest radial excitation of the nucleon, which experimentally is the so-called Roper resonance ”(1440). The calculation is performed in the quenched approximation to QCD, using the the standard Wilson gluon action and the non-perturbatively improved “clover” fermion action. The quark propagators are computed using both local and smeared sources. Where possible, errors on the fitted masses are computed using a bootstrap procedure, but simple uncorrelated x2 fits are employed in the chiral extrapolations. 3
Results
The masses of the nucleon and its parity partner are obtained from fourparameter fits to the two-point correlators of N1. For the chiral extrapolation of the masses, we adopt the ansatz
+
(arnxl2= ( u M ~ )b z~( ~ r n , ) ~
(2)
where X is either N1I2+ or N1i2-. The leading non-analytic term in the quenched approximation is linear in rn,, but results for a M x are insensitive to this term, and indeed in the case of N112+ we find a coefficient whose central value differs in sign from that predicted. In order to compare our data to experiment, we show in Figure 1 the masses of the nucleon and its parity partner at each lattice spacing; we find good consistency between the lattice calculation and the physical values, despite systematic uncertainties due to the chiral extrapolation, finite-volume and the use of the quenched approximation.
629 I1
LO
3
I
I
-
GI-
t a
%l
I
I
nl
-
L
-
N(939) 0 Jacobi 0 Fuzzed
-
-
Figure 1. Masses of nucleon and its parity partner in units of TO’ where TO 0.5 fm. The labels “Jacobi” and “Fuzzed” refer t o two different nucleon smearing techniques used t o improve the signal for the ground-state masses.
The nature of the Roper, the first nucleon excitation, has long been debated. In Figure 2, we show the effective masses of the positive- and negativeparity states constructed from N l , and of the positive-parity state constructed using Nz for a quark mass around that of the strange; it is clear that the latter mass is considerably higher than that of the negative-parity state, and therefore much heavier than the Roper (1440). The ordering of the masses at each quark mass is also shown in the figure, revealing a mass splitting between the radial excitation and the nucleon parity partner comparable to that between the parity partner and the nucleon, in accord with other lattice calculations. 1,2,3 4
Conclusions
We have seen that the low-lying excited nucleon spectrum is accessible to lattice calculation, and that lattice calculations are already providing valuable insight, most notably through the lack of evidence for the Roper resonance as a naive three-quark state. Increasingly energetic excitations are subject to increasing statistical noise, and thus further precise calculations will require the full panoply of lattice technology, such as the use of anisotropic lattices. 2,8 Such lattice calculations will provide the vital theoretical complement to the experimental programme at Jefferson Laboratory and elsewhere.
630
1-
$ -
I
v
% +
* *
vNY ANY-
8 8 05-
a a = =
0 Ni"'
-
0 N:"'
I
OQ
u
s
tu
IS
1u
01
2s
I
Figure 2. The left-hand plot shows the effective masses of the positive-parity states using Ni (circles) and N2 (bursts), and negative-parity using N1 (diamonds). The right-hand plot shows the corresponding fitted masses at ( a / ~ o ) 0.02, ~ the middle points in Figure 1.
-
Acknowledgements This work was supported in part by DOE contract DEAC05-84ER40150 under which the Southeastern Universities Research Association (SUM) operates the Thomas Jefferson National Accelerator Facility, by EPSRC grant GR/K41663, and PPARC grants GR/L29927, GR/L56336 and PPA/P/S/l998/00255. MG acknowledges financial support from the DFG (Schwerpunkt "Elektromagnetische Sonden").
References
1. F.X. Lee and D.B. Leinweber, Nucl. Phys. (Proc. Suppl.) 73, 258 (1999). 2. F.X. Lee, Nucl. Phys. (Proc. Suppl.) 94, 251 (2001). 3. S. Sasaki (RBC Collaboration), Nucl. Phys. (Proc. Suppl.) 83 (2000) 206; S. Sasaki, T. Blum and S. Ohta, Phys. Rev. D65, 074503 (2002). 4. W. Melnitchouk et al., hep-lat/0202022. 5. D.G. Richards (LHPC and UKQCD Collaboration), Nucl. Phys. (Proc. Suppl.) 94, 269 (2001). 6. M. Gockeler et al. (LHPC/QCDSF/UKQCD Collaborations), Phys. Lett. B532, 63 (2002). 7. J.N. Labrenz and S.R. Sharpe, Phys. Rev. D54, 4595 (1996). 8. LHP Collaboration (R. Edwards et d.), in preparation.
NUCLEON MAGNETIC MOMENTS, THEIR QUARK MASS DEPENDENCE AND LATTICE QCD EXTRAPOLATIONS
A
T.R. HEMMERTA AND W. WEISEAlB Theoretische Physik, Physik Department, T U Miinchen 0-857‘7 Garching, Germany ECT*, Villa Tambosi, I-38050 Villazzano (Trento), Italy
1
Introduction
The chiral symmetry of QCD is spontaneously broken at low energies, leading to the appearance of Goldstone Bosons. For 2-flavor QCD we identify the resulting 3 Goldstone Bosons with the 3 physical pion states, the lowest lying modes in the hadron spectrum. In addition to being spontaneously broken, chiral symmetry is broken explicitly via the non-zero quark mass 7jl. in the QCD lagrangian. This explicit breaking is responsible for the non-zero masses m, of the pions. In the now experimentally established large-condensate scenario with parameter Bo one obtains m: = 2 7jl. Bo (1
+ O(hB0))
(1)
for this connection. At low energies QCD is represented by a chiral effective field theory (xEFT) with the dynamics governed by the Goldstone Bosons, coupling to matter fields and external sources. The important aspect for this work i s the fact that this xEFT incorporates both the information on the spontaneous and on the explicit breaking of chiral symmetry. We report on recent work utilizing xEFT to study the quark mass (pion mass) dependence of the magnetic moments of the nucleon. 2
The Calculation
We use xEFT with pions, nucleons and deltas as explicit degrees of freedom. When including matter fields with differing masses-as is the case between A(1232) and the nucleon-one has to make a decision on the power counting one employs. Throughout this work we follow the so called Small Scale Expansion (SSE) of refs.2. However, in one crucial aspect we differ from refs2: For the leading order N A transition lagrangian we employ
631
632
Figure 1.
which treats vector and axial-vector couplings C V , C A to this transition on a symmetric footing. Usually the (leading order) N A vector coupling is relegated to subleading order based on standard (“naive”) power counting arguments. Nevertheless, we find it necessary to resort to Eq.(2) to capture essential quark-mass dependent effects in the anomalous magnetic moments already at leading one-loop order, resulting in a better behaved perturbative expansion. Our goal is to study the quark (pion) mass dependence of the magnetic moments of the nucleon. Treating the electromagnetic field as an external vector source, to leading one-loop order-according to SSE-one has to evaluate 11 diagrams, displayed in Fig.1.
3
Isovector Anomalous Magnetic Moment
For the isovector anomalous magnetic moment one obtains
633
+N~LO,
(3)
where A is the nucleon-delta mass difference. Most of the parameters in this expression are known and specified in ref. ', except for K:, c v 1El. At a chosen regularization scale X we fit these 3 parameters to reproduce quenched lattice results for K , reported in ref. 3 . Note that these lattice data correspond to lattice pions heavier than 600 MeV. With the parameters now fixed one obtains the full curve in Fig.2, which at m, = 140 MeV comes very close to the physical isovector anomalous magnetic moment, indicated by the full circle. A priori it is not guaranteed that this extrapolation curve over such a wide range of quark (pion) masses would come anywhere near to the physical value, but remarkably it does so, albeit with a large error band (dashed curves). We also note that our approach rests on the assumption that for lattice data with effective pion masses larger than 600 MeV the differences between quenched and fully dynamical lattice simulations are small ', allowing us to utilize "Standard" instead of LLQuenchedl' xEFT methods. 4
Isoscalar Anomalous Magnetic Moment
To the same leading-one loop order in SSE one only obtains analytic quark mass dependence for the isoscalar anomalous magnetic moment K ~ : K,
= K:-- 8 E 2 M m ;
+N2L0.
(4 1
The 2 unknown couplings &t1Ez-parameterizing short-distance physics beyond the realm of XEFT-can again be fitted to lattice data
'.
5
Comparison with Pade-Formula
Combining isovector and isoscalar results one obtains the quark (pion) mass dependence of the magnetic moments of proton and neutron, as shown in the full line of Fig.3. Surprisingly our result is rather close-at least within the present error band-to the Pade-fit extrapolation formula of the Adelaide group 3 , shown as the dashed curve.
Acknowledgments The authors acknowledge partial support by BMBF and DFG.
634
6 5
4 Kv
3 2 1
0
0.2
0.6 m, [GeVI
0.4
0.8
1
Figure 2.
Figure 3.
References 1. T.R. Hemmert and W. Weise, preprint no. [hep-lat/0204005]; submitted to EPJA. 2. T.R. Hemmert, B.R. Holstein and J. Kambor, J. Phys. G24, 1831 (1998); Phys. Lett. B395, 89 (1997). 3. D.B. Leinweber, D.H. Lu and A.W. Thomas, Phys. Rev. D60, 034014 (1999).
