Vernon W. Hughes
Proceedings of the Memorial Symposium in Honor of Vernon Willard Hughes
Yale University, USA
14 - 15 November 2003
editors
Emlyn Willard Hughes California Institute of Technology, USA
Francesco Iachello Yale University, USA
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IN MEMORY OF VERNON WILLARD HUGHES Proceedings of the Memorial Symposium in Honor of Vernon Willard Hughes Copyright 0 2004 by World Scientific Publishing Co. Re. 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.
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Preface On November 14-15, 2003, the Vernon Willard Hughes Memorial Symposium was held at Yale University in New Haven, Connecticut. This volume contains the Proceedings of that Symposium. The Symposium was organized by a Committee composed of Charles Baltay, David DeMille, Paul Fleury, Emlyn Hughes and Francesco Iachello (Chair). About 100 scientists attended the Symposium from the international community, Yale, surrounding universities and the country as a whole. The Symposium commenced with a welcoming address by Susan Hochfield, Provost of Yale University. Talks were presented by scientists from several countries on topics related to Vernon’s work, in particular his discovery of muonium, his major contributions to the spin structure of the proton and to the muon (g-2) experiment. Other subjects were also discussed. A Symposium banquet was held on Friday evening with D. Allan Bromley presiding. Gisbert zu Putlitz was unable to be present, but D. Allan Bromley read his remarks. Daniel Kleppner and Nicholas Samios said some nice words. John Marburger Jr., Science Adviser to the President, was also present and made remarks. We are grateful to all the banquet speakers for their words. The biographical memoir of Vernon, written by Robert K. Adair for the National Academy of Sciences, is included in this volume as an important contribution to Vernon’s legacy. For future reference, we have also included in this volume the complete publication list of Vernon Willard Hughes comprising over 400 articles, a true account of major developments in atomic, nuclear and particle physics in the years 1950-2003. We are also grateful to the Provost Office, the Physics Department through its Chairman R. Shankar and the School of Engineering through its Chairman Paul Fleury for grants to support outside speakers. We owe a great deal of gratitude to the Physics Department for providing the infrastructure and technical services, and to the Conference Secretary, Diane Altschuler, and the staff of the Physics Department, Laurelyn Celone and Marguerite Scalesse, for their help. Without them, this important event, commemorating the contributions of one of the leading world figures in 20th Century Physics would not have been possible.
Emlyn Hughes Prancesco Iachello V
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Contents
Preface
V
Vernon Hughes and the Early Years of Molecular Beam Resonance Norman F. Ramsey, Higgins Professor of Physics Emeritus, Harvard University
1
The 46 Years of Muon g-2 Francis Farley, Visiting Senior Research Scientist, Yale University
8
Muonium - The Early Experiments Richard Prepost, Professor of Physics, University of Wisconsin Muonium Lifetime and Heavy Quark Decays (Lessons Learned from Muonium) William J. Marciano, Senior Scientist, Brookhaven National Laboratory
26
42
Recent Developments of the Theory of Muon and Electron g-2 Toichiro Kinoshita, G. Smith Professor of Physics Emeritus, Cornell University
58
Vernon Hughes and the Quest for the Proton’s Spin Robert L. Jaffe, Morningstar Professor of Physics, Massachusetts Institute of Technology
78
The Spin Structure of the Nucleon: A Hughes Legacy Gordon D. Cates, Professor of Physics, University of Virginia
96
vii
viii
Muon g-2: The Last Word? Ernst Sichtermann, Division Fellow, Lawrence Berkeley National Laboratory
116
Past, Present and Future of Muonium Klaus P. Jungmann, Professor of Physics, University of Groningen
134
Parity Nonconservation in Electron-Electron Scattering Emlyn W. Hughes, Professor of Physics, California Institute of Technology
154
Exploring the Nucleon Spin: The Next Decade Abhay L. Deshpande, RIKEN Fellow, Brookhaven National Laboratory
171
Remarks at the Symposium Banquet Honoring Vernon Hughes D. Allan Brornley, Presiding, Sterling Professor of the Sciences, Yale University
191
Banquet Talk in Honor of Vernon W. Hughes Gisbert zu Putlitz, Professor of Physics, University of Heidelberg
193
Tests of CP T for Muons Vernon W. Hughes, Yale University
196
Vernon Willard Hughes, 1921-2003 (A Biographical Memoir) Robert K. Adair, Professor of Physics, Yale University
204
Publication List of Vernon W. Hughes
223
VERNON HUGHES AND THE EARLY YEARS OF MOLECULAR BEAM RESONANCE NORMAN F. RAMSEY Faculty of Arts and Sciences, Harvard University Cambridge MA 02138
The first phase of molecular beam resonance studies began with 1.1. Rabi's invention [ 11 of the molecular beam magnetic resonance method in September of 1937. This invention was stimulated by Rabi's brilliant theoretical paper [a] entitled "Space Quantization in a Gyrating Magnetic Field," by C.J. Gorter's publication [a] entitled "Negative Result of an Attempt to Detect Nuclear Magnetic Spins" and by a visit of Gorter to Rabi's Columbia laboratory. Imme,diately after the invention, two of Rabi's research groups modified their apparatus [I] as shown in Fig. 1 to detect the resonance frequencies at which transitions occurred.
Y
v 0 magnet
A magnet
Fig. 1 . Schematic diagram showing the principle of the first molecular beam magnetic resonance experiments. The two solid curves indicate two paths of molecules having different orientations that are not changed during passage through the apparatus. The two dashed curves in the region of the B magnet indicate two paths of molecules whose orientation has been changed in the C region so the refocusing is lost due to the change in the component along the direction of the magnetic field.
1
2
With these apparatuses, Rabi, S. Millman, P. Kusch, J.R. Zacharias, J.M.B. Kellogg and N.F. Ramsey during the next few years measured a number of spins and magnetic moments of nuclei including the proton, the deuteron, and the nuclei of 'Li and many other atoms [a]. Kellogg, Rabi, Ramsey and Zacharias [a] discovered that the deuteron had a quadrupole moment which implied the existence of a nuclear tensor force. Although the magnetic resonance method was originally developed to study nuclear magnetic moments in nonparamagnetic molecules, Kusch, Millman and Rabi [a] in 1940 applied it to the paramagnetic atoms Li, K, Na, Rb and Cs. They measured both the atomic moments and the hyperfine separations.
The first publication with the molecular beam magnetic resonance method was in 1938, but by 1941, after only three years of great productivity, research in the field was exclusively at Columbia University. This research was coming to an end, however, as the scientists and the laboratories became involved in World War I1 defense-related research. Vernon Hughes was too young to have been involved in this first short but productive period of molecular beam resonance research. However he was deeply involved in the next phase.
In the fall of 1945, Rabi and I returned from our war time research work to revive the Columbia molecular beam laboratory. It was a difficult but exciting period. Since the ONR program for supporting basic research had not yet been established, there was little financial support, in marked contrast to the generous funding for our wartime research. Although two molecular beam apparatuses had been left more or less intact, the remainder had been hastily dismantled with many of the components dumped into attic trashcans so the research rooms could be used for defense research. I spent many hours searching the attic and identifying useable components.
After a few months Vernon and other graduate students began to arrive. They were a great group of students since many of them had already spent one to five years doing research in defense laboratories. Vernon, for example, worked in the MIT Radiation Laboratory group developing accurate timing circuits. As a result he was much more skillful with electronics than either Rabi or 1. In some respects it was embarrassing to have Vernon as a student be more
3
knowledgeable about many research techniques than we on staff, but the skill and knowledge he brought to the lab more than made up for the embarrassment. The conditions at the time were rather unfair to Vernon. I had received one of the last Ph.D's granted before the war and was working as a tenured associate professor whereas Vernon, who had almost as much research experience, was officially a graduate student.
Since initially we could not afford to build a major new apparatus, Vernon started with an atomic beam electric resonance apparatus built before and during the War by Harold Hughes [a] and further improved by John Trischka and Vernon. A schematic diagram of the apparatus is shown in Figure 2.
etec tor-
7 "1.0
0
Fig. 2. Schematic diagram of electric-resonance apparatus showing paths of molecules. The transverse scale of the drawing is much larger than the longitudinal scale.
The vertical scale in this diagram is tremendously magnified. The molecular states in the diagram are identified by giving the values (J, m J). Vernon [2-51 and his fellow student, Lou Grabner measured "RbF, s7RbFand 3 k F in the first rotational and zero'th vibrational states. Their values for the electric quadrupole interaction parameters e2qQ/h in MHz were -70.31 f 0.06, -34.00 f 0.06 and 7.938 f 0.040 for 85RbF,"RbF and 39KFrespectively. They also showed that for 85RbFand 87RbFthe value of e2qQ/h decreased by 1.1% in going from one
4
vibrational state to the next higher one whereas for 39KFthe corresponding decrease was 1.3%.
As this work progressed, Vernon and Lou [2,3,5] observed that they were getting a resonance transition not only at the frequency for the quadrupole moment interaction but at half that frequency as well. They attributed this to a two-photon transition, which had never before been seen in spectroscopy. They confirmed that the transition was not due to a second harmonic from the oscillator by using two different frequencies and finding the two-photon resonance when the sum of the two frequencies was correct. Vernon at this time also developed the theory for a two-photon transition in a microwave resonance spectrum [5,7].
Vernon's interest in simple fundamental experiments showed up at this time by his undertaking, at Rabi's suggestion, an experiment [9] to see if a molecule could be significantly deflected by a uniform electrostatic field. ~ Since then Vernon and others His negative result showed that 1q e +q ~ l < l O - ' e. [lO,l 11 have lowered the limit to (qe+q p(<10-" e.
Vernon's interest in studying simple systems, that could be theoretically interpreted, was well manifested in his beautiful series of fundamental papers [ 15-23], on 4He and 3He published between 1950 and 1980. He studied these atoms with the atomic beam resonance apparatus shown in Fig. 3.
R.F. Electron collector
Discharge Pirani Wire C-field A-field tube detector detector B-field Fig. 3. Diagram ofapparatus used to study He in its nictastnble triplet state (HUG 53)
5 He fmt studied these atoms in the metastable 23S1 state which he produced by electron bombardment of the atoms in their ground state and measured the gJ value for 4He in this state. Vernon and his students and associates then went on to measure other properties of these atoms in the 23S1, 23P, 23P,, 23P1, and z3P2states as shown in Table 1.
Table 1. Yale measurements of helium properties
Quantity
Av(He,2’S1)
vOlfHe, 23Po. 4He, 23Pi] vo2fHe, 23Po- 4He, 23P2]
Measured value 2.002243(22) [10 ppm] 0.999867(9) [lo ppm] 6739.7013(4) MHz [0.8 ppm] 0.76181237(46) [0.6 ppm] 2291196(5) kHz [2.2 ppm] 29616864(36) kHz [1.2 ppm] 31908106(27) kHz [0.6 ppm]
Vernon made all of these measurements primarily as a test of QED theory which could predict these values. To the 1 ppm accuracies of the measurements and theory, there was agreement between experiments and theory.
Soon after the e‘e- atom, positronium was discovered and measured by M. Deutsch [25,26], Vernon and his associates set out to improve the measurement of the 13SIto l’S, interval, Dn which they did in a series of papers [27-301. Their best experimental value [32] was DnYale= 203 389.10(74)(3.6 ppm) whereas the best theoretical value [34] in 1999 was DnTheo, = 203 392.01(46)(2.3 ppm). There is now a discrepancy of more than a three standard deviations between theory and experiment. It is unfortunate that Vernon can not now study this problem and I hope someone will soon do so. I would like to conclude with a few comments about Vernon’s contributions to the community of atomic physicists and the establishment of
6
one of the most successful series of international meetings, the International Conferences on Atomic Physics (ICAP). These conferences can be traced back to a meeting I called in 1947 when I was the Chairman of the Physics Department of the then new Brookhaven National Laboratory. I had hired Bill Cohen, one of Rabi's early graduate students and we had tentatively decided that a program for measuring nuclear spins, magnetic moments and electric quadrupole moments of radioactive isotopes would be a great research field for the laboratory, since Brookhaven would provide excellent facilities for handling the radioactivity. But just in the previous year, the new techniques of NMR and microwave spectroscopy had just been invented and we did not want to start off a big research program with the techniques that were about to become obsolete. We therefore called a meeting of the principal inventors of all the alternative methods for making such measurements, including Rabi, Ed Purcell, Felix Bloch, Charles Townes, Polykarp Kusch and Vernon Hughes. In most respects the meeting was very interesting and a great success. However the meeting reached the wrong conclusion on the best methods for radioactive isotope resonance measurements and delayed the U.S. program for measuring such spins and moments by a year or two. The advocates of the new methods described in glowing terms the speed with which they could make such measurements whereas the molecular beam advocates, who already had experience with such measurements, were convinced the molecular beam experiments would be feasible but often difficult. The advocates of the new methods had so far only measured nuclei with large and easily detected magnetic moments, like the proton. They soon discovered that when the magnetic moment was small and unknown, it was difficult to locate the resonance. Ken Smith in England had not been invited to the first Brookhaven conference and was not inhibited by its conclusions, so by the time the next conference was planned, he had measured with an atomic beam the spin and magnetic moment of radioactive 24Na, whereas the new methods had not yet measured any previously unknown moment. From then on most of the unknown magnetic moments of radioactive isotopes were made with an atomic beam, since the first search can be quickly done with a broad resonance over a small range in a weak magnetic field.
Despite the misleading conclusion of this first conference, all participants agreed the conference provided a valuable interchange and it should be repeated and that Victor and Vernon should organize it. After one more molecular beam conference, Vernon urged that the subject be extended to
7 atomic physics and after one or two such atomic physics conferences, it became ICAP, with Vernon being a principal organizer.
References [a.] 'N.F. Ramsey, Molecular Beams, Oxford University Press (1956, 1990) [b.] V.W. Hughes, Annu. Rev. Nucl. Part. Sci. 2000.50: i-xxxvii 1-93. (The reference numbers in this paper are the same as those in the above article (b) by V. W. Hughes.)
THE 46 YEARS OF MUON G - 2
F.J.M. FARLEY Yale University, New Haven, Connecticut 06520 contact address: 8 Chemin de Saint Pierre, 06620 le B a r sur Loup, fiance
This talk is really about Vernon and the muon (g - 2) . He got interested in the measurement about 40 years ago and worked on it seriously for the last 20 years. You can read in his memoirs how he could have worked with Rabi on the g-factor of the electron, but he chose another project - a decision which he lived to regret. So after discovering muonium in 1960, to attack the muon (g - 2) was a natural next step. The story starts in 1956 when the magnetic anomaly a = (g - 2)/2 of the electron was already well measured by Crane et al. Berestetskii et al. pointed out that the postulated Feynman cutoff in QED at 4-momentum transfer q2 = A2, would reduce the anomaly for a particle of mass m by
'.
Sala = (2m2/3A2)
(1)
Therefore a corresponding measurement for the muon with its 206 times larger mass would be a far better test of the theory at short distances (large momentum transfers). (At present the comparison with theory for the electron is 35 times better than for the muon; but to be competitive it needs to be 40,000 times better! The muon is by far the better probe for new physics). In 1956 parity was conserved and muons were unpolarized, so there was no possibility of doing the experiment. But in 1957 parity was violated in the weak interaction and it was immediately realised that muons coming from pion decay should be longitudinally polarized. Garwin, Lederman and Weinrich 3,4, in a footnote to their classic first paper confirming this prediction, used the (g - 2) precession principle (see below) to establish that its gyromagnetic ratio g must be equal to 2.00 to an accuracy of 10%: This was the first observation of muon (g - 2) over 46 years ago. In 1958 the Rochester conference took place at CERN; Panofsky reviewing electromagnetic effects said that three independent laboratories, two in the USA and one in Russia, were planning to measure (g - 2) for the 8
9
muon. Theorists such as Tamm and Marshak expected a major departure from the predicted QED value, either due to a natural cutoff (needed to avoid the well known infinities in the theory) or to a new interaction which would explain the mass of the muon. How do these experiments work? For muons at rest in a magnetic field B the spin rotates at angular frequency w, = ( 9 / 2 ) ( e B / m c )
(2)
and the distribution of decay electrons must rotate with it. This precession frequency has been measured many times in fields calibrated in terms of the proton spin frequency wp. The ratio X = w,/wp = ,+/pup, where p,, and p p are the magnetic moments of the muon and proton, has been determined in this way, as also from measurements of the hyperfine splitting in muonium. The current best result from muonium is 6 , X = 3.183 345 39 (10).