HEAVY QUARK SPECTRUM FROM ANISOTROPIC LATTICES X. LIAO AND T. MANKE Physics Dept., Columbia University, New York, N Y 10027, USA
We present our results for the heavy meson spectrum from quenched lattice QCD calculations. By employing a fully relativistic anisotropic lattice action with very fine temporal resolution, we are able to calculate the heavy quark spectrum for a wide range of quark masses including both charm and bottom. Higher excitations such as the exotic hybrids and orbitally excited mesons are also obtained for the charmonium spectrum. Using several different lattice spacings, we perform a continuum extrapolation of the spectrum.
1
Introduction
The rich phenomenology and abundant accurate experimental data make the heavy quark system an ideal test bench for QCD and lattice QCD technique. It is crucial that we reproduce the observed hadron spectrum from first principles to justify predictions for more complicated quantities such as the weak matrix elements. However, the large separation of energy scales in the heavy quark system makes it difficult to study heavy quarks on a conventional isotropic lattice. This intrinsic space-time asymmetry of a system containing heavy quarks motivated the non-relativistic QCD However, the difficulty in controlling the systematic errors of NRQCD, including relativistic corrections, radiative corrections, and lattice discretization errors, calls for a fully relativistic study. The relativistic anisotropic lattice QCD 3,4 can be used to address these problems. In addition to bound states of quarks and anti-quarks, QCD also predicts the existence of states with explicit gluonic excitations such as glueballs and hybrids. The observation of such states will provide additional insight into the gluonic degrees of freedom in the non-perturbative regime of QCD.
635
636
2
Simulation details
We use a lattice gauge action in which the spatial-temporal and spatial-spatial plaquettes are weighted differently corresponding t o an explicit anisotropy:
where p and t o are the bare coupling and bare anisotropy. Similarly, we employ an anisotropic fermion action SgloVer= C,q(z>Q Q(Z) with Q given by
Q
= mo f vt
a, w070-tvs wiyi - 2 [Ct g o k p o k f Cs ‘ J k l F k l ] .
(2)
We choose Wilson’s combination of first and second order derivative, W, = V, - (a,/2)y,A,, to ensure the full projection property and to remove all doublers. For the clover coefficients, we use tree-level mean-field improved values t o remove the leading O ( a ) errors. We fix vs = l(or vt = 1 alternatively) and tune vt non-perturbatively by requiring that the lowest S-wave meson satisfy the relativistic dispersion relation at low momentum. The bare quark mass mo is tuned to reproduce the experimental mass value of the lowest spin-averaged S-wave meson. Our action is a generalization of the “Fermilab action” 6 , which can be considered as the special case with = 1. We construct meson operators using bilinears in the form of O i j k ( z ) = q(z) riAjAk q(z) ( ri is one of the 16 y matrices and Ai is lattice derivative). To vary the overlap of meson operator with the states of interest, we apply various smearing techniques for both the quark and gluon fields. As expected, we find link fuzzing quite important in suppressing the excited states of the hybrid mesons. The simulations we performed are listed in table 1. The lattice scales are set by 1P - 1s splitting.
3
Results and conclusions
We obtained a fairly complete charmonium spectrum (Fig. 1) including both the low lying mesons below the OD threshold and higher excitations such as the exotic hybrids ( J p c = l-+,Of-, a+-) and orbitally excited mesons (with orbital angular momentum up to 3). It has been shown that the velocity expansion of NRQCD has poor convergence for charmonium spin splittings. Our result for the P triplet splitting ratio R f s = ( 3 P-~’Ps)/(~S - 3P0)is
’
637 Table 1. Charmonium and Bottomonium Quenched Simulations. ~
Charmonium simulations
(6I ) Lat. Size ( N , , N t ) # Configurations - a;' [Gev]
(5.7, 2) (8, 32) 1950 1.945(26)
(5.9, 2) (16, 64) 1080 3.021(34)
(6.1, 2) (16, 64) 1010 4.292(49)
Bottomonium simulations
(P,0 Lat. Size ( N , , N t ) # Configurations a;' [Gev]
(5.9, 4) (8, 96) 700 6.76(24)
(6.1, 4) (16, 96) 660 10.57(31)
(6.3, 4) (16, 128) 450 15.15(81)
(6.5, 4) (16, 160) 710 20.9(2.2)
0.47(13) in the continuum limit, which agrees well with the experimental value of 0.478(5). This ratio removes the systematic errors from fixing the scale in a quenched calculation, but it is highly sensitive to relativistic corrections. A selection rule analysis shows that the width of a charmonium hybrid meson is narrow if it lies below the D**D ( S P wave) threshold which is 1.220 Gev above 1s. Our result for the 1-+ hybrid excitation is 1.361(41) Gev, slightly above the D**D threshold. However, the conclusion is not final due to known ambiguities in the the scale setting procedure for quenched simulations. We compare our 1-+ result to previous lattice results in Fig. 2 (left). We study in detail the spin splittings for bb states. Fig. 2 (right) shows the continuum extrapolation of the hyperfine splitting 3S1- 'So. Our result deviates significantly from NRQCD results, which we attribute partly to relativistic corrections. A linear fit gives 58.7(5.5) MeV, while a quadratic fit(assuming no O(au) errors) gives 51.1(3.1) MeV. For more detailed discussions, please refer to Ref. '. We demonstrate that a fully relativistic treatment of the heavy quark system is well suited to control the large systematic errors from isotropic lattices (Mat errors) and NRQCD simulations (Mwn corrections). In addition, the high temporal resolution of anisotropic lattices has dramatically reduced the statistical error of highly excited states. Remaining discrepancies with experiment should be addressed in full QCD calculations.
+
Acknowledgments
This work is supported by the U.S. Department of Energy. The numerical simulations were conducted on the QCDSP machines at Columbia University and Brookhaven's RIKEN-BNL research center.
638 References
1. G. Lepage et al., Phys. Rev. D, 46:4052, 1992. 2. C.T.H. Davies, The heavy hadron spectrum. hep-ph/9710394. 3. F. Karsch, Nucl. Phys. B, 205:285, 1982. 4. Colin Morningstar., Nucl. Phys. (Proc.SuppZ.), 53:914, 1997. 5. T.R. Klassen, Nucl. Phys. (Proc.SuppZ.), 73:918, 1999. 6. A.X. El-Khadra et al., Phys. Rev. D, 55:3933, 1997. 7. N.H. Shakespeare and H.D.Trottier, Phys. Rev. D, 58:034502, 1998. 8. P.R. Page et al., Phys. Rev. D, 59:034016, 1999. 9. P.R. Page, Nucl. Phys. A , 663:585, 2000. 10. X. Liao and T. Manke, Phys. Rev. D, 65:074508, 2002.
4.8 L::0
32
2.8
0- 1JPC
Figure 1. Charmonium spectrum from anisotropic lattice.
0
relativistic.5=5, N,=O
9
NRCICD, 5=1. N,=O [23]
4
NRCICD, +I.
N,=2
[a
45
20 I
0
0.1
,
,
,
,
0.2
as (fm)
Figure 2. Comparison to previous lattice results of charmonium hybrid meson 1-+ mass above 1.9 (Left) and bottomonium hyperfine splitting 3S1 - 'So (Right).
THE DOUBLY HEAVY BARYONS IN THE NONPERTURBATIVE QCD APPROACH I.M.NARODETSKI1 AND M.A.TRUSOV ITEP, Moscow, Russia E-mail: naro @heron.itep.ru We present some piloting calculations of the masses of the doubly heavy baryons in the framework of the simple approximation within the nonperturbative string approach. The simple analytical results for dynamical masses of heavy and light quarks and eigenvalues of the effective QCD Hamiltonian are presented.