(3)
Professor Crane at Ann Arbour was the first to note that at low velocities the orbit frequency wc = e B / m c of an electron (or muon) in a magnetic field B is almost the same as its spin frequency w, Eq. ( 2 ) . At low velocities the spin frequency is not affected by the motion and the difference frequency is a measure of the magnetic anomaly, w,
= w, - w,
= ( g / 2 ) ( e B / m c )- ( e B / m c ) = a ( e B / m c )
(4)
so that the small quantity a E ( g - 2 ) / 2 can be measured by observing the spin angle relative to the momentum vector. Thus the quantum correction to g can be determined directly. If the magnetic field is measured in terms of the proton NMR frequency wp, one can combine with Eq. (2) and eliminate ( e l m c ) from the equation u = W,/(w, - w,) = R/(X - R)
(5)
where R = w,/wp and X = ws/wp. So a can be obtained directly from a simple ratio of laboratory frequencies. At CERN, the work centred on the belief that it should be possible to store muons in a conventional bending magnet with a more or less uniform vertical field between roughly rectangular pole pieces. In a typical field of 1.5 T , the muon orbit would make 440 turns during the muon lifetime of 2.2 pus. The polarized muon beam from the CERN synchrocyclotron could fairly easily be trapped inside a magnet. The particles were aimed at an absorber in the field; they lost energy and therefore turned more sharply
10
Figure 1. First evidence of muons making several turns in an experimental magnet, shown in fig. 2. The time of arrival of the particles at a scintillator fixed inside the magnet is plotted horizontally (time increases to the left). The first (right-hand) peak coincides with the moment of injection. The equally spaced later peaks correspond to successive turns. Owing to the spread in orbit diameters and injection angles, some muons hit the counter after nine turns (lower right), while others take 18 turns to reach the same point (Charpak et al., unpublished).
and remained inside the magnet. To prevent them re-entering the absorber after one turn, a small transverse gradient of the magnetic field was added, causing the orbits to drift sideways perpendicular to the gradient. For an orbit of radius T the sideways displacement per turn, called the step size, is s = u 1 m 2 where a1 = ( l / B ) ( d B / d y )is the field gradient. Vertical focusing was added by means of a parabolic term in the field. Fig.1 is of historical interest. It shows the first evidence of particles turning several times inside a small experimental magnet. In fig.2 you can see this magnet, borrowed from the University of Liverpool, with the group
11
around it (see caption). You may recall that Dick Garwin was employed by IBM to do whatever he liked and among other things he spent a year with us at CERN. I met him again at George Charpak’s farewell dinner in the Auberge des Chasseurs in Gex and asked “By the way, Dick, what have you done for IBM recently?” He thought for a moment and then said “I invented the laser printer.” ! ! ! *?***! Who can do better than that?
Figure 2. First experimental magnet in which muons were stored at CERN for up to 30 turns. Left-to-right: Georges Charpak, Francis Farley, Bruno Nicolai, Hans Sens, Antonio Zichichi, Carl York, Richard Garwin
After storing the muons for many turns in a magnet, one still has to measure the final direction of the spin relative to the momentum vector; and to do this one must stop the particle and wait for it to decay. If it is stopped inside the magnet it will continue to precess and the information will be scrambled. Getting the muons into the field was easy; getting them out is more difficult. According to an adiabatic theorem the flux through a walking orbit is invariant, so it is theoretically impossible to get them out. Learned experts told us we could never do it and must abandon the project! CERN had just got its first computer and I wrote what was probably the first computer tracking code. This showed that in small gradients the particles did indeed stay in the magnet, but with a steep gradient and large
12
step size per turn, they were ejected. These results gave the laboratory sufficient confidence to order a very long magnet for the experiment.
Figure 3. The 6 m bending magnet used for storing of muons for up to 2000 turns. A transverse field gradient makes the orbit walk to the right. At the end a very large gradient is used t o eject the muons which stop in the polarization analyser. Coincidences 123 and 466’53, signal an injected and ejected muon respectively.
An overall view of the final storage system is shown in Fig. 3. The magnet pole was 6 m long and 52 cm wide, with a gap of 14 cm. Muons entered at the left through a magnetically shielded iron channel and hit a beryllium absorber in the injection part of the field. Here the step size s was 1.2 cm. Then there was a transition to the long storage region, where s = 0.4 cm with the field gradient (l/B)(dB/dy) = 3.9 x per cm. Finally, a smooth transition was made to the ejection gradient where s = 11 cm per turn. The time t spent by a muon in the field was determined by coincidences in counters 123 at the input, and counters 466‘57 at the output. The time interval was measured with a 10 M H z crystal. The shimming of this large 718
13 magnet t o produce the correct gradients was a tour de force. This was assisted by the adiabatic theorem that in weak gradients the flux through a wandering orbit is an invariant of the motion. Therefore, if the field along the centre line of the magnet was constant, unwanted sideways excursions would be avoided, and this could be checked more exactly by moving a flux coil, of the same diameter as the orbit, all along the magnet. There were no pulsed magnets in this apparatus; the muons were poured into the magnet at one end, and after making up to 1200 turns inside the field they emerged spontaneously at the other end. After ejection, the muons fell onto the polarization analyser, where they were stopped and decayed to e+. This analyser was first used to study the muon beam available for injection. For muons that had been through the magnet, the analyser recorded the transverse asymmetry A as a function of the time t the particle had spent in the field. This showed a sinusoidal variation due to the (g - 2) precession in the magnet. Using Eq. (4) it follows that
A = A0 sine, = A0 sin{a(e/mc)Bt
+ q5}
(6) where q5 is an initial phase determined by measuring the initial polarization direction and the orientation of the analyser relative to the muon beam. The experimental data are given in Fig. 4, together with the fitted line obtained by varying A0 and a in Eq. (6). The result was a measurement* to 0.4% and to everybody’s surprise it agreed with theory:
u = .001165(5). The higher order diagrams which make (g - 2) for the muon larger than for the electron were apparently there. QED was better that anyone expected (Feynman himself anticipated a breakdown around q2 1 GeV2 ’). Already in 1962 Vernon was interested in the experiment. I was visiting the U.S.A. and gave a talk at Brookhaven and Vernon invited me to come on to Yale. In those days the lab had its own 2-engined plane which flew me across the water t o New Haven. After my talk, he invited me t o his house for a drink and I met Emlyn who was a toddler, about one year old. And I have to say that he was rather a mischievous little boy. But Vernon was very kind and tolerant, characteristics which we have all appreciated and enjoyed. Little did I know that this little fellow would turn into a famous professor. By now the CERN proton synchrotron (PS) was running and it was interesting to consider storing high energy muons. The lifetime would be
-
14
Figure 4. Asymmetry A of observed decay electron counts as a function of the storage time t. The time t spent in the magnet depended on the transverse position of the orbit ~ ~ 1600 turns on the parabolic magnetic field. The muons that were stored for 7 . 5 made in the magnet and then emerged spontaneously at the far end. The sinusoidal variation results from the ( 9 - 2) precession; the frequency is measured to f0.4%.
dilated but there is no factor gamma in Eqn.(4), so there would be more precession cycles t o measure with a corresponding increase in accuracy. The experiment is made possible by four miracles of Nature! First find your miracle: then put it to work for what you want to do. The first miracle is that it is easy to store high energy muons in a ring magnet. You simply inject pions and wait for them t o decay; some muons will fall onto permanently stored orbits. When pions decay in flight, the muon momentum spectrum is flat. At high energy the end point is just above the pion momentum. These muons will follow the pion orbit, hit something and be lost. But the muons of slightly lower momentum fall onto slightly smaller orbits and these can circulate without hitting anything. The second miracle is that the stored muons come from almost forward decay, and so they are forward polarized. The third miracle is that when the muons decay in flight, the electrons have less energy (because some goes to neutrinos) and so they are bent more by the magnet, and emerge spontaneously on the inside of the ring. They can be detected in lead-scintillator calorimeters which give a pulse height proportional t o energy. To have high energy in the lab, the electrons must come from forward decay in the muon rest frame: (selecting energy in the lab is equivalent to selecting decay direction in the moving frame). High energy (forward) decays are selected, so as the spin rotates the counting
15
Figure 5. First Muon Storage Ring : diameter 5 m, muon momentum 1.3 GeV/c, time dilation factor 12. The injected pulse of 10.5 GeV protons produces pions at the target, which decay in flight to give muons.
rate is modulated by the (g - 2) precession frequency, which can be read from the record. The first Muon Storage Ring was a weak-focusing ring (Fig. 5) with n = 0.13, orbit diameter 5 m, a useful aperture of 4 cm x 8 cm (height x width), a beam momentum of 1.28GeVlc corresponding to y = 12 with a dilated muon lifetime of 27ps. The mean field at the central orbit was 1.711 T . The target inside the ring was struck by 10.5 GeV protons from the CERN proton synchrotron, producing pions of 1.3 GeV/c which started to turn around the ring. The pions made, on the average, four turns before again hitting the target; in each turn about 20% decayed and some of the muons fell onto permanently stored orbits. The proton beam consisted of either two or three radio-frequency bunches (fast ejection), each 10 ns wide, spaced 105 ns. The rotation time in the ring was chosen t o be 52.5 ns, so these bunches overlapped exactly inside the ring. Fig. 7 shows the results. The dilated muon lifetime was now 27ps so the muon precession could be followed out to storage time t = 130ps. Data for t less than 20ps could not be used because of background due t o neutrons and other effects created when the protons hit the target in the ring. The initial polarization angle of the muons is not needed: one just fits the oscillations that are seen. With thirty (g - 2) cycles to fit, the accuracy in w, was now much better. The muons are bunched a t injection so there is a strong modulation 1oy11t12
N
16
Figure 6. Group in the counting room: from the left, John Bailey, Manfred Giesch, Robin Brown, Emilio Picasso, Francis Farley, Simon van der Meer, Hans Jostlein.
of the counts at the rotation frequency, fig. 7, lower curve. Because of the spread in momenta and correspondingly different rotation periods, the muons slowly spread round the ring, and the modulation dies away. The envelope of the signal is the Fourier transform of the frequency spectrum, or equivalently of the radial distribution. By making the inverse transform one recovers the radial distribution of the muon equilibrium orbits, fig. 8. This was used with the map of the magnetic field to find the mean field for the muon population. A conservatively assigned error of f 3 mm in radius implied an error of 160 p p m in the field. The result 11*12 was
a = (116 616 f 31) x
(270 p p m )
(7)
Initially, this was 1.7 standard deviations higher than the theoretical value, suggesting that there was more to be discovered about the muon. In fact the discrepancy resulted from a defect in the theory. Theorists had originally speculated that the contribution of the six diagrams involving photon-photon scattering in the QED expansion for a would be small, and perhaps these terms would cancel exactly; but they had never been calculated. The experimental result stimulated Aldins, Brodsky, Dufner and Kinoshita l3 to tackle the problem and they obtained the surprisingly large
17
Figure 7. First Muon Storage Ring: decay electron counts as a function of time after the injected pulse. The lower curve 1.5 - 4.5 p s (lower time scale) shows the 19 M H z modulation due to the rotation of the bunch of muons around the ring. As it spreads out the modulation dies away. This is used to determine the radial distribution of muon orbits. Curves A , B, and C are defined by the legend (upper time scale); they show various sections of the experimental decay (lifetime 27 11s) modulated by the (g - 2) precession. The frequency is determined to 215 p p m , B to 160 p p m leading to 270 p p m in a.
coefficient of 18.4 ! The theory then agreed with the measurement.
aezp - ath = 240 5 270 p p m .
(8)
We were rather happy about that. Towards the end of this experiment, Vernon visited us a t CERN and we had discussions on how t o do a better measurement. I recall that he was already exploring the possibility of using a high field superconducting solenoid, which he studied later with Gordon Danby. Because of the disagreement with theory, it was not difficult t o get money for a better experiment 14. But the problem was how to eliminate the
18
Figure 8. The radial distribution of muons (horizontal axis, cm) derived from the analysis of the decay electron data at early times. The muon rotation frequency has been analyzed from 1.8 - 5.5p.5. The reconstructed muon number versus equilibrium radius (dashed line) may be compared with the radial distribution of muons predicted by the injection calculations (solid line).
radial gradient in the magnetic field and still focus the particles vertically.
It was considered impossible to know the muon radius to better than 1 mm and this implied 50 p p m in the field. One could use electric quadrupoles with positive voltage at the top and bottom to repel the positive muons back towards the centre. But then there would be a radial electric field, outwards a t large radii and inwards at small radii. Radial electric fields were known to change the (g - 2) frequency, so if one could not locate the muons accurately one would be no better off. However, at a special muon energy the radial electric field does not affect the spin motion! The so called ‘magic gamma’ y = correponds to 3.096 GeV. The fourth miracle is that muons of this energy were readily available from the CERN proton synchrotron. To understand the magic energy consider fig. 9 which shows a longitudinally polarized particle being bent through 90° by a radial electric field. At low energy the electric field has no effect on the spin which ends up pointing outwards. But at very high energy, as you all know, electric and magnetic fields are indistinguishable, so there will be a (g - 2) precession and the spin will end up pointing slightly inwards. At some intermediate energy the spin will track round exactly with the momentum vector, so there will be no (g - 2 ) effect; this is the magic energy.
d
m
19
Figure 9. Bending particles in a radial electric field. At low energy, no effect on the spin. At very high energy the spin turns inwards following the (g - 2) precession. At the magic energy the spin tracks round with the momentum. The 6 m bending magnet used for storing of muons for up to 2000 turns. A transverse field gradient makes the orbit walk to the right. At the end a very large gradient is used to eject the muons which stop in the polarization analyser. Coincidences 123 and 466’57, signal an injected and ejected muon respectively.
The muons can only have the magic energy, at the centre of the aperture, where anyway there is no electric field. At larger radii they are above magic and the electric field is outwards; a t lower radii they are below magic, but the electric field is reversed, so the correction has the same sign. Two linear effects combine t o give a parabolic variation of (g - 2) frequency with radius, with a maximum a t the centre. Maxima are flat, so there is only a very small change of frequency with radius. The systematic errors in the experiment were suddenly reduced t o a few parts per million. Another major improvement was t o put the primary target outside the ring and inject a momentum-selected beam of pions. This increased the muon polarization, gave more stored muons and a huge reduction in the background counts. Fig. 10 shows part of the ring with the calorimeters being installed on the inside, and Fig.11 shows some of the people involved. Now we had much more stored intensity and fig. 12 shows the data display on the on-line computer for a few hours of running. You can see the rotation frequency of the muon bunch a t early times, combined with a
20
Figure 10. Second Muon Storage Ring, 14m diameter, with electron detectors being installed; one sees the air light pipes and iron shielding for the photomultipliers.
slow modulation due to the (g - 2) precession. Fig. 13 shows the counting room with the online display. Fig. 14 shows the precession curve for the whole experiment, going out t o 534 ps 14. This gave a result to 7 pprn in agreement with theory and we checked the Einstein time dilation in a circular orbit a t y = 29.3 to 1 part in 1000. Bob Williams thought that this was the last (g - 2) experiment, the end of the line; and for many of us it was. Emilio Picasso became director of LEP, I moved to a job in England and the group dispersed. But for Vernon it was only the beginning. He considered doing a new experiment a t Los Alamos where there was a very high intensity muon beam, albeit of low energy, but this could be compensated by using a high magnetic field. Then the AGS was upgraded and provided 100 times more beam than we had used a t CERN. So Vernon set t o work and persuaded someone to fund a one week workshop, held a t BNL in August 1984, fig. 15. Kinoshita and Marciano (probably stimulated by Vernon) called for a check on the weak interaction contribution t o the muon (9-2), then expected to be 2 p p m . Vernon tabled two propositions for discussion (a) a high field solenoid with axial injection
21
Figure 11. Participants in the Second Muon Storage Ring - back to front, left to right, Krienen, Muhlemann, Lange, Bailey, LebBe, Pertucci, Flegel, Picasso, Drumm, von Riiden, Fremont, Field, Farley
Figure 12. Counting rate vs. time showing rotation pattern and (g - 2) modulation, (online computer output for one run.) The Fourier transform of the rotation data gives the radial distribution of muons.
modeled on Crane’s famous electron measurement, and (b) an upgraded 3.1 GeV ring at the magic energy with much better statistics. It proved difficult to inject pions into the solenoid, so we ended up with a ring at the magic energy, with muon injection suggested by Fred Combley. He pointed out, to our surprise, that pion decay outside the ring would give many more
22
Figure 13. Herbert Drumm in the counting room looking at the online display. The rotation pattern of the muons combined with some (g - 2) modulation on the upper curve; longer time scale (g - 2) precession on the lower curve
Figure 14. Second Muon Storage Ring: Decay electron counts versus time (in microseconds) after injection. Range of time for each line is shown on the right (in microseconds).
23
Figure 15. Some of the participants in the 1984 workshop organised by Vernon: back to front, left t o right, Danby, Field, Farley, Picasso, Krienen, Bailey, Hughes, Combley.
muons, as well as killing the background. This was the beginning of the Brookhaven experiment with Vernon in the driving seat. It was a long struggle t o get it off the ground, but a t every stage he had a clear vision of what needed t o be done, and he got on with it. He set up a collaboration, invited groups t o join, got funding (which was never enough). Many people contributed to the formal proposal with a large input from Boston University. Vernon persuaded Brookhaven t o manufacture the magnet and got Heidelberg to build the NMR equipment for the magnetic measurements. He realised that the hadronic contribution t o the theory needed t o be improved, so he inspired the team at Novosibirsk to upgrade their measurement of hadron production in ef e- collisions. We heard that a similar experiment was planned at Beijing, but Vernon was the man who went there. Over the years, many improvements in the experiment were introduced by various people, but Ernst Sichtermann is going to speak about this. So let me just say a few words about Vernon’s style. He was quiet, thoughtful, persistent and on the phone. He kept tabs on everything and if it was going right he let it run. If there was a hiatus, he would intervene, consult colleagues and try t o improve. He was very active
24
in getting political support and raising the money. Here are some examples of his thoughtfulness. Vernon heard that Yuri Orlov had been released from exile in Siberia and was coming t o America. He invited him t o join the (g - 2) group and arranged a job for him at Cornell. Yannis Semertzidis was spending a year in CERN working with Vernon on high energy p - p and p - d scattering, the spin structure of the nucleon. But he had no car. Vernon lent him one and got his secretary t o phone him every day t o make sure he was all right. You will remember the Year 2000. This was an enormous anniversary, a once-in-a-lifetime event, everyone was celebrating, and we were all waiting for the lights t o go out, the computers to go crazy and the stock market t o crash. But the (g - 2) experiment was running; and Bill Morse was on shift with two students, missing all the fun. What would happen? Just before midnight, Vernon and Miriam turned up in the counting room with champagne and snacks. They had driven all the way from New York at night t o be with the workers and see the New Year in together. As Bill said, this was a class act .... and this was Vernon’s style. In the end the experiment worked and we got numbers, which were rather above the theory. The theorists scrambled t o check everything and two important errors were corrected; but they still did not quite match our number. Vernon was always very cautious about this. Soon we will have a result on p- and I have been asking my friends how they would react if its (g - 2) value was different from p f . Picasso said, that would be fabulous, you should publish at once. But Vernon said, “That would be a disaster”. He wanted t o check the theory, but deep down, I think, he expected it to be correct. Finally I would like to end on a personal note. I owe an enormous debt to Vernon. I count myself most fortunate t o have been invited by him to join the new (g - 2) experiment. He gave me an appointment at Yale and organised the funding. So instead of mouldering in retirement, I have been visiting the U.S.A since 1985, many times per year, interacting with bright young people, arguing with learned professors, seeing a new apparatus gradually take shape, and in short having a most enjoyable time. So my warm thanks to the chairman, faculty and secretaries at Yale for their unfailing support. Thank you t o my colleagues for putting up with me. And most of all, thank you Vernon ....... thank you very much.
25 References 1. W.H. Louisell, R.W. Pidd and H.R. Crane, Phys. Rev. 91, 473 (1953); A.A. Schupp, R.W. Pidd and H.R. Crane, Phys. Rev. 121,1 (1961). 2. V.B. Berestetskii, O.N. Krokhin and A.X. Klebnikov,Zh. Eksp. Teor. Fiz. 30, 788 (1956), [Transl. JETP 3,791 (1956)l; W.S. Cowland, Nucl. Phys. 8,397 (1958). 3. R.L. Garwin, L. Lederman and M. Weinrich, Phys. Rev. 105, 1415 (1957); J.I. Friedman and V.L. Telegdi, Phys. Rev. 105, 1681 (1957). 4. R.L. Garwin Physica, B326,1 (2003). 5. W.K.H. Panofsky, Proc. 8th Int. Conf. on High Energy Physics, Geneva, (1958), B. Ferretti ed., CERN, Geneva (1958) 3. 6. W. Liu et al., Phys. Rev. Lett. 82,711 (1999); D.E. Groom et al., Eur. Phys. J. (215,l(2000). 7. G. Charpak, F. J.M. Farley, R.L. Garwin, T. Muller, J.C. Sens, V.L. Telegdi and A. Zichichi, Phys. Rev. Lett. 6, 128 (1961); G. Charpak, B. F. J.M. Farley, R.L. Garwin, T. Muller, J.C. Sens and A. Zichichi, Nuovo. Cim. 22, 1043 (1961); G. Charpak, F. J.M. Farley, R.L. Garwin, T. MulIer, J.C. Sens and A. Zichichi, Phys. Lett. 1,16 (1962). 8. G. Charpak, F. J.M. Farley, R.L. Garwin, T. Muller, J.C. Sens and A. Zichichi, Nuovo Cim. 37,1241 (1965). 9. R.P. Feynman, Proc. 12th Solvay Conf., Brussels, 1961 (Interscience, New York), (1962) 61. 10. F. J.M. Farley, J . Bailey, R.C.A. Brown, M. Giesch, H. Jostlein, S. van der Meer, E. Picasso and M. Tannenbaum, Nuovo Cim. 45, 281 (1966). 11. J. Bailey, G. von Bochmann, R.C.A. Brown, F.J.M. Farley, H. Jostlein, E. Picasso and R. W. Williams, Phys. Lett. B 28,287 (1968). 12. J. Bailey, W. Bartl, G. von Bochmann, R.C.A. Brown, F.J.M. Farley, M. Giesch, H, Jostlein, S. van der Meer, E. Picasso and R.W. Williams, Nuovo Cim. 9, 369 (1972). 13. J . Aldins, T. Kinoshita, S.J. Brodsky and A.J. Dufner, Phys. Rev. Lett. 23, 441 (1969); J. Aldins, S.J. Brodsky, A. J. Dufner and T. Kinoshita, Phys. Rev. D 1,2378 (1970). 14. J. Bailey, K. Borer, F. Combley, H. Drumm, C. Eck, F. J.M. Farley, J.H. Field, W. Flegel, P.M. Hattersley, F. Krienen, F. Lange, G. Lebee, E. McMillan, G. Petrucci, E. Picasso, 0. Rfinolfsson, W. von Ruden, R.W. Williams and S. Wojcicki, Nucl. Phys. B. 150, 1 (1979).
MUONIUM-THE EARLY EXPERIMENTS
RICHARD PREPOST Department of Physics University of Wisconsin Madison, WI 53706 E-mail:
[email protected] During the period from 1957 to 1964 a series of experiments led by Vernon Hughes was conducted at the Columbia University Nevis Cyclotron. The formation of the p+e- atom, muonium, in purified argon was established through the observation of the Larmor precession frequency characteristic of muonium. The ground state hyperfine splitting was first roughly measured with a depolarization quenching experiment and subsequently with a precision microwave resonance experiment. At the end of this period the hyperfine splitting had been measured to 4 ppm establishing that the ground state hyperfine splitting of muonium ( A u ) could be calculated with high accuracy from the quantum-electrodynamic bound-state two body equation. Any breakdown of this basic assumption, such as unknown couplings to the muon or electron fields, would alter the theoretical value of Au.
1. Introduction An INSPEC search on the topic LLmuonium77 back to 1969 will report 4597 papers with 124 of these in 2003-2004 alone. The current muonium literature indudes papers not only on precision measurements of the ground state hyperfine splitting where the current precision is 12 parts per billion, but on muonium applications in Solid State and Chemistry. For Vernon Hughes, muonium represented 47 years of continuous involvement from 1957 t o 2003. This article will review how this came about and describe the early muonium experiments. To do this we will have t o turn the clock back to 1957.
2. Early Background and History After the discovery of parity non-conservation in the weak interactions and the realization that stopping muon beams could be highly polarized, Chicago and Columbia groups studied muon depolarization in various materials. It was discovered that the stopping muon polarization could range
26
27 from 0 to a value consistent with 100% polarization depending on the stopping material. While the p- largely form mu-mesic atoms and disappear by muon capture, the p+ disappear by free decay and the resultant positron asymmetry with respect to the muon spin direction can be used t o determine the muon polarization a t the time of decay. The Chicago group under Val Telegdi noted in one of their 1957 papers that “The formation of a p+e- atom “muonium” can be the possible cause for the reduced asymmetry of p - e decay in certain materials. The history of the early muonium searches and various remarks on formation are partly in Bulletin of the American Physical Society abstracts for short talks presented at Society meetings.The formation of muonium and its depolarizing effects was specifically discussed in several papers.’ A subsequent paper by Breit and Hughes pointed out that microwave induced transitions between muonium magnetic substates could be used to test assumptions regarding muonium formation and that the microwave frequencies a t which the transitions are induced depend upon the muonium hyperfine splitting.2
3. Early Experiments There followed a number of experiments at Chicago and Columbia to detect muonium directly. In the Columbia experiment It was suggested that muonium is formed when positive muons are stopped in nitrous oxide gas.3 Hughes, together with student D. McColm and A. Lurio subsequently searched for muonium in N20 and Ar by looking for a change in muon polarization upon the application of low frequency RF a t the muonium Zeeman f r e q ~ e n c y .No ~ muon polarization change was observed, but the authors pointed out that gas impurities, particularly 0 2 and NO could inhibit the formation of free muonium. I joined the small Yale Hughes group, then consisting of K. Ziock and Yale student D. McColm, in 1958 a t the suggestion of L. Lederman who was my Columbia advisor. The group was systematically studying muon depolarization in gases, searching for muonium formation candidates. The idea was t o start with gases known to support the formation of positronium. The gases studied were 0 2 , N 2 0 , SFc, and Ar. At the same time an argon purification system was under construction due t o the oxygen contamination concern. On the basis of the depolarization measurements we decided that purified argon was the best candidate for muonium formation. Once the argon purification system was ready, we set up a low transverse field experiment to search for the direct precession of the muonium triplet state.
28
The triplet state would be expected to precess at one half the free positron precession frequency since the g factor is one compared to the positron g factor of two. The procedure was to observe the positron rate at fixed angle in about a 4 gauss transverse magnetic field. Since the muonium precession frequency is about 1.4 MHz/gauss, more than 10 precession periods would be observed in a 4 gauss field in a muon lifetime. The observed effect would then be a sinusoidal modulation of the decay rate as a function of time.
4. First Observation of Muonium Precession After several runs in late 1959 ruling out all gas targets except purified argon, the muonium precession signal was observed in the purified argon target early in 1960.5 The target fully depolarized the muons in a transverse field of 3-5 gauss and the time dependence showed the precession modulation at the muonium frequency. The stainless steel target contained argon at 50 atm. The gas was circulated through an in-line titanium getter heated to 500'. The experimental arrangement is shown in Fig.1 A photograph of
Figure 1. Experimental arrangement. Lefktarget; Right:purifier
the beam line showing the target, helmholtz coils and the brick enclosed purifier is shown in Fig. 2. The electron decay signals were fit to an exponential modulated by a
29
Figure 2.
Beam-line photo showing target and purifier.
muonium Larmor precession term as:
+
y'a -- e - t i / T { ~ ~ e - ~ isin[a.rrf(ti / ~ '
+to)])
Here T is the muon lifetime, 7' is a parameter introduced to allow for line broadening and f is the trial value for the precession frequency of the magnetic moment of muonium. A typical positron decay distribution is shown in Fig. 3. The Larmor precession wiggles are not apparent by inspection due to the relatively poor statistics, but the Fourier analyses always showed a strong peak at the larmor frequency. Results of the frequency analysis of the decay data for several different values of the magnetic field are shown in Fig. 4. The solid curves were obtained from the analysis of the data and represent the percent amplitude of A compared to the total counting rate. The error bars correspond to an error of one sigma in the percent amplitude. The dashed curves are are theoretical line shapes centered in each case at the muonium precession frequency predicted from the measured value of the magnetic field. Resonances are clearly seen at the frequencies which are predicted for muonium precession on the basis of the magnetic field measurements. The observed amplitudes of the resonances are 4 to 5 standard deviations. Additional runs with unpolarized muons showed no resonance signal. These data are
30
40
20 Ch8.n.l
60
80
YunCw
Figure 3. A typical set of positron decay data from the time t o pulse height converter, obtained with H = 4.96 G.
Figure 4. Frequency analysis of the positron decay signal
31
consistent with close to 100% muonium formation in purified argon.5
5. First Measurement of Av The discovery of muonium made it possible to continue with the original goal of measuring the ground state hyperfine splitting. The decision was made t o design a high field microwave experiment. Under the assumption that the muon is a Dirac particle, the lowest order theoretical value for the the hyperfine splitting Au is:
G)-3 + E)
AU = ( ~ Q ~ c R (1 , ~+ )
(1 PO where Q = fine structure constant, c = velocity of light, R, = Rydberg constant for infinite mass, m = electron mass, M = muon mass, P O = Bohr magneton, and p p = muon magneton. Known values of the constants gives Au = 4460.0 MHz. The magnetic field dependence of the magnetic substates is given by the Breit-Rabi diagram shown below. 0
a-
1
2
3
H ILG) 4 3
6
7
8
1
I
I
I
1
I
i
A v f4500
I
IMj#p)
YC/LCI
2-
-2
-
-3
-
I
I
I
I
I
Figure 5. Muonium Breit-Rabi diagram
In the figure x = ( g j - gp)poH/AW where AW/h = Au and H is the external magnetic field. As a preliminary to the microwave experiment, in order t o obtain a rough measurement of Av and t o confirm the expected behavior, a static field repolarization experiment was planned. If a strong magnetic field along the direction of the original muon polarization is applied, the muon and electron m, and mJ are good quantum numbers. In
32 this limit the muon will tend to retain its initial polarization according to:
1 The experimental procedure then is to have forward and backward counters and measure the forward-backward asymmetry as a function of magnetic field. For this experiment an old cloud chamber magnet, capable of operating to 7 kg, was used in a longitudinal field configuration together with the same stainless steel 50 atm gas target used in the Larmor precession experiment. The experimental arrangement is shown is Fig. 6. The results of the
PLASTIC SCINTILLATOR BRASS
gx] GRAPHITE Figure 6.