The purpose of this talk is to present the results of the calculation of the masses and wave functions of the heavy baryons in a simple approximation within the nonperturbative QCD (see and references therein). The starting point of the approach is the Feynman-Schwinger representation for the three quark Green function in QCD in which the role of the time parameter along the trajectory of each quark is played by the Fock-Schwinger proper time. The proper and real times for each quark related via a new quantity that eventually plays the role of the dynamical quark mass. The final result is the derivation of the Effective Hamiltonian, see Eq. (1) below. In contrast to the standard approach of the constituent quark model the dynamical mass mi is not a free parameter but it is expressed in terms of the current mass m,(O)defined at 1 GeV from the condition of the minimum of the appropriate scale of p = 0. Technically, this has the baryon mass MB as function of mi: been done using the einbein (auxiliary fields) approach, which is proven to be rather accurate in various calculations for relativistic systems. This method was already applied to study baryon Regge trajectories and very recently for computation of magnetic moments of light baryons ‘. The essential point of this talk is that it is very reasonable that the same method should also hold for hadrons containing heavy quarks. As in we take as the universal parameter the QCD string tension CT fixed in experiment by the meson and baryon Regge slopes. We also include the perturbative Coulomb interaction with the frozen coupling a s ( l GeV) = 0.4. Consider the ground state baryons without radial and orbital excitations in which case tensor and spin-orbit forces do not contribute perturbatively. 5survives in the perturbative approximation. The EH has the following form N
639
640 where Ho is the non-relativistic kinetic energy operator, m y ) are the current quark masses and mi are the dynamical quark masses to be found from the minimum condition, and V is the sum of the perturbative one gluon exchange potential V, and the string potential Vstring. The string potential has been calculated in as the static energy of the three heavy quarks: K t r i n g ( T 1 , ~ 2T Q , ) = DRmin, where Rminis the sum of the three distances Iril from the string junction point, which for simplicity is chosen as coinciding with the center-of-mass coordinate. We use the hyper radial approximation (HRA) in the hyper-spherical formalism approach. In the HRA the three quark wave function depends only on the hyper-radius R2 = p2 X2, where p and X are the three-body
+
Jacobi variables: pij = f
i ( ~ i - ~ j ) X, i j
=
@(
m i mi+mj ri+mjrJ
- T k ) , where
(mi+m.)mc
mim. mi+,&
and p is an arbitrary parameter with the = ? k j , k = mi+mj;mk 7 dimension of mass which drops off in the final expressions. Introducing the reduced function x ( R ) = R5I27)(R)and averaging V = V, -t over the six-dimensional sphere one obtains the Schrodinger equation
b j
'(
)+2p
2 dR2R
a E,+--bR-R
[
where
We use the same parameters as in Ref. 5 : o = 0.17 GeV, as = 0.4, m$) = 0.009 GeV, mLo)= 0.17 GeV, mio)= 1.4 GeV, and mp) = 4.8 GeV. We solve Eq. (2) by the variational method introducing a simple variational Ansatz x ( R ) N R5/2e-ppZR2, where p is the variational parameter. Then the threequark Hamiltonian admits explicit solutions for the energy and the ground state eigenfunction: E M min E(p),where P
The dynamical masses mi and the ground state eigenvalues Eo are given for various baryons in Table 1 of Ref. '. The dynamical values of light quark mass m, N &?I 450 - 500 MeV ( q = u, d , s ) qualitatively agree with the results of Ref. obtained from the analysis of the heavy-light ground state mesons. For the heavy quarks (Q = c and b ) the variation in the values of their dynamical masses mQ is marginal. This is illustrated by the
-
641 Table 1. Comparison of results of analytical and numerical variational calculations for Ab and Ac baryons (all quantities are in units of GeV)
Baryon
0.56 4.84
mn
0.52 1.50
0.56 4.82
0.53 1.47
simple analytical results for Qud baryons. These results were obtained from = 0 in the form of expansion in the approximate solution of equation
I
P=Po
the small parameters [ = &/m$) and a,. Omitting the intermediate steps one has
E~ = 3 6
( n-5 )
mQ = m$) (1
114
(1
+ A . [ - -53B
. ff,
+ . ..
)
+ 2A.E2-t. . . )
fi.
(8)
where for our variational Anzats A = Accuracy ‘I4, B = of this approximation is illustrated in Table 1. To calculate hadron masses we, as in Ref. 3 , first renormalize the string C Ci, where the constants Ci take into account potential: ---f
+
i
the residual self-energy (RSE) of quarks. In what follows we adjust the RSE constants Ci to reproduce the center-of-gravity for baryons with a given flavor. As a result we obtain C, = 0.34, C, = 0.19, C, Cb 0. We keep these parameters fixed to calculate the masses given in Table 2, namely the spin-averaged masses (computed without the spin-spin term) of the lowest double heavy baryons. In this Table we also compare our predictions with the results obtained using the additive non-relativistic quark model with the power-law potential 6, relativistic quasipotential quark model ’, the Feynman-Hellmann theorem and with the predictions obtained in the approximation of double heavy diquark ’. In conclusion, we have employed the general formalism for the baryons, which is based on nonperturbative QCD and where the only inputs are u , N
N
642 Table 2. Masses of baryons containing two heavy quarks
State E{qcc} fl{scc} Z{qcb} R{scb} E{qbb} R{sbb}
present work 3.69 3.86 6.96 7.13 10.16 10.34
Ref. 3.70 3.80 6.99 7.07 10.24 10.30
Ref. 3.71 3.76 6.95 7.05 10.23 10.32
Ref. 3.66 3.74 7.04 7.09 10.24 10.37
Ref. 3.48 3.58 6.82 6.92 10.09 10.19
a, and two additive constants, C, and C,, the residual self-energies of the light quarks. Using this formalism we have also performed the calculations of the spin-averaged masses of baryons with two heavy quarks. One can see from Table 2 that our predictions are especially close to those obtained in Ref. using a variant of the power-law potential adjusted to fit ground state baryons. Acknowledgements
This work was supported in part by RFBR grants ## 00-02-16363 and 0015-96786. References
1. 1.M.Narodetskii and M.A.Trusov, Yad. Fiz., 65, in press [hepph/0104019] 2. Yu.A.Simonov, Lectures given at the XVII International School of Physics ”QCD: Perturbative or Nonperturbative” , Lisbon 1999 [hep-ph /9911237] 3. M.Fabre de la Ripelle and Yu.A.Simonov, Ann. Phys. (N.Y.) 212, 235 (1991). 4. B.O.Kerbikov, Yu.A.Simonov, Phys. Rev. D62, 093016 (2000). 5. Yu.S.Kalashnikova and A.Nefediev, Phys. Lett. B 492, 91 (2000). 6. E.Bagan et al. Z.Phys. C 64, 57 (1994). 7. D.Ebert et al., Z. Phys. C 76, 111 (1997). 8. R.Roncaglia et al., Phys. Rev. D 52, 1248 (1995). 9. A.K.Likhoded and A.I.Onishchenko, hep-ph/9912425
EXCITED BARYONS AND CHIRAL SYMMETRY BREAKING OF QCD FRANK X. LEE Center for Nuclear Studies, George Washington University, Washington, DC 20052, USA and Jefferson Lab, 12000 Jefferson Avenue, Newport News, VA 23606, USA N* masses in the spin-l/Z and spin-3/2 sectors are computed using two nonperturbative methods: lattice QCD and QCD sum rules. States with both positive and negative parity are isolated via parity projection methods. The basic pattern of the mass splittings is consistent with experiments. The mass splitting within the same parity pair is directly linked to the chiral symmetry breaking QCD.
1
Introduction
There is increasing experimental information on the baryon spectrum from JLab and other accelerators (as tabulated in the particle data group I ) , and the associated desire t o understand it from first principles. The rich structure of the excited baryon spectrum provides a fertile ground for exploring how the internal degrees of freedom in the nucleon are excited and how QCD works in a wider context. One outstanding example is the parity splitting pattern in the low-lying N* spectrum. The splittings must be some manifestation of spontaneous chiral symmetry breaking of QCD because without it, QCD predicts parity doubling in the baryon spectrum. 2
Lattice QCD
Lattice QCD plays an important role in understanding the N* spectrum. One can systematically study the spectrum sector by sector, with the ability to dial the quark masses, and dissect the degrees of freedom most responsible. Given that state-of-the-art lattice QCD simulations have produced a ground-state spectrum that is very close to the observed values 2 , it is important to extend the success beyond the ground states. There exist already a number of lattice studies of the N* spectrum focusing mostly on the spin-1/2 sector. All established a clear splitting from the ground state. Here, we focus on calculating the excited baryon states in the spin-312 sector. We consider the 334,5967778,
following interpolating field with the quantum numbers I ( J p ) =
643
(:+),
644
The interpolating fields for other members of the octet can be found by appropriate substitutions of quark fields. Despite having an explicit parity by construction, these interpolating fields couple to both positive and negative parity states. A parity projection is needed to separate the two. In the large Euclidean time limit, the correlator with Dirichlet boundary condition in the time direction and zero spatial momentum becomes
where f,,is a function common to both terms. The relative sign in front of provides the solution: by taking the trace of GCly(t) with (1f y4)/4, one can isolate M+ and M-, respectively. It is well-known that a spin-3/2 interpolating field couples to both spin312 and spin-1/2 states. A spin projection can be used to isolate the individual contributions in the correlation function G,, g . Numerical test of spin projection in the spin-3/2+ channel reveals two different exponentials in G ( t )from the spin-3/2+ and spin-1/2+ parts, with the spin-3/2+ state heavier than the spin-1/2+ one, which is consistent with experiment. One would mistake the dominant spin-1/2+ state for the spin-3/2+ state without spin projection. Figure 1 presents preliminary resuIts for mass ratios extracted from the correlation functions for the 3/2+ N* states to the nucleon ground state as a function of ( ~ / p ) Mass ~ . ratios have minimal dependence on the uncertainties in determining the scale and the quark masses, so that a more reliable comparison with experiment can be made. These ratios appear headed in the right direction compared to experiment where available] but more study is needed to address the systematics. Figure 2 shows the similar plots for the 3/2- N* states.
74
3
QCD sum rules
The QCD Sum Rule method l o is a time-honored method that has proven useful in revealing a connection between hadron phenomenology and the nonperturbative nature of the QCD vacuum via only a few parameters (the vacuum condensates). It has been successfully applied to a variety of observables in hadron phenomenology, providing valuable insights from a unique, QCDbased perspective, and continues an active field. The method is analytical (no path integrals!)] is physically transparent (one can trace back to the QCD
645 2.2 2.0 1.8
l.8
I
I
2.2
1
-*
-
- 1720+/938
+ 1.4 -
ih$
c 1.2 1.0
-
0.8
-
-
Iai
-
-
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-
0.8
-
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"
. . " . ..... ".*
A,
*.
I
22
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1.6
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1.8
h + 1.6
h + 1.6
2
12
e 1.2
w
1.0
k
N 1.4 \
N 1.4
1.0 0.8
0.6
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nu
0.6
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A.