ABSORBERS
0 6 L-I-U SCALE IN INCHES
Experimental arrangement
experiment are shown in Fig. 7.697 The quantity R is the ratio of the positron counting rate for a dummy target to the positron counting rate for the gas target with both rates normalized to 1 at H = 0. The data points are indicated together with their error bars. The solid curve is the theoretical curve which corresponds to the expected theoretical
33
1.10
T
3 5
t1
A U = 2250 MWSEC
1
H (GAUSS)
I
1000
0
I
2ooo
t YKW)
I 404)
I 5000
I
5ooo
1
I
7000 F a 13
Figure 7. Experimental data and the theoretical curves for the quantity R vs the magnetic field H.
value of A u = 4500 MHz, whereas the two dashed curves correspond t o A u = 2250 MHz and Au = 9000 MHz. The theory curves are drawn on the assumption that all the muons stopped in the argon gas form muonium, which is supported by evidence from the earlier experiment. The data are consistent with the assumptions that Av = 4500 MHz, that all muons form muonium, and that Au lies between 2250 MHz and 9000 MHz. 6. The First Microwave Experiment
While the high field repolarization experiment was in progress in 1961, J. Bailey, a Yale Post-Doc, and Yale student W. F. Cleland joined the group. A major effort was underway to design and build the high field microwave experiment. It was now necessary t o have a more accurate prediction of the hyperfine splitting, so additional corrections from the literature' resulted in an improved calculation:
Au(theory) = ( 16 p 2 C R - E ) (1
+ $)
-3
(1
+ $a2)(1 +
1 + 2 + 0.75%) (1 - 1 . 8 1 ~ ~ '(1 ) ( Use of the fundamental constants gives: x
-
Au(theory) = 4463.13 f 0.10 MHz.
In
- 0.328s)
2 ).
34
-
The experiment was designed t o induce microwave transitions between two hfs magnetic substates of muonium designated by their strong-field quantum numbers ( m ~ , m , )= (f,f) (f,-f). The transition is observed under approximate strong field conditions for which the transition frequency is roughly Au/2. The Breit-Rabi formula allows an exact calculation of Au from the observed resonance condition of the microwaves and the static magnetic field. The microwave source was a Varian 802B 1 kW klystron driving a thin aluminium cavity operating in the TMllo mode. The unloaded Q was about 26,000. The aluminium RF cavity was inside a 55 atm stainless steel pressure tank. The trigger counters defined a stopping muon (123) and the decay positron was a forward direction decay defined by (342). The magnet was the same one used in the depolarization quenching experiment described above. The ratio R was defined as events(microwaves on) divided by events(microwaves off). At resonance the angular distribution of the decay positrons changes and with a resultant increase in R at resonance. In practice, the microwave frequency was fixed and the static magnetic field was varied. For the early runs the hyperfine transition was driven in power broadened modes resulting in linewidths ranging from 44 to 120 gauss. The experimental arrangement is shown in Fig. 8. One of the the first resonance curves obtained, plotted during the run and taken directly from the log book, is shown is Fig. 9. Additional resonance curves taken at different combinations of microwave power and gas pressures are shown in Fig. 10. The result from the combination of all the early microwave runs is:
AueZpt= 4461.3 f 2.0 MHz. in excellent agreement with the theoretical value t o within the experimental error of 1 part in 2200.9110 The pressure shift extrapolated from hydrogen values was found to be -0.81 MHz a t 50 atm and considered as part of the error.
7. The Final Microwave Experiments at Nevis In the period from 1962 to 1964 the high field microwave measurements were substantially improved. The group grew in size when Yale Post-Doc M. Eckhause, Yale student R. M. Mobley, and Columbia student J. E. Rothberg joined the group. The measurement precision was greatly increased by (1) obtaining much narrower resonance lines through use of a more homogeneous magnetic field and low microwave power, (2) improving counting
35 hilarowore Power
Figure 8. Experimental arrangement. 0, 1, 2, 3, and 4 are scintillation counters.
statistics with longer runs and detecting both forward and backward decay positrons, (3) improving reliability and stability of all the components in the experiment. The argon pressure shift was measured directly showing a linear dependence with the quadratic term consistent with zero. The argon pressure shift data are shown in Fig. 11. The final Nevis high-field measurement for Au gave:” Av(ezpt) = 4463.24 -I0.12 MHz (27ppm)
The newest theoretical value a t this time was:
Av(theory) = 4463.326 f 0.019 MHz (4.2ppm) The excellent agreement provided a confirmation of the theoretical formula for Au to the order a3R,. After this time, the group activities moved to Los Alamos. The Nevis era had ended. A beautiful series of Los Alamos weak field experiments that the Yale group conducted with new collaborators resulted in the precision today of 12 ppb.
36
Figure 9. First muonium hyperfine resonance obtained. The microwave frequency is 1850.08 MHz with an Ar pressure of 55 atm. The line center is is at Hcenter = 5725 g with a line width of 120 g.
8. Muonium in Semiconductors
During the period 1959-1960, George Feher was a Visiting Associate Professor a t Columbia University from Bell Labs. While at Bell Labs Feher originated and developed the Electron Nuclear Double Resonance (ENDOR) technique and was an expert in paramagnetic impurities in solids. At Columbia he became aware of the muonium work and suggested that muonium would form in solids as shallow doner hydrogen-like states and the system so formed would be well suited as a structural probe in lesswell-understood materials. Allan Sachs and I offered t o do the experiment and Feher supplied a large number of silicon and germanium ingots from Bell Labs. To my knowledge, Feher was the first person t o suggest that muonium would be of interest to the semiconductor community. The apparatus which was used for the muonium depolarization quenching studies was suitable, and we proceeded to build a cryogenic target for the Si and Ge target samples. This work was decoupled from the Yale group, and since I was a Columbia student I was free to work on this experiment. Vernon was not terribly excited about this project but never said
37
Figure 10. Three resonance curves taken under the following conditions: (a) 50 atm, 800 W, (b) 50 atm, 240 W; (c) 35 atm, 400 W. The zero of the horizontal axis is the expected line center.
anything negative. The samples ranged from p-type Si consisting of five samples with doping ranges between lOI3 and lo1' holes/cm3 to n-type Si with a comparable doping range. The samples provide a continuous range of electron concentration from about 102 to 10l8 electrons/cm3. These samples were run at room temperature and in addition there was an n-type Ge sample with 1015 electrons/cm3 run at both room and liquid nitrogen temperature. The results for these samples in shown in Fig. 12. The results show that with increasing electron concentration there is increasing depolarization consistent with the formation of muonium. After about 1014 electrons/cm3 the polarization starts to rise with increasing electron concentration as the semiconductor shows a behavior similar to positive muons in a metal. The Ge sample at liquid nitrogen temperature showed almost complete depolarization. A preliminary depolarization quenching measurement of sample 11 found that a field of 1000 gauss quenched more than half of the muon depolarization. l5 Feher left after the first experiment, taking a position at UC, San Diego,
38
A~~m4463.15 I 0.06
-
4463.0
-
*8
-
f
t
-
a
‘
-6-
0
4462.4
Jon. 1984
ow.
-
I002 ( 8
1
o
I
to
I 20
I
so
I 40
50 Argon Dmnrlty (arm)
60
J
ro
Figure 11. Au as a function of argon gas density assuming a perfect gas law. The density is given in units of equivalent pressure at 0’ C.
where he is to this day. We continued the program with a cryogenic target capable of going to liquid helium temperatures. The work became the thesis of Bob Eisenstein, a student of Allan Sachs. The targets were expanded from Si and Ge to include LiF, MgO, Red P, and Black P. Depolarization quenching measurements were made on all the sample at room, liquid nitrogen, and liquid helium temperatures. The data were fit to a model which allowed for multiple muonium formation. Some of the low temperature samples quenched the more than half the depolarization with as little as 100 gauss. The results showed that some of the samples a t the low temperatures were consistent with a small number of muonium formations.16 After Eisenstein finished his thesis we had all moved on to other things and the program was never continued a t Nevis. Subsequently, muonium in semiconductors became a full-fledged field with considerable experimental and theoretical work.”
39
Figure 12. Experimental value of the asymmetry parameter vs. free electron concentration in n-type Si and free hole concentration in in p-type Si at room temperature, and the asymmetry parameter in one Ge sample at room and liquid nitrogen temperature.
9. The naming of muonium
Vernon always claimed that the p+e- atom was first called muonium by Pontecorvo.12 However, the term used in Pontcorvo's paper is not muonium but mesonium. The paper in the original russian uses the same term. The student lore was that the term muonium was coined by Rabi, but I do not recall that anyone ever asked him. The first mention of muonium in the literature that I know of is a paper by Friedman and Telegdi, looking for parity non-conservation of muon decay in nuclear emu1si0n.l~Both Telegdi and Hughes had positronium experiments to their credit, so it seems quite sensible that it should have been named muonium. However, critics abound. One common complaint was that muonium should be reserved for the p f p - bound state akin t o positronium and that the p f e - bound state should have been called muium. Why did this not happen? The excuses were listed as follows:
No one could pronounce muium. 0
The name became popular before conventions were formally estab-
40
0
lished, and you can’t change all the literature retroactively. No one has ever observed p+p-, so there is no practical conflict.
Finally everything was set straight by the International Union of Pure and Applied Chemistry (IUPAC) when in 2001 recommendations were made for naming conventions of muonium and muonium compounds. They state “Although chemical reactions of muonium reactions have been studied for two decades, the nomenclature of muoniumm and related species has not been addressed by the IUPAC.” They formally endorse the name muonium for the p+e- bound state with the symbol “Mu”.14 As for the annoyance of naming p+p-, they recommended “muonic muonium” . So after 44 years, muonium is official.
10. Acknowledgements
The time during which these experiments were done was a very exciting period, following so closely the discovery of parity non-conservation in the weak interactions. We worked very closely together in an era where experiments were done by just a few people. I would like to thank J. Bailey, W. Cleland, D. McColm, and K. Ziock for their friendship and collaboration. Vernon provided the inspiration for all of us. He will be sorely missed.
Figure 13. Vernon, at about the time (1967) of the Nevis period. From the left: N. Ramsey, G. Zacharias, C. Townes, 1.1. Rabi, VWH, J. Schwinger, E. Purcell, W. Nierenberg, and G . Breit
41
References 1. V. W. Hughes, Bull. Am. Phys. SOC.Ser. 11, 2 , 204 (1957); N. P. Campbell et al., Bull. Am. Phys. SOC.Ser 11, 2, 205 (1957); J. I. Friedman and V. Telegdi, Phys. Rev. 105, 1681 (1957); 106, 1290 (1957). 2. G. Breit and V. W. Hughes, Phys. Rev. 106, 1293 (1957). 3. Hughes, Lurio, McColm, Lederman, and Weinrich, Bull. Am. Phys. SOC.Ser. 11, 3,229 (1958). 4. D. McColm, V. W. Hughes, and A. Lurio, Bull. Am. Phys. SOC.Ser. 11, 4, 82 (1959). 5. V. W. Hughes, D. W. McColm, K. Ziock, and R. Prepost, Phys. Rev. Lett. 5, 63 (1960). 6. V. W. Hughes, D. W. McColm, K. Ziock, and R. Prepost, Phys. Rev. A 1, 595 (1970). 7. R. Prepost, V. W. Hughes, and K. Ziock, Phys. Rev. Lett. 6, 19 (1961). 8. R. Karplus and A. Klein, Phys. Rev. 85, 972 (1952); N. M. Kroll and F. Pollack, Phys. Rev. 86,876 (1952); R. Arnowitt, Phys. Rev. 92, 1002 (1953). 9. K. Ziock, V. W. Hughes, R. Prepost, J. Bailey, and W . Cleland, Phys. Rev. Lett. 8, 103 (1962). 10. J. M. Bailey, W. E. Cleland, V. W. Hughes, R. Prepost, and K. Ziock, Phys. Rev. A, 3,871 (1971). 11. W. E. Cleland, J. M. Bailey, M. Eckhause, V. W. Hughes, R. Prepost, J. E. Rothberg,and R. M. Mobley, Phys. Rev. A 5, 2338 (1972). 12. B. Pontecorvo, Sov. Phys. JETP, 6 ,429 (1958). 13. J. I. Friedman and V. L. Telegdi, Phys. Rev. 105, 1681 (1957). 14. IUPAC, Pure and Applied Chemistry, 73,377 (2001). 15. G. Feher, R. Prepost, and A. M. Sachs, Phys. Rev. Lett. 5, 515 (1960). 16. B. Eisenstein, R. Prepost, and A. M. Sachs, Phys. Rev. 142, 217 (1966). 17. Bruce. D. Patterson, Rev. Mod. Phys. 60, 69 (1988).
MUONIUM LIFETIME AND HEAVY QUARK DECAYS* (LESSONS LEARNED FROM MUONIUM)
WILLIAM J. MARCIANO+ Brookhaven National Laboratory Upton, New York 11973
Environmental effects on the muon lifetime are described. A general theorem on the cancellation of bound state phase space suppression and final state interaction enhancement is illustrated for muonium and muonic atoms. Lessons from those bound muon examples are applied to the b decay puzzle and apparent inconsistencies in Ke3 decay rates.
1. Introduction
When asked to speak at this Symposium honoring the distinguished scientific career of Vernon Hughes, I knew the word “muon” would have to appear in my title and some property of that particle would provide my theme. Indeed, everyone at Yale knows the answer to 1.1. Rabi’s famous question, uttered when confirmation of the muon’s existence was announced: “Who ordered that?” It must have been Rabi’s student Vernon Hughes. Who else was able to forge such a distinguished research career based to a large measure on studies of or with that particle? Better yet, why not talk about muonium. If Vernon Hughes liked anything more than the muon, it was muonium, the hydrogen like bound state of p+ and e-. He and his collaborators discovered muonium’ and lovingly studied its properties. Someday, I believe that muonium will have numerous as yet unimagined applications in physics, chemistry and life sciences,2 a glorious tribute to its discovery. So, I decided to talk about the muonium lifetime. That may seem like a peculiar topic for an entire talk. Doesn’t everyone know that muonium and the muon have the same lifetime? Well, *Invited talk present at the Vernon Hughes Symposium, Yale University, November 1415, 2003. t Work supported by DOE Grant DEAC02-98CH10886
42
43 they are almost the same, but not quite. In fact, why the difference is so small provides an instructive lesson on universal bound state principles that find applications in atomic, nuclear and particle physics; three communities that all claim Vernon Hughes as a favorite son. So, I think “lessons learned from muonium” is an appropriate theme to share with this diverse audience that has gathered to recall memories of Vernon Hughes and his scientific legacy. The contents of this talk are based on work done with Andrzej Czarnecki and G. Peter L e ~ a g eWe . ~ studied modifications of the p+ lifetime in matter due to muonium ( M = p + e - ) formation. Our study was motivated by an experiment underway at PSI4 which is designed to measure the muon lifetime to one part per million. That experiment will use electronic timing technology developed for the muon g - 2 measurement5 at Brookhaven; so, it can be considered a descendent of that heroic effort by Vernon Hughes. The question we addressed was how do bound state effects in muonium impact the muon lifetime? Is there a correction that must be made? To our surprise, the leading phase space suppression due to atomic binding turned out to be cancelled by final state e+e- interactions that follow the decay process. That cancellation was no accident and is not special to muonium decay. In fact, similar cancellations have been discussed in the literature for atomic screening of nuclear beta decay,6 muonic atoms ( P - N ) , b~quark decays,’ etc. Here, I hope to describe the universal physics responsible for such cancellations. I will also discuss what small residual bound state effects do not cancel. They can be very accurately computed for muonium, making that bound state system a model for considerations of more complicated systems such as b hadron lifetimes. So, my plan in this talk is to first discuss the utility of a precise muon lifetime measurement for testing the Standard Model and searching for ((newphysics“ effect^.^ Then I describe our work on muonium decay.3 Similar but more pronounced effects discovered by Uberall in 1960 for muonic atoms7 are then briefly explained. An analogous situation exists for hadronic b quark bound states. I try to explain, using muonium based physics, what analogous effect might be responsible for the unexpected short Ah lifetime. Then I comment briefly on a little puzzle in the kmn system that is well known here at YalelO “Why do charged and neutral Ke3 decay rates disagree with one another by about 9.5%even after isospin violation corrections are applied?” That situation has important implications for the determination of the CKM matrix element lVu31and tests of unitarity. Finally, I will end with some concluding remarks.