$ 1.2 -
2.0 ~
1.6
N 1.4
*
1
4 1890+/938
h + 1.6
I
0.6
1
2.0
0.2
0.4
0.8
1.0
0.0
0.2
0.4
0.8
1.0
Figure 1. Mass ratios for the 3/2+ N* states as compared to experimental values where available.
operators responsible), and has minimal model dependence. The accuracy of the approach is limited due to limitations inherent in the operator-productexpansion (OPE), but well understood. One progress in this area is the use of Monte Carlo-based analysis to explore the predictive ability of the method for N* properties The idea is to probe the entire QCD parameter space and map the error distribution on the OPE side to the phenomenological side. It is found that some QCD sum rules are truly predictive for N* masses, while others are marginal. Another progress is that a parity separation similar to that in lattice QCD can be performed in the QCD sum rule approach, resulting in the so-called parity-projected sum rules which has the general structure 11712713.
14115t16
A(M,w+)+ B(M,w+)
646 2.2 2.0 1.8
>=1 1.8 \
1.4
e
1.2
k
1.0 0.8
I
I
2.0
€
-*
-
1620-/938
A
*A*
I
I
-
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-
-
2
-
4 1.0
I
3 1.2 N 1.4
8
-
,
I
,
-*
1.8 -1820-/938 - h 1.6 - NI 1.4 1.2 - IZI 1.0 0.8 -
$
.A
I
-
%
2.2
' a
I
0
1520-/938
0.6
I
-
I
1
6
-*
1.2 -
2.0
*
,
N 1.4
I
hI 1.8 -k30-/938
I
-
2
>=I 1.6
0.8 I
2.0
0.8
*,
-
2.2
0.8
-
a .
0.6
1.0
2.2
I
-
€ li i
0.8
1
. I
Figure 2. Similar to Figure 1, but for the 3/2- N* states.
A(M,w-)- B(M,w-)= A-exp -2
(5)
where M is the Bore1 mass parameter, (mB,X2,w) are the phenomenological parameters (mass, coupling, threshold). The term B controls the mass splitting: if B = 0, then m+ = m-. Term B involves only dimension-odd condensates, such as the quark condensate (ijq) and the mixed condensate (ijgu . Gq). So a direct link is established between the mass splitting of parity pairs and dynamical chiral symmetry breaking of QCD. Fig. 3 shows a numerical confirmation in the case of nucleon. As (44)is decreased, both masses decrease, but with a different rate. N L - falls faster than N ; + . As a result, the mass splitting decreases. In the fimit that chiral-symmetry is restored ((qq)=O), it is expected that N;+ and N + - become degenerate. In conclusion, we can compute the baryon spectrum in the spin-1/2 and spin-3/2 sectors for all particle channels using two methods: lattice QCD and QCD sum rules. Parity projection further reveals that the mass split-
647
2.0
-
T
-1
I
I
I
I
I
1.8
A
% 0
-
1.6
/ /
ul K!
/
/
4 1.4 FI
s
1.2
ZZ
1.0
d
; 0.8 0.4
I\
/
1/;
/
I
I
0.6
I
0.8 1.0 1.2 1.4 Quark Condensate Ratio
1.6
Figure 3. Mass splitting between N L - and N I
as a function of the quark condensate. The ratio is relative to the standard value of a = - ( 2 7 ~ ) (~q q ) = 0.52 GeV3. 2
z+
ting within the same baryon pair is directly controlled by spontaneous chiral symmetry breaking of QCD.
Acknowledgments
This work is supported in part by U S . Department of Energy under grant DE-FG02-95ER40907.
648
References
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649
Reception at the Mariner's Museum
Dinner at the Mariner's Museum
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List of Participants Afanasev, Andrei Jefferson Lab 12000 Jefferson Avenue Newuort News. VA 23606. USA afan&Mab.org (757) 269-725 1
Agbakpe, Peter Jefferson Lab 12000 Jefferson Avenue Newuort News, VA 23606, USA pagbakuekjlilablorg (757) 269-5028
Ahmidoueh, Abdellah North Carolina A&T State University Department of Physics 1601 East Market Street Greensboro, NC 27407, USA abdellah@,ilab.org (336) 334-7646
Alessandro, Braghieri INFN-Pavia 6, Via Bassi Pavia, 27100 Italy braghieri@,uv.infn.it +39 0382 507628
Anderson, Bryon Kent State University Physics Department 105 Smith Hall Kent. OH 44242. USA anderson@huaca:kentedu (330) 672-4899
Arrington, John Argonne National Lab 9700 S Cass Avenue Building #203 Areonne .IL 60439 joL*,ah, gov (630) 252-3619
Avagyan, Harut Jefferson Lab 12000 Jefferson Avenue Newuort News. VA 23606 [email protected] (757) 269-7764
Baker, Keith Hampton University 130 East Tyler Street Hampton ,VA 23668 USA baker@,ilab.org (757) 727-5239
Barnes, Peter Los Alamos National Lab Physics Division, MS H846 Los Alamos ,NM 87545 USA [email protected] (505) 667-2000
Beeher, Thomas SLAC, MS81 2575 Sand Hill Road Menlo Park, CA 94025 USA tpbecher@,SLAC.stanford.edu (650) 926 4415
Beise, Elizabeth University of Maryland Department of Physics College Park. MD 20742 USA beise&hvsics.umd.edu (301) 405-6109
Bennhold, Cornelius George Washington University Department of Physics Washington, DC 20052 USA bennhold@,m.edu (202) 994-6274
651
652 Bernstein, Aron MIT 26-419 Cambridge, MA 02139 USA [email protected] (617) 253-2386
Bertin, Pierre Universite Blake Pascal 28 rue des Meuniers Clermont Ferrand, 63000 France [email protected] +33 73 40 72 76
Bianchi, Nicola INFN Frascati Casella Postale 13 Frascati ,00044 Italy bianchi@hermes,desV.de +39 0694 032320
Bisplinghoff, Jens University of Bonn Inst. her Strahlen- u. Kernphysik Nussallee 14-16 BOM.D 53115 Germanv [email protected] +49 228 i3 2543
Black, Deirdre Jefferson Lab Theory Group MS 12H2 12000 Jefferson Avenue Newport News, Va 23606 USA [email protected] (757) 269-7412
Bloch, Frederic Basel University Department of Physics and Astronomy Klingelbergstrasse 82 Basel ,CH-4056 Switzerland frederic.bloc~unibas.ch +41 61 267 37 31
Borasoy, Bugra Technische Universitaet Muenchen Institut h e r theoretische Physik T39 Physik Department Garching -, D-85747 Germanv borasov@,Dhvsik.tu-muenchen.de +498928912390
Boyarinov, Sergey Jefferson Lab 12000Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-5795
Brash, Edward University of Regina Department of Physics 3737 Wascana Parkway Regina. SK S4S OA2 Canada brash@,urepinaca (306) 585-4201
Briscoe, William George Washington University Department of Physics 725 21st Street, NW Washington ,DC 20052 USA briscoe(ii,gwu.edu (202) 994-6788
Brooks, Will Jefferson Lab 12000 Jefferson Avenue NewDort News. VA 23606 USA [email protected] (757) 269-7391
Bruell, Antje MIT 26-551 77 Massachusetts Avenue Cambridge, MA 02139 USA [email protected] (617) 253-3208
-
~
-
I
653 Burkert, Volker Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7540
Butuceanu, Cornel College of William &Mary P.O. Box 8795 Williamsburg ,VA 23187-8795 USA [email protected] (757) 221-1987
Capstick, Simon Florida State University Department of Physics Tallahassee, FL 32306-4350 USA [email protected] (850) 644-1724
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Carlini, Roger Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7255
Carlson, Carl College of William and Mary Physics Department P.O. Box 8795 Williamsburp.. VA 23187 USA [email protected] (757) 269-7376
Cassing, Wolfgang Universitaet Giessew Institut h e r Theoretische Physik Heinrich-Buff-Ring 16 Giessen ,35392 Germany Wolfgang.Cassm4xheo.Dhvsik.uni-giessen.de +49 6419 933310
Cha, Jinseok Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-5326
Chen, Jian-ping Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA jpchenO,ilab.org (757) 269-7413
Christy, Micheal Hampton University 130 East Tyler Street Hamoton. VA 23668 USA CHR~STYQJLAB.ORG (757) 269-5327
Chudakov, Eugene Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-6959
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654 Cords, Dieter Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7526
Covrig, Silviu Caltech 12000 Jefferson Ave. MS16,Rm116 Newport News, VA ,23606 USA covrig@,ilab.org (757) 269-5804
Crannell, Hall The Catholic University of America Physics Department Washington. DC 20064 USA crannell@cuaedu (202) 319-5313
D'Angelo, Annalisa Universita' di Roma Dip. di Fisica Via della Ricerca Scientifica, 1 Rome, 1-00133 Italy [email protected] + 39 06 72594562
Davies, Christine University of Glasgow Department of Physics and Astronomy Glasgow , G62 6BB UK [email protected] +44 141 3304710
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De Vita, Raffaella INFN Genova Dipartimento di Fisica via Dodecaneso 33 Genova , 16146 ltaly devit&,ge.infn.it +390103536382
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Diakonov, Dmitri NORDITA Blegdamsvej 17 Couenhaaen ,DK-2100 Denmark diakonov&ordita.dk +45 35 32 53 12
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I
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655 Diehl, Markus RWTH Aachen lnst. f. Theoret. PhysikE Aachen ,52056 Germany mdiehlf&hysik.rwth-aachen.de +49 241 8027 049
Domingo, John Jefferson Lab 12000 Jefferson Avenue Newoort News. VA 23606 USA dom&ol@ilab:org (757) 269-7124
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Huber, Garth University of Regina Department of Physics Regina, SK S4S OA2 Canada [email protected] (306) 585-4240
Ibrahim, Hassan Old Dominion University 1049 W 49 th Street Apt 317 Norfolk, VA 23508 USA [email protected] (757) 683-3484
Ilieva, Yordanka George Washington University 344C Street Thomas Drive Newport News, VA 23606 USA jordanka@,ilab.org (757) 269-6671
Ito, Mark Jefferson Lab 12000 Jefferson Avenue Newoort News. VA 23606 USA [email protected] (757) 269-5295
Janssen, Stijn Ghent University Dep. of Subatomic & Radiation Physics Proeftuinsttaat 86 Gent, 9000 Belgium [email protected] +32 9 265 65 53
Jenkins, David Virginia Tech Physics Department Blacksburg, VA 24061-0435 USA jenkins@,ilab.org (540) 552-3747
Jeschonnek, Sabine The Ohio State University 310 A, Science Building 4240 Campus Drive Lima. OH 45804 USA [email protected] (419) 995 8201
Jiang, Xiaodong Rutgers University/JLab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-70 1 1
Jones, Mark Jefferson Lab 12000 Jefferson Avenue Newport News ,VA 23606 USA jonesO.ilab.org (757) 269-7255
Joo, Kyungseon Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7764
658 Kaiser, Ralf University of Glasgow Department of Physics and Astronomy Kelvin Building Glasgow , G 12 SQQ UK r. kaiser@,~hvsics.ala.ac.uk +44 141 3305287
Kasagi, Jirohta Tohoku University LNS Mikamine 2-1-2, Taihaku Sendai ,982-0826 Japan kasagi@,lns.tohoku.ac.iu +81 22 743 3420
Keppel, Cynthia Hampton U. I Jefferson Lab Physics Department, Olin 102 Hamoton. VA 23668 USA ketmel@,ilab.org (757) 269-7580
Klein, Fritz University of Bonn Physikalisches lnstitut Nussallee 12 Bonn , D-53 1 I5 Germany
.