44
2. The Muon Lifetime and Fermi Constant G ,
Why measure the muon lifetime, rcLwith high precision? I recently discussed that issue in an article “The Muon: A Laboratory for New physic^"^ written in celebration of the 70th birthday of Albert0 Sirlin (also a muon pioneer, but on the theory side). Here, I will briefly summarize some of the relevant points. In the Standard Model, the only decay modes available to a free muon are p- -+ e-Deu, and its radiative extensions e-De,v,y, e-Deu,yy, e-De,v,e+e-. . . The total inclusive decay rate, corresponding to the sum of those rates is related to the muon lifetime, T,, and Fermi constant, G,, via
where
f(z)= 1 - 8z + 8z3- z4- 12z2ena:
(2)
is a phase space factor and RC = radiative corrections includes virtual QED corrections to an effective four fermion interaction as well as bremsstrahlung and efe- emission. Currently, the RC are known to rather high orderloill
where C is an unknown constant assumed to be O(1). Comparing the expression in eq. (1) with the well measured muon lifetime12
r, = 2.197035(40) x lOP6sec
(4)
gives the Fermi constant
G,
= 1.16637(1) x lo-‘
GeV-2
(5)
which is thereby known to Sppm, making it the most precisely determined weak interaction parameter (not counting lepton masses). I note, that if more exotic decays exist (such as p- -+ e-v,D,, i.e. the wrong neutrinos),
45
they should, in principle, be subtracted out before G, is determined. Similarly, if the muon’s environment allows additional decays, they should not be included (an example considered in section 4 is muon capture p - p -+ v,n in muonic atoms). An experiment4 under construction at PSI will aim for further improvement in T, and G, by a factor of 20! Future high intensity muon sources could probably push much further. However, on its own, G, is just a number. To utilize its precision requires a theoretical framework in which G, can be compared with other observables measured to comparable precision in a meaningful way. The Standard Model provides just such a renormalizable framework that relates G, to other electroweak parameters naturally. By natural, I mean that the radiative corrections are finite and calculable. Perhaps the best known example of such a relationship i d 3 Ira GF = (6)
f i m k ( 1 - m k / m ; ) ( l - Ar)
where Ar is an O ( a ) radiative correction that depends on mt, mHiggsand, in principle any new physics that occurs in the quantum loop corrections to muon decay, a, mZ and mw. Notice that I refer to the Fermi constant as GF in eq. ( 6 ) . That is meant to suggest that G, = GF in the Standard Model, but new physics would show up as a deviation, G, # GF,due to unaccounted loop effects in Ar.g314So, a strategy for testing the Standard Model is to determine GF with high precision in numerous ways, i.e. directly through G, and indirectly such as in eq. ( 6 ) ,including known radiative corrections. That procedure currently restricts the Higgs mass mHiggs< 180 GeV and provides powerful constraints on dynamical symmetry breaking,14 exotic muon decay^,^ properties of potential extra dimensions14 etc. To illustrate the state of the art in those comparisons, I list in table l the current values of experimental quantities that are compared in relationships such as eq. ( 6 ) . Then I give in table 2 the values of GF that follow from various
input^.^ Table 1 illustrates the fact that a , G, and mz are all measured with exteme precision. However, the other quantities that they must be compared with to gleam information about mHiggsor new physics are not known nearly as well. That point is also clear in table 2, where the current 9ppm value of G, is contrasted with the other determinations of the Fermi constant which have not yet reached *O.l% accuracy. A good goal for the future would be to push the other GF determinations to f O . O l % . At that level, they constrain the Higgs mass to about f 5 % , could see supersymmetry loop effects, might uncover effects due to extra dimensions etc.
46 Table 1. Current experimental values for measured quantities that can be turned into Fermi constant determinations. a-1
G, mz mW sin2 Ow ( m z ) m
r(z e+e-) -t
= = = = = =
r(Z 4 CVD)
=
r(T -, evP(-y))
= =
r(T + jwD(-y))
137.03599959(40) 1.16637(1) x GeV2 91.1875(21) GeV 80.426(33) GeV 0.23085(20) (Leptonic Asymmetries) 83.91(10) MeV 500.1(18) MeV 4.035(19) x GeV 3.933(19) x GeV
Table 2. Various determinations of the Fermi constant using mt = 174.3 f 5.1 GeV and mHiggs = 125'ig5 GeV in the radiative corrections.14
GF (GeV-') x lo5
Input
1.16637(1) 1.1700(70) 1.1661(20) 1.1672(20) 1.1650(20) 1.1666(45) 1.1666(28) 1.1679(28)
7,
+ Rad. Corrections
a,m z , m w a,m w , sin2 Ow (mz);c?s a,mz,sin2 O w ( m z ) q r(z -+ !+e-),mz,sin Bw(mz)m r(z + C v ~ ) , r n z , s i n ~ O w ( m z ) ~ r(T --+ evD(r))
r(7
+
L4-Y))
But why measure G, to better than ~0.0001%via the muon lifetime? It is already 100 times better known than the G F with which it is compared. One answer is: It is a fundamental quantity and should be, therefore, measured as precisely as possible. A second answer might be: Why not stay a few steps ahead of the other measurements. However, there is a more persuasive argument based on current physics requirements, in particular, the study of p- capture in hydrogen. The basic point is that comparing the p+ and p - lifetimes in matter provides indirect determinations of the p - N + u,N' capture rates via the relation
Acapture
=
z-1
-1
- T,+
(7)
That has been the traditional way of obtaining capture rates for various elements2 It works very well for high Z nuclei where the capture rate is large (it grows roughly as Z 3 Z4),but becomes very difficult for hydrogen where one expects N
47
A,(pp-
--+ nvP) 21
10-31'(p
--+
evD)
(8)
Of course, capture on hydrogen is the simplest and most interesting capture process. Furthermore, a puzzle exists from past studies of muon capture in hydrogen. The induced pseudoscalar constant g p , has been directly measured in radiative muon capture15 and found to be about g 7
N
12;
(9)
however, chiral perturbation theory predicts
The discrepency can be resolved by measuring A, for hydrogen using the p--p+ reciprocal lifetime difference and extracting g p from the total capture rate. Since it only contributes a fraction of the capture rate, one must measure AA,/A, to f l %to determine g p to f7%. That will require a lOppm measurement of T ~ in - hydrogen (now an approved PSI experiment16>17) along with the lppm rP+ experiment mentioned b e f ~ r eSo, . ~ in my opinion, the g p puzzle currently provides the main near term motivation for high precision muon lifetime measurements. The PSI experiments will stop both the p+ and p- and then basically count the decays as a function of time. The p- stopping material (hydrogen) will reduce the lifetime due to the capture mode, but what about modifications of the ordinary decay mode p- .+ e-FevP due to nuclear binding effects. Similarly, will bound state effects due to muonium M = p+eformation in the stopping material affect the p+ lifetime at lppm? These issues have been addressed in the l i t e r a t ~ r e In . ~the ~ ~next ~ ~ ~two sections I summarize what are rather surprising and interesting results from those studies. 3. Muonium (p+e-) Decay
Measurement of the p+ lifetime (at rest) requires stopping the p+ in matter and counting the number of outgoing muons as a function of time. At the lppm, one might worry about environmental effects on the lifetime. For example, will electron screening or muonium (p+e-) formation modify the decay rate? The easiest case to examine is muonium, a simple bound state with very well defined properties.lg
48
Modifications of r, for the 1s bound state of muonium, due to Coulombic interactions, can be expressed as an expansion in terms of the two small dimensionless parameters a = 1/137 and m,/m, N 1/207. Such effects must vanish as a -, 0 or m,/m, --t 0. Hence, one expects corrections of the form an(me/m,)mwhere n and m are integers. Before considering the leading corrections, let me review some basic properties of muonium’s ground state. The binding energy, average potential and kinetic energy, as well as average electron and muon velocities are given by
E = &&rne N -13.5 eV
(1la)
( V )= -a2m, N -27 eV ( T )= ia2m, 2 13.5 eV
(1lb)
(Be) 2
(114
(P,)
21
(114
(1le)
The muon rest frame and lab frame differ because (p,) # 0. That effect gives some spectral distortion due to Doppler smearing of the positron energy by terms of O(am,/m,). However, Lorentz invariance tells us that there are no corrections to the lifetime linear in velocity. Instead, that small muon lifetime velocity only gives rise to a very small time dilation increase
which is about 6 x a negligible increase. The next-to-leading spectral distortion will entail effects of order - ( V ) / m , = a2me/m,. Naively, one might expect a potential energy shift in the outgoing positron energy to give rise to a decay rate reduction due to the phase space change rn;
-+
(m, i- ( v ) 4 ) ~mE(1- 5a2m,/m,)
(13)
That small 21 1 x reduction would, if real, be about the same size as the expected PSI experiment’s ~ensitivity.~ However, it has been shown3 that final state e+e- interactions give rise to an equal but opposite sign effect that cancels the shift in eq. (13). In fact, electromagnetic gauge :~ are no anme/m, invariance, can be used to prove a general t h e ~ r e mThere corrections! The absence of such l / m , corrections is very well known to people who work on b quark physics where the operator product expansion
49
is used to show that there are no l/mb correctionssI2' t o the b quark lifetime when placed in different hadronic bound state environments, i.e. Bd, B,, A b etc. In other words, through first order in l/mb all b hadrons should have the same lifetime, a somewhat anti-intuitive feature. I return to this point in section 5. Note also that the cancellation of phase space effects due t o the electron screening potential with final state interactions also occurs for nuclear beta decays.21 but is usually disguised because the standard ,@decay formalism employs Q values for atoms rather than fully ionized nuclei. That approach hides the phase space effect; so only the final state interaction is corrected for. It has also been observed for the decay of the p - while in a muonic atom bound state. Indeed, the cancellation is a universal phenomenon. A simple illustration of the above cancellation is provided by a static sphere model in which one thinks of muonium as a p + surrounded by a fixed thin electron sphere with radius Bohr radius. The effect of that sphere gives rise to a potential V = -a2me which shifts the entire positron decay spectrum by V . The fully integrated decay rate r ( p + --+ e+vP) for a p + in the sphere is modified such that
-
There is an apparent change in phase space (limits of integration) which is cancelled by the final state interaction of the e+ with the electron sphere which shifts the differential decay rate. Overall, the shifts in eq. (14) correspond t o a simple change of variables with no net effect. So, we have learned that the very small time dilation shift in eq. (12) is in fact the leading correction and it represents a totally negligible effect for lppm muon lifetime measurements. A similar argument can be made for electron screening effects in metals which collectively give rise t o potentials similar to muonium. What are some of the higher order (in a and me/m,) corrections t o the muonium lifetime? That question is not of phenomenological importance for the muon lifetime issue, but muonium is such a simple system that we should be able to learn some useful lessons from such a study. One such correction is due to the muon-electron hyperfine interaction which modifies the lifetime by terms of order a4m2/mi. The QCD analog of that effect provides a leading l/mg correction t o b hadron lifetimes (along with time dilation), see section 5.
50
What are the leading l/mE corrections? Muonium exhibits two such effects. The first is the availability of a capture mode M --+ vep, in muonium3
Although that effect is tiny 6.6 x it demonstrates an important feature. The 2 vs 3 body final state gives rise to a very large 4 8 enhance~ ment fact. This type of capture effect can be quite important for bhadron lifetimes where 2 body annihilation or scattering can play a significant role. A final order (arr~,/m,)~ muonium decay correction is well illustrated by the simple example in eq. (14). Classically, the entire range of integration down to me-a2me is allowed. However, the real lowest energy state positronium has only 3V. So, part of the lower range of the integration in eq (14) are actually not allowed. That effect is the real quantum phase space reduction. It suppresses the muon decay rate in muonium by a tiny correction -16(am,/m,)3 I I-7 x Although very small, it also exhibits a large factor N 16 enhancement factor. Overall, one finds the following lessons learned from the relationship between the muon and muonium total decay rates3 N
N
+
+ 4 8 ~ ( ~ ~ m , / m-, 1 ) ~6 ( ~ t m , / m ~ )* ~* .
where the 4 corrections exhibited correspond to time dilation, hyperfine effects, annihilation and quantum phase space reduction respectively. Similar types of corrections will occur for other bound states, as we now illustrate by several examples. 4. p- Decay in Atomic Orbit
Muonic atoms have much larger Coulomb interactions than muonium because of their small radii and tight binding to nuclei. The average bound state potential and muon velocity are
51
For high Z nuclei, pfl will give rise to large spectral distortions. Again, the naive phase space reduction due to ( V )cancels with the electron-nucleus final state interaction, as observed by Uberall in 1960.7The leading remaining effect is a time dilation increase of the p- in orbit lifetime by a 1++Z2a2 factor which can be important for high 2 as well as a lOppm p- lifetime measurement in 2 = 1 hydrogen. There are also capture proce~ses'~ which provide a new decay mode which grows significantly with 2,
hcapture N 1000(Za)31'(p evD) -+
(18)
and again has the large 2 body enhancement factor. (It actually grows as Z4 modulo final state Pauli exclusion.) There is also a quantum state reduction of O ( Z 3 a 3 )due to the suppression" of decays with Ee- < Z2a2m,. m2 +m:
due to the posAnother interesting effect is decays with Ee- > sibility of nuclear recoil. In fact, the e- spectrum will have a tail extending all the way to m,(l - Z2a2). All such corrections are calculable;18 so they should not cloud the interpretation of the p- lifetime in hydrogen. Nevertheless, for a lOppm experiment they must be closely scrutinized.
,&
5 . b-Hadron Lifetimes
A very nice illustration of the lessons learned from muonium is provided by the lifetimes of b mesons and baryons. QCD rather than QED bound state potentials are involved, but the physics is universal. To a good first approximation all b-hadrons should have the same ( b quark) lifetime. That is a remarkable feature when one considers the broad range of b-hadron masses and the complexity of final state decay interactions. Nevertheless, the cancellation of naive phase space effects and QCD final state interactions will occur due to QCD gauge invariance. As a result, there are no l/mb corrections to the b quark lifetime induced by its hadronic environment. That property is well known to b physics workers. It is usually proven by using the operator product expansion20i22to show the leading lifetime corrections are of order l/m;. There are O(l/m;) time dilation corrections (due to the b quark Fermi motion) as well as QCD hyperfine interactions that vary from one b hadron to another. However, those corrections are expected to represent only few percent effects. Of course, the l/m: corrections to lifetimes can be potentially important. Two body processes b u -+ c d in b baryons and b d -+ c fi in the B d meson are relatively suppressed by l/m: but
+
+
+
+
52 can have large 2 body phase-space enhancements similar to the 48r factor observed for M 4 ueDp in section 3. But, are those corrections enough to bring all b-hadron lifetimes into accord with one another? To illustrate the current situation, I give in table 3 some b hadron properties along with their lifetimes12 Table 3. bhadron properties and lifetime ratios. State
Mass (MeV)
Lifetime (ps)
Lifetime/TBo
Bi = bd
5279 5279 5370 5624
1.542(16) 1.674(18) 1.461(57) 1.229(80)
1 1.083(17) 0.947(38) 0.797/53)
B l = bii B, = bB Ah = bud
How do those lifetime ratios compare with theoretical expectations, after time dilation, hyperfine interactions, and 2 body “capture” interactions are taken into account?20i22The predicted ratios are12 TB-/TB;
=1
+ O.O5(f~/200MeV)2
(19a)
TB,/TB; = 1f 0.01
(19b)
TAb/TB: = 0.9
(194
Those theoretical expectations seem to be in some disagreement with the lifetimes observed for B, and Ab. In fact, the direction of the disagreement appears to be correlated with their larger masses, i.e. looks like a phase space effect. The difference between theory and experiment, particularly for the Ab is sometimes called the b lifetime puzzle. How will it be resolved? and T? will change. Maybe the O(l/mi) 2 body rates are Perhaps T? larger than theory estimates. Large O(l/m:) effects may be the source.23 Here, I would like to suggest that a lesson learned from muonium may be the cause. The quantum phase-space reduction may be giving additional different l / m i corrections for the various 6-hadrons. (Sometimes called a breakdown of quark-hadron duality by b physics workers.) It is a tiny effect for muonium but could be a few percent for the b-hadron system. How this b lifetime puzzle issue is resolved will be interesting to watch. 6. The K + + nOe+vevs KO + n-e+ve Decay Puzzle
Another interesting puzzle has recently surfaced in Ke3(K + rev) decays. That special decay is important because it is traditionally used to obtain
53
the CKM quark mixing matrix element lVusl = sin8cabibbo. The neutral K L -+ r+e--Fe K L -+ r-e+ue decay rates together give rise to12
+
r ( K L 4 r e v ) = 0.494(5) x
MeV
(20)
On the other hand, a recent measurement by the E865 c ~ l l a b o r a t i o nat~ ~ Brookhaven found
r ( K + -+ roe+ve)= 0.273(5) x MeV (21) If isospin were a perfect symmetry, one would expect the ratio of those two rates to be 2 (because 2 modes are included in eq. (20)). However, one currently finds r ( K L -+ r*ev) = 1.81(2)(3) r ( K + 3 roev) a significant 9.5%deviation from the isospin limit. That difference gives rise (even after isospin violating corrections) to quite different determination^^^ of IV,, I from neutral and charged Ke3 decays, an unacceptable situation. What does the above problem have to do with lessons from muonium? Well, there are 2 sources of isospin violation in eq. (22), the md - mu mass difference and QED (electromagnetic) effects. The first of those gives rise to a factor ofL6
3 md-mu 1+21 1.034 (23) 2 m, - (md mu)/2 correction (from T-77 mixing) that is accounted for in extractions of lVusl from K A . It is not enough to account for the 9.5% difference on its own. In fact, it is essentially cancelled by the mKL - mK+ mass difference effect which is primarily (but not totally) due to md - mu. That gives rise to a
+
(m~+/m~ N 0.96 ~)' (24) compensating correction. The 9.5% difference must be due to electromagnetic effects or experimental error(s). Now is where the lesson from muonium comes in; specifically, the cancellation between electromagnetic phase space effects and final state interactions. Of the kaon and pion mass differences mKL - m K + , m,+ - m,o 12 involved in the Ke3 decays
54 mK+ = 493.65 m,o
MeV
= 134.97 MeV
m K L = 497.67 MEV
m,+ = 139.57 MeV
the latter is primarily of electromagnetic origin. It gives rise to a phasespace reduction of the expected ratio of 2 in eq. (22) by26 0.1561 0.9726 (26) 0.1605 That 2.6% change goes in the right direction. However, there is a fairly large final state electromagnetic (Coulombic) interaction (FSI) between the x+e- (or r e + ) which enhances the neutral Ke3 relative to the charged Ke3 by Pion Mass Phase Space reduction
FSI
N
+
1 xcr
N
11 -=
1.023
(27)
Multiplying eq. (27) times eq. (26) demonstrates the near cancellation as expected from the general theorem found for muonium, beta-decay, b decays etc. It is again a consequence of electromagnetic gauge invariance ; albeit a more subtle demonstration. In a sense, the cancellation confirms the claim made above that the pion mass difference is primarily of electromagnetic origin. Where does that leave us? The product of the 4 isospin violating corrections give rise to an overall factor of (1.034 * 0.96)/(0.9726. 1.023) = 0.998
(28)
The 9.5% deficit remains and leads to about a 4.7% difference in the Valextracted from charged and neutral Ke3 results. Something ues of /Vusl is wrong and it doesn’t appear to be the up-down mass difference or the electromagnetic effects (since the theorem works). There are various possibilities or some combination of them: 1) One of the Ke3 results is incorrect. It could be an actual branching ratio measurement or the use of an incorrect K* or K L lifetime employed to convert t o the partial decay rates in eqs. (20) or (21). In the case of both K* and K L , their properties are obtained using overall fits to all kaon data. New dedicated measurements would be welcome. 2) Perhaps the up-down quark mass difference is a factor of 2 or more larger than assumed in eq. (23). That would favor the
55
smaller value of lVusl5 0.220 extracted from neutral Ke3 decays, a value that unfortunately does not seem to respect CKM ~ n i t a r i t y 3) . ~It~ ~ ~ ~ ~ is possible that the form factors and used in the extraction26 of lVus/differ by more than the m d - mu correction effect in eq. (23). How will the Ke3 puzzle be resolved? We will have to wait and see. Note Added: After the symposium, a more detailed study of radiative and chiral corrections to Ke3 decays appeared.2g It found an increase of about +1.5% due to isospin violation, thus, also suggesting that the 9.5% in eq. (22) difference is of experimental origin and perhaps more likely in the neutral kaon system. Also, a new Ke3 result by the KTeV Collaboration at Fermilab? finds a 5% increase in that branching ratio, reducing the 9.5% difference t o 4.51
fto f?'
7. Concluding Remarks
I have tried to describe how lessons learned from our study of the muon lifetime in muonium can by analogy teach us something interesting about other bound state decay effects. Naive phase space decay rate reduction was shown to be canceled by final state interactions. Other effects such as p+e- capture and quantum state reductions, although tiny for muonium, can have significant analogous implications for muonic atoms and b-hadrons. The examples discussed have interesting puzzles associated with them. The induced pseudoscalax coupling, g p , in muon capture on hydrogen is too large. The Ab lifetime is too short. The charged and neutral Ke3 decay rates appear t o be in disagreement. Which one, if either, gives the right value of IVusl? Those types of puzzles are very healthy for physics. They stimulate new experiments and new ideas. Their resolution can lead to new discoveries and scientific or technological advances. It is the excitement of those discoveries and satisfaction of our intellectual appetites they provide that draws us to scientific research. On a personal note, I would like to end by expressing my gratitude for the work and discoveries of Vernon Hughes. His prized discovery, muonium, provided me with insights into bound state physics. He introduced me to the muon g - 2. I had the pleasure to work on some theory related to his famous polarized eD experiment at SLAC and a number of his other adventurous discoveries. He was the champion of muon physics. Hopefully, those of us who were inspired by his devotion to science will continue his tradition of excellence.
56 References 1. V.W. Hughes et al. Phys. Rev. Lett. 5,63 (1960); Phys. Rev. A l , 595 (1970); V.W. Hughes, Ann, Rev. Nucl. Sci. 16,445 (1966) 2. see Introductory Muon Science by K. Nagamine, Cambridge U. Press, 2003. 3. A. Czarnecki, G.P. Lepage and W. Marciano, Phys. Rev. D61,073001 (2000). 4. R. Carey and D. Hertzog et al, “A precision measurement of the positive muon lifetime using a pulsed muon beam and pLan detector”, PSI Proposal R-99-07. 5. V.W. Hughes, Int. J . Mod. Phys. A1851,215 (2003); G.W. Bennett et al., Phys. Rev. Lett. 89,101802 (2002); hep-ex/0401008. 6. R. Serber and H.S. Snyder, Phys. Rev. 87,152 (1952). 7. H. Uberall, Phys. Rev. 119,365 (1960). 8. 1.1. Bigi, N.G. Uraltsev and A.I. Vainshtein, Phys. Lett. B293,430 (1992). 9. W. Marciano, J . Phys. G: Nucl. Part. Phys. 29,23 (2003). 10. T. Kinoshita and A. Sirlin, Phys. Rev. 113, 1652 (1959); S. Berman, Phys. Rev. 112,267 (1958). 11. T. van Ritbergen and R. Stuart, Phys. Rev. Lett. 82,488 (1999). 12. K. Hagiwara et al. (Particle Data Group), Phys. Rev. D66, 010001 (2002). 13. A. Sirlin, Phys. Rev. D22, 471 (1980); W. Marciano and A. Sirlin, Phys. Rev. D22,2695 (1980). 14. W. Marciano, Phys. Rev. D60,093006 (1999). 15. T. Gorringe and H. Fearing, Rev. Mod. Phys. 76,31 (2004); nucl-th/0206039. 16. A. Adamczak et al., PSI Proposal R-97-05. 17. G. Bardin et al., Nucl. Phys. A352,365 (1981); T.Suzuki, D. Measday and J. Roalsvig, Phys. Rev. C35,2212 (1987). 18. V. Gilinsky and J. Mathews, Phys. Rev. 120,1450 (1960); R. Huff, Annals of Phys. 16,288 (1961); P. Hanggi, R. Viollier, U. Roff and K. Alder, Phys. Lett. 51B,119 (1974); F. Herzog and K. Alder, Helvetica Physica Acta 53, 53 (1980); 0.Shanker, Phys. Rev. D25, 1847 (1982). 19. V.W. Hughes and G. zu Putlitz in Quantum Electrodynamics, ed. T. Kinoshita (World Scientific, Singapore, 1990) p. 882. 20. N. Uraltsev, hep-ph/9804275; B. Blok and M. Shifman, Nucl. Phys. B399, 441 and 459 (1993). 21. M. Rose, Phys. Rev. 49,727 (1936). 22. M. Voloshin, Phys. Rev. D61, 074026 (2000); hep-ph/9908455; Phys. Rept. 320,275 (1999); 1.1. Bigi, hep-ph/0001003. 23. F. Gabbeani, A. Onishchenko and A. Petrov, Phys. Rev. D68,114006 (2003); hepph/0303235. 24. A. Sher et al., Phys. Rev. Lett. 91,261802 (2003). 25. W. Marciano, in Kaon Phys., eds. J. Rosner and B. Winstein, Chicago 1999, p. 603; hep-ph/9911381. 26. H. Leutwyler and M. Roos, Zeit fiir Physilc C25,91 (1984). 27. Quark Mixing, CKM Unitarity, eds. H. Abele and D. Mund (2002) Mattes Verlag, Heidelberg. 28. W. Marciano, hep-ph/0402299.
57 29. V. Cirigliano, H. Neufeld and H. Pichl, hepph/0401173. 30. T. Alexopoulos et al., (2004), hep-ex/0406001
RECENT DEVELOPMENTS OF THE THEORY OF MUON AND ELECTRON G - 2 *
TOICHIRO KINOSHITA Laboratory for Elementary Particle Physics Cornell University Ithaca, N Y 14853, USA E-mail: tk0hepth.wrnell.edu
This paper is dedicated to Vernon Hughes to honor his fundamental contributions to high precision measurements in atomic and particle physics throughout his long and fruitful research career.
1. Introduction
In 1986 Hughes and I submitted a proposal of high precision muon g - 2 experiment at Brookhaven National Laboratory, which was approved in 1987. The goal of experiment E821 was to improve the precision of the last CERN experiment by a factor 20 to about 4 x 10-l'. This will test the Standard Model (SM) prediction of electroweak effect and significantly enhance the sensitivity to new physics. After years of painstaking preparation and test it has finally approached the designed precision and begun to produce exciting physics. The latest measured value of the anomalous magnetic moment of negative muon is N
a,- (ezp) = 11 659 214 (8)(3) x 10-l'
(0.7 ppm),
(1)
where up = 51 (9, - 2) and the numerals 8 and 3 in parentheses represent the statistical and systematic uncertainties in the last digits of measurement. The world average value of a, obtained by combining this and earlier measurements is 233*435
a,(ezp) = 11 659 208 (6) x 10-l'
(0.5 ppm).
(2)
'This article is based upon the work supported by the National Science Foundation under Grant No. PHY-0098631.
58
59
This result provides the most stringent test available thus far of the Standard Model, which is written traditionally as a sum of three parts:
+ a,(had) + a,(weak),
a,(SM) = a,(QED)
(3)
although such partition is unambiguous only in the lowest order. The contribution of the three terms are roughly 100 %, 60 ppm, and 1.3 ppm, respectively. Unfortunately, the hadronic contribution a, (had) has a large uncertainty (- 1 ppm) and prevents us from carrying out the test of the Standard Model to the extent achieved by the measurements of a,. The lowest order hadronic vacuum-polarization effect has been determined in two ways: (i) e+e- annihilation cross section, and (ii) hadronic T decay. Several recent evaluations of the effect are 6*79899
~ t ) ( h ~ d . l=O6963 ) (62)e,p(36),,d x a ~ ) ( h a d . l O= ) 6948 (86) x ~ F ) ( h a d . l O= ) 6924 (59)ezp(24)radx a f ) ( h ~ d . L O=) 6996 (85),,p(19),,d(20)pr.,
x
~P( ~ ~ ) ( h ~= d 7110 . l O (50),,,(8),,d(28)~~(2) ) X
(4)
Together with the terms given later in Eqs. (6), (8), (9), and higher-order hadronic vacuum-polarization term 8Jo, the values in (4) lead to predictions which deviate from the measurement (2) by 2.70, 2.60, 3.30, 2.10, and 1.40, resp. Differences among the first four lines are due to different interpretations and treatments of basically identical data. However they all agree that the measurement of the e+e- annihilation cross section must be improved, in particular in the region below the p w resonances. Such efforts are underway at several laboratories. Particularly interesting and promising is the new radiative-return measurements 11J2: e+e-
+ y + hadrons.
(5)
A new theoretical development is an attempt to calculate the hadronic vacuum-polarization effect on muon g - 2 by lattice QCD13. The contribution of hadronic light-by-light scattering to a, is harder to evaluate reliably because it cannot utilize any experimental information and must rely solely on theory. After correction of a sign error, it seems to have settled down to around 14315316317118919
a,(had.ZZ)
-
80 (40) x
(6)
60 More recently, however, a considerably different value was reported a,(had.ZZ)
-
20:
136 (25) x
(7)
In view of the fact that this moves the prediction of the Standard Model closer to the experiment, it is important that it is checked by an inde pendent calculation. A first principle calculation in lattice QCD would be particularly welcome. The weak interaction contribution is known to the 2-loop order 21i22
a,(weak) = 152 (1) x a,(weak) = 154 (1) (2) x
(8)
where the first error on the second line is from theory and the second error is from Higgs mass uncertainty. The numerical difference between these two values is insignificant for comparison with experiment. Nevertheless it is desirable to have it resolved in one way or another. The best value of a,(QED) quoted previously was 23
uJP’~)(QED) = 116 584 705.7 (1.8) x
(9)
Terms of order a, a2 and a3 are known exactly The a4 term contributes 3.3 ppm, which is larger than the weak term (8) and the experimental error (2). Thus it must be known accurately and reliably for a meaningful test of the Standard Model. Unfortunately, the QED term a,(QED) was mostly evaluated by only one group and in only one way until recently. This is not a desirable situation, in particular, in view of the recent discovery of program error in eighteen a* diagrams 28. An independent evaluation of remaining a4 terms is urgently needed to assure the validity of this complicated calculation. Another concern about a,(QED) is of computational nature: The uncertainty given in (9) ( which is about (- 0.016 ppm)) was estimated by the integration routine VEGAS 29 assuming that they are purely statistical. This assumption is not exactly valid since any numerical work dealing with a finite number of digits suffers to varying degrees from non-statistical errors caused by rounding off of digits. Indeed we have found that some of our integrals suffer from sizable non-statistical errors. Thus this digitdeficiency (or d-d) error must be sorted out and controlled. Of course all this painstaking work may eventually become unnecessary when integration is carried out completely analytically. (A promising development in the analytic integration of multi-loop Feynman integrals was reported recently
-
24125126,27.