>
kleint&hvsik.uni-bonn.de +49 228 73 2340,-234
Klein, Franz Catholic University of America Physics Department Hannon Hall 210 Washington, DC 20064 USA kleinf@,cua.edu (202) 319-6190
Klempt, Eberhard University of Bonn Institut fuer Strahlen- u. Kemphysik Nussallee 14-16 Bonn. ~, D 531 15
Klimenko, Alexei Old Dominion University 1134 Bolling Ave, Apt 21 1C Norfolk, VA 23508 USA [email protected] (757) 683-5806
Kolomeitsev, Evgeni European Centre for Theoretical Studies Villa Tambosi Strada delle Tabarelle 286 Villazzano(TN),1-38050 Italy [email protected] +390461314745
Kondratyuk, Sergey TRIUMF 4004 Wesbrook Mall Vancouver, B.C. ,V6T 2A3 Canada [email protected] (604) 222 1047(ext:64
Kudryavtsev, Aleksander ITEP 25 B. Cheremushkinskaia Street Moscow. RU 117259Russia25 kudryavt@,heron.iteo.ru +70953349354
Kuhn, Joaehim RPI 110 8th Street Troy, NY 12180 USA [email protected] (5 18) 276-6918
Kuhn, Sebastian Old Dominion University 1021 47th Street Norfolk. VA 23508 USA [email protected] (757) 683-5804
klemot@,isko.uni-bonn.de +49228732202
659 LeRose, John Jefferson Lab 12000 Jefferson Avenue Newport News. Va 23606 USA [email protected] (757) 269-7624
Lehmann, Albert James Madison University Brookhaven National Laboratory LEGS Group, Bldg. 5 10A Upton, 11973 NY [email protected] (631)344-8137
Liao, Xiaodong Columbia University 538 West 120th Street #74 New York ,NY 10027 USA xdliao&hvs.columbia.edu (212) 854-3801
Ligterink, Norbert University of Pittsburgh Department Physics & Astronomy 3941 O'Hara Street Pittsburgh ,PA 15260 USA no1 l&itt.edu (4 12) 624-9041
Liu, Keh-Fei University of Kentucky Department of Physics and Astronomy Lexineton . KY 40506 USA [email protected] (859) 257-4849
Liyanage, Nilanga University of Virginia 12000 Jefferson Ave MS 12H Newoort ews , VA 23693 [email protected] (757) 269-7254
Lomon, Earle MIT 6-302 77 MassachusettsAvenue Cambridge, MA 02140 USA lomon@,ns.mit.edu (617) 253-4877
Lung, Allison Jefferson Lab 12000Jefferson Avenue Newport News, VA 23606 USA lung@,iIab.org (757) 269-7255
Lutz, Matthias GSI Planckstrabe 1 Darmstadt ,D-6429 1 Germany m.lutz@,gsi.de +496159 71 0
Lvov, Anatoly Lebedev Physical Institute Leninsky Prospect, 53 Moscow, 119991Russia Ivov@,x4u.loi.mheo.ru
LlJring, Ulrich UniversiUt Bonn Institut Air Theoretische Kernphysik Nussallee 14-16 Bonn .53115 Germanv loenng~itku.uni-bonn.de +49228732374
Maas, Frank Maim University Institut h e r Kernphysik Johann-Joachim-Becher-Weg45 Maim. D-55099 Germanv maas@,koh.uni-mainz.de +49 6131 3925807
660 Mack, David Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7255
Madey, Richard Kent State University Physics Department Jefferson Lab Newport News, VA 23606 USA madey@uhvsicskentedu (757) 269-5510
Manley, Mark Kent State University Physics Department 105 Smith Hall Kent, OH 44242 USA manlev@,kent.edu (330) 672-2407
Markowitz, Pete Florida International University CP 208 /Physics Department Miami, FL 33199 [email protected] (305) 348-1710
Mecking, Bernhard Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7561
Melnitchouk, Wally Jefferson Lab Theory Group, MS 12H2 12000 Jefferson Avenue Newoort News. VA 23606 USA meIr;ita,i.ilab.o& (757) 269-5854
Menze, Dietmar Physikalisches Institut University Bonn BOM, 53115 Germany menze0.Dhvsik.uni-bonn.de +49 228 733248
Merkel, Harald Universitaet Mainz Institut h e r Kernphysik Bechenveg 45 Mainz, 55099 Germany
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Messchendorp, Johan University of Giessen I1 Physikalisches Institut Heinrich-Buff-Ring 16 Giessen , D-35392 Germanv Johan.Messchendo&uhyii k.uni-eiessen.de +49 6419 933272
Mestayer, Mac Jefferson Lab 12000 Jefferson Avenue Newport News ,VA 23606 USA mestaver@,ilab.org (757) 269-7252
Meb, Andreas Free University, Amsterdam Division of Physics and Astronomy, Faculty of Science De Boelelaan 1081 Amsterdam ,1081 HV The Netherlands [email protected] +31204447851
Michaels, Robert Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA romO.ilab.org (757) 269-7410
661
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Miller, Gerald University of Washington Department of Physics P.O. Box 351560 Seatle ,WA 98195-1560 USA [email protected] (206) 543-2995
Minehart, Ralph University of Virginia Physics Department Charlottesville ,VA 22901 USA rcm4v@,vir~inia.edu (434) 924-6785
Miskimen, Rory University of Massachusetts Department of Physics LGRT 417L Amherst. MA 01003 USA [email protected] (413) 545-2400
Morel, Danielle Florida State University Physics Department Tallahassee. FL 32306-4350 USA [email protected] (850) 644-1257
Nakano, Takashi RCNP, Osaka University 10-1 Mihogaoka Ibaraki .Osaka 567-0047 Jauan [email protected] +81 6 6879 8938
Nanda, Sirish Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA nand@,iIab.org (757) 269-7176
Narodetskii, Ilia ITEP BCheremushkinskaya 25 Moscow, 117218 Russia [email protected] +7 095 1299547
Niculescu, Gabriel Ohio University/JLab MS28F 12000 Jefferson Ave Newuort News. VA 23606 USA [email protected] (757) 269-7310
Niculescu, Ioana Jefferson Lab 12000 Jefferson Avenue Newuort News. VA 23606 USA [email protected] (757) 269-7255
Niyazov, Rustam Old Dominion University 1110 Bolling Ave #11A Norfolk, VA 23508 USA [email protected] (757) 683-5807
Noguera, Santiago Universidad de Valencia Departamento de Fisica Teorica C. Dr. Moliner, 50 Burjassot (Valencia) ,46100 SPAIN [email protected] +34 963 86 45 11
Michel, Bernard Clermont-Ferrand Laboratoire de Physique Corplsculaire Universite Blake Pascal de Clermont-Ferrand Aubiere ,63177 France
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662 Normand, Kristoff Basel University Institut h e r Physik Klingelbergstrasse82 Basel, 4056 Switzerland [email protected] +41612673746
Norvaisas, Egidijus Institute of Theoretical Physics and Astronomy Gostauto 12 Vilnius ,2600 Lithuania [email protected] +370 2 612906
Nozar, Mina Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA nozarm@,ilab.org (757) 269-7175
Ostrick, Michael Physikalisches lnstitut University Bonn Nussallee 12 BOM , 5 3 1 15 Germany
Page, Philip Los Alamos National Laboratory T-16, MS B283 Los Alamos ,NM 87545 USA p r o a l an].gov (505) 667-4835
Paris, Mark Los Alamos National Laboratoly T-16, MS B283 Los Alamos ,NM 87545 USA [email protected] (505) 667 0673
Pasquini, Barbara European Centre for Theoretical Studies Villa Tambosi, Strada dellaTabarelle, 286 Villazzano (Trento) ,I-38050 Italy pasauini@,ect.it +39 0461 314729
Pasyuk, Eugene Arizona State University Jefferson Lab, MS16B 12000 Jefferson Avenue Newport News , VA 23606 USA [email protected] (757) 269-6020
Price, John UCLA 14340 Addison Street #210 S h e w Oaks .CA 91423 USA [email protected] (310) 206-4943
Protopopescu, Dan University of New Hampshire Physics Department DeMeritt Hall 205 Durham. NH 03824 US protooo&ilab.org (603) 862-1685
Qattan, Issam Northwestem University/JLab 12000 Jefferson Avenue Newport News ,VA 23606 USA aattan@,ilab.org (757) 269-5794