61 30.) For some years to come, however, the numerical integration method will be the only practical approach available.
In this talk I report the latest work on a,(QED) and ae(QED): (a) All a4 terms contributing to a, - a, have been verified by at least two independent formulations. (b) The d-d problem has been reduced to a manageable level. (c) The uncertainty of a,(QED) in the a5 term is being examined. (d) New (tentative) values of a, (electron g - 2) and cr(a,) are obtained. The term a,(QED) can be written in the general form:
ap(QED) = A1 + A2(m,/me) +Az(m,/m,) where
+ A3(m,/me, mp/m,),
(10)
A1 is calculated to order a4. (See Sec. 4 for the values of A?), A?), A?), and A?).) A?), A?), A f ) have been evaluated by numerical integration, analytic integration, asymptotic expansion in mp/me, or power series expansion in m,/m,. Thus they are known “exactly” 24825926927:
Ap)(mp/m,)= 1.094 258 282 7(104), A?’(mp/mr) = 7.8059 (25) x AP)(mp/me)= 22.868 379 36(22), A r ) ( m , / m , ) = 36.054(21) x low5, Ar)(mp/meymp/m,) = 0.527 63 (17) x lov3.
(12) The errors come only from measurement uncertainties of a,m, and m,. On the other hand, the analytical values of A?), A?), and A?’) are not yet known. Numerical approach has been the only available means to evaluate these terms. The best reported value of A?) was 31932:
Ar)(mp/me)= 127.50(41).
(13)
A$ was given a crude numerical estimate 31: Ar)(mp/me,mp/m,)= 0.079(3). (14) A P ) was also given a very crude estimate based on the renormalization group argument and a lot of guesswork 31,33: A$l”(m,/m,) = 930 (170).
(15)
62
Thus the theoretical uncertainty in a, (QED) comes primarily from AP) and A t o ) . Clearly there is still a lot of room for improvement in the context of numerical approach. Let us first discuss the improvement of A,(8 1.
2. Evaluation of AF)(mr/m,)
Ar)(m,/m,) consists of 469 Feynman diagrams. For the sake of analysis it is convenient to classify them in four (gaugeinvariant) sets. Group I. Second-order muon vertex whose virtual photon line has insertion of lepton vacuum-polarization (v-p)loops. This group consists of 49 Feynman diagrams. It is further subdivided into gauge invariant subsets I(a), W), I(c), I(d). Group 11. Fourth-order muon vertices with lepton v-p loops. This group contains 90 Feynman diagrams. Group 111. Sixth-order muon vertices with electron v-p loop of 2nd order. This group consists of 150 diagrams. Group IV.Muon vertex containing light-by-light scattering subdiagram with further radiative corrections. This group has 180 diagrams. It is further classified into gauge invariant subsets IV(a), IV(b), IV(c), IV(d).
Figure 1. Typical diagrams of Groups I(a) and I(b). In this and subsequent figures fermions propagate in the external magnetic field. I(a) has 7 diagrams. I(b) has 18 diagrams.
Groups I and I1 had been evaluated by more than one method, numerical, analytic, or others 32334935.The best results obtained are u y ) = 16.720 359 (20),
(16)
u g ) = -16.674 591 (68).
(17)
63
Figure 2.
Typical diagrams of Group I(c), which consists of 9 diagrams.
P6a
Figure 3.
P6b
P6c
P6d
Diagrams of Group I(d). It has 15 diagrams.
Figure 4. Typical diagrams of Group 11, which has 90 diagrams.
Groups I11 and N ( a ) had been evaluated only numerically. But their codes are fully tested since they are obtained from the sixth-order codes
64
Figure 5.
Some of 150 diagrams of Group 111.
Figure 6. Some of 54 diagrams of Group IV(a).
which give results identical with those of the analytic approach. We find 35 111 -
10.793 43 (414),
(18)
= 116.759 18 (30),
M,$ilp2 =
2.697 44 (15),
=
4.328 89 (30),
(19)
where the first and second members of the superscripts such as (e,e) refer to 1-1 and w p loops and e and p indicate that the loop is made of electron and muon, respectively. The remaining diagrams of Groups IV consist of three subgroups: IV(b) (LLA, LLB, LLC, LLD: 60 diagrams), IV(c) (LLE, LLF, LLG, LLH, LLI: 48 diagrams), and IV(d) (LLJ, LLK, LLL: 18 diagrams). Group IV integrands consist of several thousand terms of complicated rational functions. Because of their size, our initial effort was focused on making FORTRAN code as small and efficient as possible. This was achieved with the help of the Ward-Takahashi identity: Q P A Y P ,a) = -c(P
a + C ( p - i), + 5)
where AP is the sum of vertex diagrams generated from the self-energylike diagram C by insertion of an external magnetic field in all muon and electron propagators in C. Differentiating both sides of (20) with respect to qu we obtain
65
LLA
LLB
LLC
LLD
LLI
LLJ
LLK
LLL
Figure 7. Qpical diagrams of Group IV(b), W ( c ) ,rV(d).
The magnetic projection of the right hand side (RHS) is more complex than that of the left hand side (LHS) but gives smaller code. The a3term was evaluated using both RHS (Version A ) and LHS (Version B) 36. Since a4 term is so huge only Version A was used initially. The momentum integration was carried out analytically, initially by SCHOONSCHIF' 37, originally written by Veltman, and more recently by its successor FORM 38. This leads to exact integrals of up to 11 Feynman parameters, all generated from a small number of templates. Their renormalization terms are related exactly to the 6th- and lower-order integrals, which are known analytically. This enabled us to thoroughly cross check all diagrams of IV(b) and IV(c). For 18 diagrams of group IV(d), however, UV terms could not be related to known lower-order diagrams, making the cross-checking less effective. Initially IV(d) was evaluated in Version A only. Not satisfied by the insufficient verification of its codes we decided to check IV(d) by formulating it also in Version B. Comparison of the two versions revealed that the template for IV(d) needed additional terms not present in IV(b) and IV(c). Let us now discuss briefly the d-d problem encountered in the numerical integration. Our renormalization is a point-wise procedure, which requires in particular subtraction of 00 from 00 at singular points. This procedure is analytically well-defined but numerically dangerous, and is the major cause
66
of our d-d problem. Numerical integration has been carried out by an adaptive-iterative Monte-Carlo integration routine VEGAS, written by Lepage 29. The FORTRAN codes of Group IV are very large and require enormous amount of computing time. Furthermore, the complication caused by the dd problem forced us frequently to go to quadruple precision, which slowed down the computation by w 20, making it difficult to accumulate large statistics. Before 1990 it was simply not practical, if not impossible, to evaluate them with large enough statistics. The discovery of an error in IV(d) prompted us to check IV(b) and IV(c) by evaluating them also in Version B. This is no longer a problem because of vastly increased computing power available now. Integrands of two versions look very different, even the numbers of integration variables are different. But numerical evaluation of two versions give identical results within the uncertainties generated by VEGAS. Having carried out an exhaustive check, we are sure that all diagrams of Group IV and hence all terms contributing to AF)(m,/me)are now free from analytic and numerical error. The new results of numerical integration are 28135
/p) Iv(a)- -0.417
04 (375),
= 2.907 22 (444), aIv(c) (8) a?$(,) = -4.432 43 (58).
(22)
Comments: The values of some individual integrals are larger than 100. In each gauge-invariant set IV(b) or IV(c), however, the integrals nearly cancel out when combined. Meanwhile their errors add up in quadrature. Thus small errors in individual terms can lead to a large relative error for the sum over a gauge-invariant set. The d-d effect is thus amplified strongly in gauge-invariant sets. The new total value is 35
Ay)(mp/me)= 132.682 3 (72).
(23)
The old value was31,32
The difference comes mostly from IV(b) and IV(c). While the size of A,(8)(m,/me) is determined by a ~ v ( ~ its) error , is dominated by a ~ v ( a ) ,
a ~ v ( , )This . is why the change in A f ) ( m , / m , ) was less than 3 % in spite of the analytical and numerical problems with IV(b), IV(c), and IV(d).
67
A?) has also been reevaluated
35:
A?)(mp/me,mp/mT)= 0.0376(1).
(25) Its difference with the old value 0.079(3) 31 comes mostly from the diagrams not included in the old estimate. The relative contributions of various QED terms are shown in Table 1. Table 1. Relative contributions of the QED terms to the muon g -2. Term
Contribution in ppm
Error in p p m
994623.88 ppm 5063.86 ppm 0.36 ppm
0.0073 ppm 0.48 x
ppm
0.12x 1 0 - ~ ppm
245.82 ppm
0.24 x
ppm
0.0039 ppm
0.23 x
ppm
0.0057 ppm
0.19 x 1 0 - ~ ppm
3.31 ppm 0.94 x
0.18 x
ppm
ppm
0.21 x 1 0 - ~ ppm
0.054 ppm
0.0099 ppm
Collecting all results of orders a4 and a5 we find
a,(QED) = 116 584 719.4 (1.5) x
(26) In conclusion we found that the improvement of the a4 term did not significantly affect the comparison of theory and experiment of a,. The net effect of our calculation is to increase the value of the QED prediction by 13.7 x and eliminate an important source of uncertainty in a,,. It is seen from Table 1 that, as far as QED is concerned, the a5 term is now the most important source of uncertainty in Q ~ The . a5 term will be examined in the next section. The overall theoretical uncertainty of the Standard Model remains dominated by that of the hadronic vacuum-polarization effect and the hadronic light-by-light scattering effect.
3. Improving ~ F ’ ) ( m , / m , ) Previously, AFo)(m,/me)was estimated to be 930 (170), which contributes only 0.054 ppm to a,, well within the current experimental uncertainty. But
68
it will become a significant source of error in the future when the accuracy improves in the next generation of a, measurements. Better estimates of AY'(m,/m,) will then be needed. At this point, however, it is more out of curiosity than necessity that I began to look into this problem. The first step is to find the number of Feynman diagrams contributing to AFo)(m,/m,). It turns out to be 9080, a very discouraging number indeed ! Nevertheless, let us go ahead and classify them into several gaugeinvariant sets. The result is shown graphically by Figs. 8, 9, 10, 11, 12, and 13.
10)
Figure 8. Some diagrams of Set I. It is built from a second-order vertex. 498 diagrams contribute to A ~ o ) ( m p / m e ) .
Fortunately, it is not difficult to identify the diagrams that may give large contributions. They are characterized by some of the following criteria: (a) Diagrams containing a light-by-light scattering (l-Z-scattering) subdiagram in which one of the photon lines represents the external magnetic field,
69
Figure 9. Some diagrams of Set 11. It is built from fourth-order proper vertices. 1176 diagrams contribute to AFO)(mp/me).
Figure 10. Some diagrams of Set 111. It is built from sixth-order proper vertices. 1740 diagrams contribute to AgO)(mp/me).
Figure 11. Some diagrams of Set IV.It is built from eighth-order proper vertices. 2072 diagrams contribute to AFo)(m,/me).
(b) Diagrams containing a vacuum-polarization (v-p) subdiagram, (c) Diagrams containing several v-p subdiagrams. Diagrams of types (a) and (b) are both sources of ln(mp/me). The presence of ln(mp/me) of type (a) in the diagrams containing a light-by-light scattering subdiagram was initially discovered by numerical calculation of the sixth-order muon g - 2 39. What makes this term really large, however, is the presence of a large coefficient r2. This was given a nice physical interpretation by Elkhovskii 40.
70
Figure 12. Some diagrams of Set V. It consists of 10th-order proper vertices with no closed lepton loop. There are 6354 diagrams in this set. But none contributes t o Aro)(m,/me).
Figure 13. Some diagrams of Set VI. Each one of W(a) - VI(k) represents a gaugeinvariant subset that consists of diagrams containing various light-by-light scnttering subdiagrams. 3594 contribute to A!jlo)(m,/ m e ) .
The logarithm of type (b) is a consequence of charge renormalization. The structure resulting from the charge renormalization procedure gives rise to the renormalization group equation, which enables us to determine
71
several coefficients of descending powers of ln(m, / m e ) (sometimes even down to the constant term) by a purely algebraic manipulation in terms of known constants of lower-order diagrams It has been applied to obtain some leading terms of the a5 term, too 43. An easy but very crude way to estimate the effect of v - p insertion is to examine the structure of the renormalized photon propagator: 24,41342.
D r ( q ) = -i---[~ gpv + -(a! 1 ln(q2/m,) 2 -5 q2 lr3 9
+ ---)I.
It is seen from this that the v - p insertion is roughly equivalent to multiplying a, with a factor (a!/x)KVwhere
Here q is a fudge factor of order 1. KV N 3 for q = 1. This enables us to make crude order-of-magnitude estimates of individual integrals. Applying it to the sum over a gauge-invariant set requires some caution, however: Since member diagrams of the set tend to have strong cancelation, simplistic application of (28) can lead to a value badly off the mark unless individual integrals are known very precisely. The case.(c) is actually a part of (b) but mentioned separately to emphasize that insertion of v-p loops in various photon lines tends to contribute with the same sign and thus the size of contribution increases roughly in proportion to the number of such insertions. Based on these criteria one may conclude that the most important diagrams are those of Set VI(a) [252 diagrams] of Fig. 13 which contain a light-by-light scattering subdiagram and two vacuum-polarization subdiagrams. A somewhat smaller but still significant contribution may come from the Set VI(b) [162 diagrams] of Fig. 13. We have thus far evaluated the contributions of several subsets of the set VI, including VI(a) and VI(b) 44: Az[Vl(a)] = 629.141 (12), Az[Vl(b)] = 181.129 ( 5), Az[Vl(c)] = -36.057 (321), Az[Vl(e)] = -4.261 (214), Az[Vl(f)] = -38.335 (281), Az[Vl(i)] = -27.337 (115).
(29)
72
Note that the contributions from the subsets VI(c), VI(f), and VI(i) are sizable and negative so that they reduce considerably the positive contributions of VI(a) and VI(b). Other sets computed thus far are 44:
A2[I(a)]= 22.566 973 (3)*, Az[I(b)]= 30.667 091 (3)*, A~[I(c= ) ] 5.141 395 (1)*, A2[I(d)]= 8.8921 (ll), Az[I(e)]= -1.219 20 (71), Az[II(a)]= -70.4716 (105)*, Az[II(b)]= -34.7718 ( 29)*, A z [ I I ( f ) ]= -77.5224 (414). (31) Parts of data with * agree with the analytic results 45. A part of I(d) was also evaluated using an exact spectral function 46. Parts of I(c), I(d), and I(e) are in approximate agreement with the leading terms obtained by the renormalization group method 43. The rest of the results will be useful in fixing the unknown constants in the renormalization group analysis. All values in (29), (30), and (31) have been obtained by FORTRAN codes that can also be used to evaluate corresponding a4 integrals by a trivial change of parameters. Since a4 codes had been fully verified, these values may be regarded as firmly established. Nevertheless we still regard them as preliminary since we want to carry out few more checks. The (partial) sum of terms evaluated thus far is 44 A2Cpart.~um]= 587.55 (50). (32) It is plausible that the largest remaining contribution comes from the diagrams of the set VI(k) [120 diagrams], which has no lower-order analogue. This was crudely estimated to be 185 (85) 33 using the method developed in 40. Another non-negligible contribution might arise from VI(j). This set has a ln(mp/m,) term coming from one of the light-by-light subdiagram according to the criterion (a), while the second light-by-light subdiagram does not generate a logarithmic term since it is not attached to any external photon line. Short of direct numerical calculation, however, it is difficult to estimate its size or sign. It was given only its likely error range 0 f 40 33. To reduce the uncertainty coming from some other diagrams, we will evaluate the contributions of the sets I(f), I(g), I(h), III(a), III(b), IV in
73
the near future. According to the criteria (a), (b), and (c) these terms will not be large and their uncertainties will be smaller than those of VI(j) and VI(k). Further reduction of uncertainties by explicit calculation of these terms is crucial for obtaining a good and reliable estimate of A Y ) ( m , / m , ) . 4. Electron g
-2
The term ae(QED) can be written in the general form:
ae(QED) = A1 + A2(me/mp)+ A2(me/m,)
+ A3(me/mp,me/m,), (33)
where
The first four coefficients of A1 are the following:
A?) = 0.5, A?) = -0.328 478 965 A?) = 1.181 241 456 A?) = -1.726 0 (50).