Radici, Marco INFN - Sezione di Pavia via Bassi 6 Pavia, I 27100 Italy [email protected] +39 0382 507451
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663 Radyushkin, Anatoly Jefferson Lab Theory Group MS 12H2 12000 Jefferson Avenue NewDort News. VA 23606 USA radv;[email protected] (757) 269-7377
Reichelt, Tilmann Physikalisches lnstitut Uni Bonn Nussallee 12 Bonn, 53 I15 Germany [email protected] +49 0228 73 36 96
Reinhold, Joerg Florida Internatioml University &Jefferson Lab Department of Physics Miami, FL 33199 USA reinhold@,fiu.edu (305) 348-6422
Reitz, Bod0 Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA reitz@,ilab.org (757) 269-5064
Richards, David Jefferson Lab Theory Group, MS 12H2 12000 Jefferson Avenue NewDort News. VA 23606 USA
Roberts, Winston Jefferson Lab Theory Group, MS 12H2 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7062
& (757) 269-7736 Roche, Julie The College of William and Mary Physics Department P.O. Box 8795 Williamsburg ,VA 23187 USA jroche@,ilab.org (757) 269-7735
Ronchetti, Federico INFN-Frascati 40, Via E. Fermi Frascati ,Rome 00044 Italy ronchetti@,ilab.org +39 069 4032569
Sadler, Michael Abilene Christian University ACU Box 27963 Abilene .TX 79639 USA sadler@,Dhvsics.acu.edu (915) 674-2189
Saez, Jorge Jefferson Lab 12000 Jefferson Avenue Newport News ,VA 23606 USA isaez@ iI ab.org (757) 269-5387
Saha, Arun Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA saha(iiilab.org (757) 269-7605
Santopinto, Elena INFN-Genova v. Dodecaneso 33 Genova, 1-16146 Italy [email protected] +39 0103 536219
664 Sargsian, Misak Florida International University Department of Physics Miami, FL 33199 USA sarpsian(ii,fiu.edu (305) 348-3954
Sato, Toru Osaka University Department of Physics, Graduate School of Science Machikaneyama 1-1 Tovonaka .Osaka 560-0043 Jaoan tsato~ehvs.sci.osaka-u.ac.io +81668505345
Schat, Carlos Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-5839
Schicrholz, Gerrit DESY Notkestr. 85 Hamburg. 22603 Germanv Gerrit.Schierholz~desv.de +49 175 9346213
Schoch, Berthold University of Bonn Physikalisches InstiM Nussallee 12 Bonn ,NRW 53 115 Germany schoch0.ohvsik.uni-bonn.de +49228732344
Seimetz, Michael University of Mainz Institut fuer Kemphysik Becherweg 45 Maim ,55099 Germany seimetzmkoh.uni-mainz.de +49 6131 3922935
Sharabian, Youri Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-5829
Simonov, Yuri Jefferson Lab Theory Group MS 12H2 12000Jefferson Avenue Newoort News, VA 23606 USA simoiovmiIab.&g (757) 269-6051
Simula, Silvano
Sirca, Simon MIT Room 26-402 77 Massachusetts Avenue Cambridge, MA 02139 USA sirc@,rnitlns.mit.edu (617) 258-5438
INFN - Sezione Roma 111 Via della Vasca Navale 84 Rome, Italy 1-00146Italy [email protected] +39 06 5517 7053
Smith, Elton Jefferson Lab 12000 Jefferson Avenue Newoort News. VA 23606 USA eltonkhlab.org (757) 269-7625 '
Smith, Cole University of Virginia Physics Department 382 McCormick Road Charlottesville ,VA 22904-4714 USA cole@,nstar.ohvs.virginiaedu (434) 924-6806
665 Smith, Greg Jefferson Lab 12000Jefferson Avenue Newport News, VA 23606 USA smithe@,ilab.org (757)269-7255
Stahov, Jugoslav Abilene Christian University 320 Foster Science Building, ACU Box 27963 Abilene , TX 79699 USA stahov@,Dhvsics.acu.edu (915)674-2166
Stibunov, Victor Institute for Nuclear Physics at Tomsk Politechic INP, Lenina 2A Tomsk ,634050Russia stib@,noi.tou.ru +7 3822 423992
Strakovsky, Igor George Washington University Physics Department 725 21st Street, NW Washington ,DC 20052 USA [email protected] (703)726-8344
Strauch, Steffen George Washington University Department of Physics 725 21st Street, N.W. Washington, DC 20052 U.S.A. strauch@,ewu.edu (202)994-6579
Suleiman, Riad MITlJLab 12000 Jefferson Avenue Newport News ,VA 23606 USA [email protected] (757)269-6990
Tang, Liguang Hampton University 130 East Tyler Street Hampton, VA 23668 USA [email protected] (757)269-7255
Tatischeff, Boris Institut de Physique Nucleaire Orsay Cedex, France Orsay, 91406 France tati@,iono.in2o3.fr +33 1691 55182
Taylor, Simon Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757)269-7130
Thoma, Ulrike Jefferson Lab 12000Jefferson Avenue Newuort News. VA 23606 USA
Thomas, Anthony Adelaide University Director CSSM Adelaide, SA 5005 Australia [email protected] +61 8 8303 3547
Tireman, William Kent State University 480-KYoung's Mill Lane Newport News, VA 23602 USA [email protected] (757)269-7035
uthoinailab.o&
(757)269-7432
666 Todor, Luminita Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA 15213 USA [email protected] (757) 269-5538
Ulmer, Paul Old Dominion University Department of Physics Norfolk, VA 23529 USA [email protected] (757) 683-5851
Urban, Jozef University of Bonn IKP FZ Juelich Leo Brand Str. 1 Juelich ,52425 Germany [email protected] +492461615884
Van Hoorebeke, Luc University or' Gent Dept. of Subatomic and Radiation Physics, RUG Proelbinstmat 86 Gent, 9000 Belgium luc@,inwfsunl .rup.ac.be + 32 9 2646543
Van der Steenhoven, Gerard NIKHEF P.O. Box41882 Amsterdam NL 1009 DB Netherlands [email protected] +31205922145
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Walcher, Thomas Universitn Mainz lnstitut f i r Kemphysik J.J. Becher-Weg 45 Mainz ,55099 Germany walcher@k&.uni-mainz.de +49 6131 3925197
Warren, Glen University of Basel Jefferson Lab,MS 16B-107 12000Jefferson Avenue NewDort News . VA 23606 USA [email protected] (757) 269-5797
Weise, Wolfram ECT* Trento Physics Department Technical University of Munich Garching ,D-85747 Germany [email protected] +39 0461 314760
Weiss, Christian Universitat Regensburg Institut fuer Theoretische Physik Regensburg, - . D-93053 Germanv christian.weiss(~hvsik.uni-repensburg.de +49 941 943 2187
Weygand, Dennis Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA wevgand(ii,ilab.org (757) 269-5926
marcvdh(ii,keh.uni-mainz.de +49 613 1 3924277
667 Wojtsekhowski, Bogdan Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA bogdanw(dilab.org (757) 269-7191
Wood, Steve Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7255
Workman, Ron George Washington University Virginia Campus 20101 Academic Way Ashburn, VA 20147 USA [email protected] (703) 726-8345
Yamazaki, Hirohito Tohoku University Kakuriken Mikamine 1-2-1, Taihaku-ku Sendai ,Miyagi 982-0826 JAPAN [email protected] +81227433433
Yan, Chen Jefferson Lab 12000 Jefferson Avenue Newport News, VA 23606 USA [email protected] (757) 269-7255
Yoshida, Rik Argonne National Lab 9700 S Cass Ave Argonne ,IL 60439 USA rik.voshida@,anl.gov (630) 252-7874
Zegers, Remco
RCNP Osaka University 10-1 Mihogaokq lmbaraki Osaka, 567-0047 Japan zegers@s~rineS.or.io +7915808083116
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Author Index HERMES, 392, 558 LEGS, 619 LEPS, 234, 506 Neutron EDM, 443 TAPS, 545 Crowder, J., 550
ACUS,A., 359 Arrington, J., 338, 550, 567 Aruga, Y., 541 Avakian, H., 319 Aznauryan, I., 460 Bacchetta, A., 311 Bagdasarian, H., 575 Barnes, P. D., 443 Becher, T., 102 Belitsky, A., 371 Belozerova, T. S., 480 Bennhold, C., 456 Bernstein, A. M., 413, 595 Biselli, A., 323 Boffi, S., 367 Borasoy, B., 599 Brash, E., 256 Braun, V. M., 363 Burkert, V., 29, 489
d’Angelo, A., 140 Dashyan, N., 575 Davies, C., 53 Debruyne, H., 571 Denizli, H., 472 Desplanques, B., 417, 421 De Vita, R., 210 Diakonov, D., 153 Diehl, M., 280 Dohrmann, F., 585 Drechsel, D., 396 Ducote, J., 498 Dugger, M. R., 476
Capstick, S., 17, 448 Cassing, W., 525 Christy, M. E., 307 Cole, L. C., 327 Cano, F., 417 Cohen, T. D., 425 Collaboration A1, 346 A2, 545 CLAS, 323, 327, 460, 464,476, 489, 498, 502, 575, 581 COSY-ToF, 409 Go, 355 Hall A, 332 Hall A E98-108, 332 Hall A/VCS, 268, 430, 434 Hall C E89-009, 589
669
Edwards, R., 43 Egiyan, H., 460 Egiyan, K., 575 Elouadrhiri, L., 384 Ent, R., 550 Eyrich, W., 409 Falter, T., 521 Fernhdez, F., 468 Fonvieille, H., 268 Forest, T., 303 Frick, P. G., 480 Fries, R. J., 363 Friman, B., 533 Funsten, H., 489 Garcilazo, H.,
494
670
Garrow, K., 562 Garutti, E., 558 Giannini, M. M., 438 Glozman L., 367, 425 Gockeler, M., 627 Goity, J. L., 611 Gonzalez, P., 417, 468, 494 Gorchtein, M., 396 GrieBhammer, H. W., 452 Hemmert, T. R., 631 Henner, V. K., 480 Hirota, K., 541 Horsley, R., 627 Huber, G. M., 529 Iijima, A., 541 Ito, Y., 541 Janssen, S., 510 Jeschonnek, S., 222 Joo, K., 464 Julia-Diaz, B., 468 Kaiser, R., 392 Kanda, H., 541 Kasagi, J., 541 Katoh, A., 541 Katsuyama, T., 541 Keppel, C., 550 Kino, K., 541 Kinoshita, T., 541 Klein, F., 489 Klempt, E., 198 Klink, W., 367 Kolomeitsev, E. E., 603 Kondratyuk, S., 514 Konno, O., 541 Kuhn, J., 323 Kundu, R., 311
Lee, F. X., 643 Lehmann, A., 619 Lenz, A., 363 Leupold, S., 521 Liao, X., 635 Lomon, E., 342 Lutz, M. F. M., 533, 603
Maas, F., 165 Madey, R., 350 Maeda, K., 541 Mahnke, N., 363 Manke, T., 635 Markowitz, P., 332 Maynard, C. M., 627 Merkel, H., 115 Messchendorp, J. G., 545 Metz, A., 311, 396 Miller, J., 65 Morel, D., 448 Mosel, U., 521 Mulders, P., 311 Muller, D., 371 Nakabayashi, T., 541 Nakano, T., 234 Narodetskii, I. M., 639 Nefkens, B. M. K., 498 Nicolet, A., 421 Niculescu, G., 502 Niculescu, I., 550 Niyazov, R. A., 581 Noguera, S., 417 Noma, T., 541 Norvaisas, E., 359 Oset, E., 456 Osipenko, M., 315 Ostrick, M., 403 Page, P., 243
67 1
Pasquini, B., 396 Pasyuk, E. A., 476 Pleiter, D., 627 Plessas, W., 367 Price, J. W., 498 Rackow, P. E. L., 627 Radici, M., 367 Ramos, A., 456 Reinhold, J., 589 Ricco, G., 315 Richards, D. G., 627 Ripani, M., 489 Riska, D. O., 359 Ritchie, B. G., 476 Roche, J., 355 Ryckebusch, J., 510, 571 Sadler, M., 189 Santopinto, E., 438 Sargsian, M. M., 554 Sato, T., 178 Schat, C. L., 485 Schierholz, G., 126, 627 Scholten, O., 514 Seimetz, M., 346 Shimizu, H., 541 Simula, S., 315, 554 Stahov, J., 615 Stein, E., 363 Strauch, S., 537 Strikman, M. I., 554
Suleiman, R., 607 Taiuti, M., 315 Tajima, Y., 541 Takahashi, T., 541 Terasawa, T., 541 Theussl, L., 421 Thomas, A., 3 Todor, L., 434 Trusov, M. A., 639 Valcarce, A., 468, 494 Vanderhaeghen, M., 396 van der Steenhoven, G., 78 van Hoorebeke, G., 430 van Orden, J. W., 222 Vasallo, A., 438 Vijande, J., 494 Wagenbrunn, R. F., 367 Weinstein, L. B., 581 Weise, W., 290, 631 Weiss, C., 388 Wolf, GY., 533 Yamazaki, H., 541 Yorita, T., 541 Yoshida, H. Y., 541 Yoshida, R., 90 Zegers, R. G. T., 506
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Baryons 2002 gth INTERNATIONAL CONFERENCE
ON THE STRUCTURE OF BARYONS Jefferson Lab Newport News, Virginia March, 3 - 8, 2002
Agenda Sunday, March 3 18:OO Reception and Registration
Monday, March 4 Plenary Session (Chair: P. Barnes) 8:30 8:45 9:40 10:25 10:50 11:35 12:20
L. Cardman A. Thomas S. Capstick V. Burkert R. Edwards
Welcome Successes and Open Issues in Baryon Physics Baryon Spectroscopy in the Quark Model Break Electroexcitation of Nucleon Resonances Baryon Spectroscopy on the Lattice Lunch
Plenary Session (Chair: B. Schoch) 14:OO C. Davies 14:45 G. Miller 15:30 16:OO Yu. Simonov 16:30 G . v.d. Steenhoven 17:15 R. Yoshida
Heavy Quark Physics on the Lattice Hadrons in the Nuclear Medium Break Baryon Spectrum and Magnetic Moments in Non-perturbative QCD Polarized Structure Functions Proton Structure Results from the HERA Collider
673
674
Tuesday, March 5 Plenary Session (Chair: D. Ernst) 8:30 9:15 1o:oo 10:30 11:15 12:oo
T. Becher H. Merkel G. Schierholz A. d’Angelo
Baryon Chiral Dynamics Experimental Tests of Chiral Symmetry Break Hadron Structure from Lattice QCD Photoexcitation of N* Resonances Lunch
Session on Structure Functions and Form Factors I
- I1
Convenors: E. Beise, A. Bruell, X. Ji, and M. Vanderhaeghen 13:30 G. Cates 13:50 T. Forest 14:lO M.E. Christy 14:30 A. Metz 14:50
S. Simula
15:lO H. Avagyan 15:30 S. Liuti 15:50 16:30 J. Kuhn 16:30
L.C. Smith
16:30 P. Markowitz 16:30 I. Niculescu 16:30
J. Arrington
16:30 E. Lomon
The Spin Structure of the Neutron and 3He at Low Q2and the Extended GDH Sum Rule The Q2-Dependence of Polarized Structure Functions Measurement of R = u ~ / inu the ~ Nucleon Resonance Region The Collins Fragmentation Function in Hard Scattering Processes Leading and Higher Twists in the Proton Polarized Structure Function GY at large Bjorken X Single-Spin Asymmetries at CLAS Signals of Local Duality from a Perturbative QCD Analysis of Inclusive ep Scattering Break Study of the A( 1232) Using Double-Polarization Asymmetries CLAS Measurement of Electroproduction Structure Functions Kaon Electroproduction at Large Momentum Transfer Moments of the Proton F2 Structure Function at Low Q2 Are Recoil Polarization Measurements of Gg /GL Consistent with Rosenbluth Separation Data? Effect of New Data on Extended VDM/GK Nucleon Form Factors
675
Session on Baryon Structure and Spectroscopy I
- I1
Convenors: T.S. Harry Lee, Mark Manley, Berthold Schoch, and Silvano Simula 13:30 13:45 14:15 14:30 14:45
15:OO 13:15 15:30 15:45 16:30 16:45 17:OO
17:15 17:30 17:45 18:OO 18:15
First Measurement of the GDH Integral Between 200 and 800 MeV The GDH-Experiment at ELSA T . Michel Meson-Photoproduction with the Crystal-Barrel M. Ostrick Detector at ELSA W. Eyrich K-Meson Production Studies with the TOFSpectrometer at COSY A. Bernstein First Simultaneous Measurements of the T L and TL' Structure Fhnctions in the y* + A Reaction P. Gonzalez Photoproduction of Resonances in a Relativistic Quark Pair Creation Model Relationship of the 3P0 Decay Model to Other B. Desplanques Strong Decay Models Partial wave analysis of the J / Q + p-fiand X. Ji Other Channels Break L. Glozman Do We See Chiral Symmetry Restoration in Baryon Spectrum? L. Van Hoorebeke Virtual Compton Scattering: Results From Jefferson Lab Virtual Compton Scattering and Neutral Pion L. Todor Electro-production from the Proton in the Nucleon Resonance Region The Hypercentral Constituent Quark Model E. Santopinto A Relativistic Quark Model of Baryons with U. Loering Instanton Induced Forces New Search for the Neutron Electric Dipole P. Barnes Moment D. Morel qQ Loop Effects on Baryon Masses H. Griesshammer Learning from Dispersive Effects in the Nucleon Polarisabilities A. Braghieri
676
Session on Hadrons in the Nuclear Medium I - I1 Convenors: Nicola Bianchi and Misak Sargsian
13:30 T. Falter
Nuclear Shadowing and In-Medium Properties of the po Scalar- and Vector-Meson Production in Hadron13:50 W. Cassing Nucleus Reactions Helicity Signatures in Subthreshold po Production 14:lO G. Huber on Nuclei From Meson- and Photon-Nucleon Scattering to 14:30 M. Lutz Vector Mesons in Nuclear Matter Polarization Transfer in the 4He(E',e ' g 3 H Reaction 14:50 S. Strauch S11(1535) Resonance in Nuclei Studied with the 15:lO H. Yamazaki C(y, Q) Reaction 15:30 J. Messchendorp Double-Pion Production in y A Reactions Break 15:50 Quark-Hadron Duality in Inclusive Electron-Nucleus 16:30 I. Niculescu Scattering Neutron Structure Function and Inclusive DIS 13:50 S. Simula From 3Hand 3He Targets at Large Bjorken-X Search for a Possible Nuclear Dependence in 17:lO M.E. Christy R ( x, Q 2)= ( T L / ( T T at Small x and Q2 Hadron Formation in Nuclei in Deep-Inelastic 17:30 E. Garutti Lepton Scattering Nuclear Transparency from Quasielastic A(e, e'p) 17:50 K. Garrow Reactions up to Q2 = 8 . 1 ( G e V / ~ ) ~ Deuteron Photodisintegration at High Momentum 18:lO X. Jiang Transfer
+
Wednesday, March 6 Plenary Session (Chair: J. Kasagi) 8:30 9:15
D. Diakonov F. Maas
1o:oo 10:30 T. Sat0 11:15 M. Sadler 12:OO E. Klempt
Instantons and Baryon Dynamics The Strangeness Contributions to the Form Factors of the Nucleon Break Electromagnetic Production of Pions in the Resonance Region - Theoretical Aspects Hadronic Production of Baryon Resonances Baryon Resonances and Strong QCD
677
Session on Structure Functions and Form Factors I11 14:OO G. Warren G; via $z,efn)p 14:15
M. Seimetz
14:30 14:45
R. Madey J. Roche
15:05
S. Covrig
15:25
E. Norvaisas
15:45
R. Fries
16:05
M. Radici
Measurement of the Electric Form Factor of the Neutron at Q2 = 0.6 - 0.8 (GeV/c)2 Neutron Electric Form Factor via Recoil Polarimetry The GoExperiment: Measurement of the Strange Form Factor of the Proton Status of SAMPLE Deuterium Experiment at 125 MeV The Nucleon Form Factors in the Canonically Quantized Skyrme Model Soft Contribution to the Nucleon Electromagnetic Form Factors Electroweak Properties of the Nucleon in a Chiral Constituent Quark Model
Session on Baryon Structure and Spectroscopy I11 14:OO C. Bennhold 14:15
H. Egiyan
14:30
K. Joo
14:45
P. Gonzalez
15:OO
H. Denizli
15:15 15:30
E. Pasyuk D. Ernst
15:45
V. Henner
16:OO C. Schat
Dynamical Baryon Resonances with Chiral Lagrangians Pion Electroproduction in the Second Resonance Region Using CLAS Electron Beam Asymmetry Measurements From Exclusive K O Electroproduction in the A (1232) Resonance Region K N N *(1440) and a N N *(1440) Coupling Constants from a Microscopic N N + N N * (1440) Potential q Electroproduction at and Above the Sll(l535) Resonance Region with CLAS 11 Photoproduction From the Proton Using CLAS Meson Cloud Contribution to the Masses of the Nucleon, Delta, and Roper Why is the Wavelet Analysis Useful in Physics of Resonances? Example of p’ and W” States L=l Baryon Masses in the l/Nc Expansion
678
Session on Lattice QCD and Heavy Quarks Convenors: Keh-Fei Liu and Shigemi Ohta 14:OO D. Richards
Lattice Calculation of Baryon Masses Using the Clover Fermion Action 14:25 W. Weise Nucleon Magnetic Moments, Their Quark Mass Dependence and Lattice QCD Extrapolations 14:50 W. Melnitchouk Chiral Extrapolation of Lattice Moments of Proton Quark Distributions 15:15 X. Liao Heavy Quark Spectrum from Anisotropic Lattices 1540 I. Narodetskii The Doubly Heavy Baryons in the Nonperturbative QCD Approach 16:05 F. Lee Excited Baryons and Chiral Symmetry Breaking of QCD Poster Session Group dinner at the Mariners Museum
16:30 18:30
Thursday, March 7 Plenary Session (Chair: E. Beise) 8:30 9:15 1o:oo 10:30 11:15 12:oo
R. DeVita
S. Jeschonnek T. Nakano P. Page
Spin Structure Functions in the Resonance Region Quark-Hadron Duality Break First Results from SPRING-8 Hybrid Baryons Lunch
Session on Structure Functions and Form Factors IV 14:OO A. Belitsky 14:20 L. Elouadrhiri 14:40
C. Weiss
15:OO B. Fox 15:20 R. Kaiser 15:40
B. Pasquini
Nucleon Hologram With Exclusive Leptoproduction Deeply Virtual Compton Scattering at Jefferson Lab, Results and Prospects Twist-3 Effects in Deeply Virtual Compton Scattering Made Simple Exclusive Processes Measured at HERMES Measurement of Hard Exclusive Reactions with a Recoil Detector at HERMES Dispersion Relation Formalism for Virtual Compton Scattering Off the Proton
679
Session on Baryon Structure and Spectroscopy IV Search for Resonance Contributions in Multi Pion Electroproduction with CLAS QCD Confinement and Missing Baryons Problem J. Vijande Photoproduction of the Z Hyperons J.W. Price Open Strangeness Production in CLAS G. Niculescu K+ Photoproduction at LEPS/SPRING-8 R. Zegers New Results on Spin Rotation Parameter A in the D. Svirida npelastic Scattering in the Resonance Region Kaon Photoproduction: Background Contributions S. Janssen and Missing Resonances S. Kondratyuk Dynamical Description of Nucleon Compton Scattering at Low and Intermediate Energies: From Polarisabilities to Sum Rules
14:OO F. Klein 14:15 14:30 14:45 15:OO 15:15 15:30 15:45
Session on Hadrons in the Nuclear Medium I11 16:30
J . Arrington
16:47 D. Debruyne 17:04 K. Egiyan 17:21 R. Niyazov 17:38 E. Piasetzky 17:55 18:12
F. Dohrmann J. Reinhold
Nucleon Momentum Distributions From a Modified Scaling Analysis of Inclusive Electron-Nucleus Scattering Medium Effects in A(Z, e l 3 Reactions at High Q2 Study of Nucleon Short Range Correlation in A(e,e') Reaction at X B > 1 N N Correlations Measured in 3 H e ( e ,e'p p)n Looking at Close Nucleons in Nuclei by High Momentum Transfer Reactions Electroproduction of Strangeness on Light Nuclei Hypernuclear Spectroscopy of i z B by the ( e ,e'Kf) Reaction
680
Session on Chiral Physics I - I1 Conven0rs:A.M. Bernstein, U. van-Kolck, and U.G. Meissner 14:OO A.M. Bernstein 14:24 B. Borasoy 14:48 E. Kolomeitsev 15:12
R. Suleiman
15:36 16:30 16:54
R. Miskimen J. Goity A. Gasparian
17:18
J. Stahov
17:42
A. Lehmann
Goldstone Boson Dynamics: Introduction to the Chiral Dynamics Session 77’ Electroproduction Off Nucleons A Unified Chiral Approach to Meson-Nucleon Interaction Measurement of the Weak Pion-Nucleon Coupling Constant 7H: , from Backward Pion PhotoProduction Near Threshold on the Proton Measurement of the Anomalous Amplitude y + 3n 7ro + y y t o NLO in ChPT A Precision Measurement of the Neutral Pion Lifetime at Jefferson Lab The Dependence of the ”Experimental” Pion Nucleon Sigma Term on Higher Partial Waves First Beam-Target Double-Polarization Measurements Using Polarized HD at LEGS
Friday, March 8 Plenary Session (Chair: T. Walcher) 8:30 9:15 1o:oo 10~30 11:15 12:oo 14:OO
E. Brash H. Fonvieille
M. Diehl W. Weise
Nucleon Electromagnetic Form Factors Virtual Compton Scattering Break Generalized Parton Distribution Baryons 2002: Outlook Lunch Tour of the experimental halls
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