. . ., .. ., (35)
A?) and A?) are known analytically. A y ) is known by both numerical integration 47 and analytical calculation 48. A?) is a newly revised (still tentative) value. A2,A3 and weak and hadronic contributions to a, are very small and known with sufficient accuracy for comparison with experiment. The correction of an error in Group IV(d) caused sizable shifts in a, and also in ~ ( a ,which ) is determined from the theory and experiment of the electron g - 2 2 8 . But the largest uncertainty in a, comes from 518 diagrams of Group V: diagrams which have no closed fermion loop. The internal consistency of codes for these diagrams was checked thoroughly in Version A. Unfortunately, it has not been checked by Version B or other means thus far since it requires an enormous amount of additional work. I should like to emphasize, however, that the complete verification of Group IV reinforces our confidencein Group V, which has actually gone through a more extensive check than Group IV.The numerical work on A?) is almost finished. The latest value is shown in (35). Note that the new uncertainty is 7 times smaller than the old one. As a byproduct of the calculation of Apo)(m,/me)in progress, many terms from the sets I, 11, and VI that contribute to the mass-independent
74
term A?') are being evaluated 44. All terms evaluated thus far are relatively small in size. However, work on more sets is needed t o obtain a better assessment of the size of the a5 term of a,. 5 . New values of a
For years the biggest obstacle in testing QED using a, was the unavailability of a with high enough precision. Recently the situation has been improved significantly by the atom interferometry m e a s ~ r e r n e n t : ~ ~
a - ' ( h / M c S )= 137.036 000 3 (10)
(7.4 p p b ) .
(36)
This leads to
ae(h/Mcs) = 1 159 652 175.7 (8.5)(0.2) x
(37)
where the first uncertainty comes from a of (36) and the second uncertainty is that of QED.This leads to ae(exp)- U e ( h / M c s ) = 12.6 (9.5) x
(38)
assuming that A(1o) has a value within the range (-3, 3). An alternative (and more sensible) test of QED is to calculate a from the theory and measurement of a,. This leads to the (still tentative) value of a(ae):
&-'(a,) = 137.035 998 84 (1.8) (2.4) (50) = 137.035 998 84 (50)
(3.7 ppb).
(39)
where the uncertainties on the first line are from the a4 and a5 terms and the experiment 5 0 , respectively. Note that the uncertainty in the a4term is smaller than the guesstimated uncertainty of the a5term. Until a reliable (even if crude) estimate of the a5 term is obtained, further reduction of uncertainty in A?) cannot improve theory significantly. This is why the a5 term must be examined. A(,'') has contributions from 12672 Feynman diagrams, in which the Set 5 (6354 diagrams) is the most difficult to evaluate. For comparison most precise values of 01-l available at present are shown in Fig. 14 51,52353,5435: If the uncertainty of a ( h / M c s )shrinks to 3.1 ppb, which Wicht et al. are trying to achieve 49, it will become more precise than the current best a(a,). Then we would have U e ( h / M c s )= 1
159 652 175.2 (3.6)(0.2) x
(40)
75
( a-'-137.036)x
lo7
I
CODATA 1998 l*l
I
I........................
.........................
ac Josephgon I
Cesium de Broglie
I-..lt.-l I
Neutron de Broilie
I............... .............. {
I
Electron 9-2 Muonium h.f.s.
1.1
I....................................
{-
I
I
-100
-200
0
Figure 14. Comparison of various
100
0-l.
and
a-'(h/Mc8) - Q-'(u,) = 150 (66) x lo-', or, about 2.3 s. d. discrepancy in two a's. Meanwhile, a new measurement of a, is making a good progress 5 6 . It is expected that it leads to a(a,) with the precision of 0.4 ppb or better, bringing the test of QED (and SM) to a higher level of rigor. If the discrepancy such as (41) persists even with the new measurement, it might indicate either an unexpectedly large asterm (about - 2 O O ( a / 7 ~ ) ~ ) or a possible breakdown of the Standard Model that cannot be attributed to short distance physics. This would be really exciting. Could it possibly be the first hint that QED is not entirely seamless after all ? Acknowledgment
I thank M. Nio for her assistance in preparation of the paper.
76 References G. W. Bennett et al., arXiv:hep-ex/0401008. G. W. Bennett et al., Phys. Rev. Lett. 89,101804 (2002). H. N. Brown et al., Phys. Rev. Lett. 86,2227 (2001). H. N. Brown et al., Phys. Rev. D 62,091101 (2000). J. Bailey et al., Phys. Lett. 68B,191 (1977); F. J. M. Farley and E. Picasso, in Quantum Electrodynamics, edited by T. Kinoshita (World Scientific, Singapore, 1990), pp. 479 - 559. 6. M. Davier, S. Eidelman, A. Hocker, and Z. Zhang, Euro. Phys. J. C 31, 503 (2003) [arXiv:hep-ph/0308213]. 7. S. Ghozzi and F. Jegerlehner, Phys. Lett. B585,222 (2004). 8. K. Hagiwara et al., arXiv:hep-~h/0312250. 9. V. V. Ezhela, S. B. Lugovsky, and 0. V. Zenin, arXiv:hep-ph/0312114. 10. B. Krause, Phys. Lett. B390,392 (1997). 11. A. Aloisio et al., KLOE Collaboration, arXiv:hep-ex/0307051. 12. M. Davier, talk given at the Cape Cod symposium, May 2003, http://g2pcl.bu.edu/ieptonmom. 13. T. Blum, Phys. Rev. Lett. 91, 052001 (2003); T. Blum, arXiv:heplat /0310064. 14. M. Knecht and A. NyReler, Phys. Rev. D 65,073034 (2002). 15. M. Knecht and A. NyfFeler, M. Perrottet, and E. de Rafael, Phys. Rev. Lett. 88, 071802 (2002). 16. M. Hayakawa and T. Kinoshita, Phys. Rev. D 66,019902 (2002) [arXiv:hepph/0112102]. 17. J. Bijnens, E. Pallante, and J. Prades, Nucl. Phys. B626,410 (2002). 18. I. Blockland, A. Czarnecki, and K. Melnikov, Phys. Rev. Lett. 88, 071803 (2002). 19. M. J. Ramsey-Musolf and M. B. Wise, Phys. Rev. Lett. 89, 041601 (2002). 20. K. Melnikov and A. Vainshtein, arXiv:hep-ph/0312226. 21. M. Knecht, S. Peris, M. Perrottet,, and E. de Rafael, JHEP 11,003 (2002) [arXiv:hep-ph/0205102]. 22. A. Czarnecki, W. J. Marciano, and A. Vainshtein, Phys. Rev. D 67,073006 (2003) [arXiv:hep-ph/0212229]. 23. V. W. Hughes, and T. Kinoshita, Rev. Mod. Phys. 71,S133 (1999). 24. T. Kinoshita, Nuovo Cim. B 51,140 (1967). 25. S. Laporta, Nuovo Cim. B 106,675 (1993). 26. S. Laporta and E. Remiddi, Phys. Lett. B 301,440 (1993). 27. S. Czarnecki and M. Skrzypek, Phys. Lett. B 449,354 (1999). 28. T. Kinoshita and M. Nio, Phys. Rev. Lett. 90,021803 (2003). 29. G. P. Lepage, J. Comput. Phys. 27, 192 (1978). 30. V. A. Smirnov and M. Steinhauser, Nucl. Phys. B672,199 (2003). 31. T. Kinoshita and W. J. Marciano, in Quantum Electrodynamics, edited by T. Kinoshita (World Scientific, Singapore, 1990), pp. 419 - 478. 32. P. A. Baikov and D. J. Broadhurst, in New Computing Techniques in Physics Research IV. International Workshop on Software Engineering and Artificial
1. 2. 3. 4. 5.
77 Intelligence for High Energy and Nuclear Physics, edited by B. Denby and D. Perret-Gallix (World Scientific, Singapore, 1995), pp. 167-172; arXiv:hepph/9504398. 33. S. Karshenboim, Yad. Phys. 56, 252 (1993) [Phys. At. Nucl. 56, 857 (1993)]. 34. S. Laporta, Phys. Lett. B 312, 495 (1993) . 35. T. Kinoshita and M. Nio, arXiv:hep-ph/0402206. 36. P. Cvitanovic and T. Kinoshita, Phys. Rev. D 10, 4007 (1974). 37. H. Strubbe, Compt. Phys. Commun. 8, 1 (1974); 18, 1 (1979). 38. J. A. M. Vermaseren, FORM ver. 2.3 (1998). 39. J. Aldins, S. Brodsky, A. Dufner, and T. Kinoshita, Phys. Rev. Lett. 23, 441 (1969); Phys. Rev. D 1,2378 (1970). 40. A. S. Elkhovskii, Yad. Fiz. 49, 1056 (1989)[Sov. J. Nucl. Phys. 49, 654 (1989)]. 41. B. Lautrup and E. de Rafael, NucI. Phys. B 70, 317 (1974). 42. T. Kinoshita, H. Kawai, and Y. Okamoto, Phys. Lett. B 254, 235 (1991); H. Kawai, T. Kinoshita, and Y. Okamoto, Phys. Lett. B 260, 193 (1991). 43. A. L. Kataev, Phys. Lett. B 284, 401 (1992). 44. T. Kinoshita and M. Nio, paper on the tenth-order QED contribution to a,,, in preparation. 45. S. Laporta, Phys. Lett. B 328, 522 (1994). 46. T. Kinoshita and M. Nio, Phys. Rev. Lett. 82, 3240 (1999); Phys. Rev. D 60, 053008 (1999). 47. T. Kinoshita, Phys. Rev. Lett. 75, 4728 (1995). 48. S. Laporta and E. Remiddi, Phys. Lett. B 379, 283 (1996). 49. A. Wicht et 01. in Proc. of 6th Symp. on Req. Standards and Metrology (World Scientific, Singapore, 2002), pp. 193 - 212. 50. R. S. Van Dyck, Jr., P. B. Schwinberg, and H. G. Dehmelt, Phys. Rev. Lett. 59, 26 (1987). 51. A. Jeffery et al., IEEE Trans. Instrum. Meas. 46, 264 (1997); Metrologia 35, 83 (1998). 52. P. Mohr and B. Taylor, Rev. Mod. Phys. 72, 351 (2000). 53. E. R. Williams et al., IEEE !iTans. Instrum. Meas. 38, 233 (1989). 54. E. Kriiger, W. Nistler, and W. Weirauch, Metrologia 36, 147 (1999). 55. W. Liu, Phys. Rev. Lett. 82, 711 (1999). 56. G. Gabrielse, Cape Cod Symposium, May 2003; G. Gabrielse, Cornell physics colloquium, Dec. 1, 2003.
VERNON HUGHES AND THE QUEST FOR THE PROTON’S SPIN
ROBERT L. JAFFE Center for Theoretical Physics Laboratory for Nuclear Science and Department of Physics Massachusetts Institute of Technology Cambridge, M A 02139 E-mail: jaffe @mit.edu Vernon Hughes dedicated much of the latter part of his career to the question “What carries the spin of the proton?” The question remains unanswered and near the top of the list of fascinating questions in QCD. I present a perspective on the question and Vernon’s pursuit of an answer.
1. Introduction
We all know that the spin of the proton is $ti. The question is: How do the contributions of quarks and gluons add up. Vernon Hughes loved this subject. There is a famous old photo which alleges to show a group of physicists discussing spin. [Figure 1.1 I believe it captures the intensity and excitement that Vernon brought to his work on spin in QCD. Vernon was a tough cookie. He pursued terrific goals with a singlemindedness that often drove his friends and collaborators to distraction. He was, however, remarkably patient with theorists, especially young ones and ones who shared his love of spin. Falling in both those categories back when spin in QCD first attracted his attention, I was lucky to have shared with Vernon twenty five years of interest in the spin of the proton. Among the high points were workshops here at Yale in the 1970’s and 1980’s when QCD spin physics was out of favor and Vernon was on a mission to stimulate interest among theorists and experimenters. Vernon managed to badger us into recognizing the importance of spin in deep inelastic phenomena, and stimulated much good work in theory as well as experiment. Looking back at his career, it is clear that Vernon had a taste for an elegant experiment that could decide a complex issue by measuring one or two numbers. His pursuit of muonium and the muon’s anomalous magnetic 78
79
Figure 1. “Two high energy physicists discussing the spin of the proton.”
moment are cases in point. In the spin substructure of the nucleon he identified a similar problem in QCD, where they are hard to come by. Once he settled on measuring the spin sum rules, he pursued the goal with characteristic intensity. The pursuit took him from SLAC to CERN by way of Fermilab, and lasted from the early 1970’s until the end of his life. He achieved his goal, but to his and everyone else’s surprise, the measurement of the nucleon’s spin sum rules raised new, pressing questions that have given birth to a new generation of QCD spin physics experiments, led by several of Vernon’s younger students and colleagues. Abhay Deshpande has described them here. Vernon’s achievements in QCD spin physics are important and easy to summarize: 0
0
0
Vernon realized that the Bjorken Sum Rule1 is fundamental to QCD. He realized that the nucleon spin sum rules2 could provide finely tuned information about how nucleons are put together. He developed and led an experimental program spanning 25 years
80
0
that culminated in precise measurements of both. He inspired and prodded theorists to respond to these experiments, especially to define the components of the nucleon spin.
A measure of his impact can be seen in the ‘&stateof the art” summary of measurements of g:p shown in Fig. 2.
10 3
--
X d . 0 2 5 ( x 512)
10
--
10
X.O.125 ( x 32)
t
Figure 2.
A recent summary of measurements of gyp as a function of
I
2
and
Q2
In this talk I will give a theorist’s perspective on the problem of the nucleon’s spin in QCD and Vernon’s contributions to it. 2. What is the issue and why should we care?
QCD is the theory of matter. More than 99% of the visible mass in the Universe is made of quarks and gluons. There is of course great current excitement about dark matter and dark energy. While it is essential to find
81
out what they are, it is almost certain that all of what actually happens in the Universe - change, structure, complexity, etc. - plays out in terms of particles made of quarks, gluons and a dash of electrons. QCD is also the only non-trivial theory that we are certain describes Nature. The electroweak sector of the Standard Model is mere perturbation theory. The world beyond the Standard Model is fascinating but the relevance of any particular suite of ideas to Nature is speculative at best. Furthermore QCD incorporates all the features one expects to encounter in future deeper, more unified theories: the interactions follow from local symmetries alone; there are no free parameters (at least in the light quark sector); mass emerges dynamically; although simple at the fundamental level, the theory is capable of generating rich, non-perturbative structure including dynamical breaking of chiral and conformal symmetries; the ground state is a mystery to us; finally, there are fascinating regularities (eg. vector dominance, the constituent quark model, diquark and instanton dynamics) that do not follow trivially from the underlying Lagrangian. String theorists do well to study QCD to see what sort of problems are in store for them when they finally figure out what string theory is! QCD is hard for the same reasons it is elegant. For light quarks there are no parameters. The coupling runs with distance scale. It is small at short distances, so we can probe hadrons in deep inelastic processes. However hadrons form at precisely the scale where the coupling is of order unity. None of the clever attacks on light-quark QCD - chiral dynamics, large N,, instanton models, QCD sum rules, constituent quark and bag models, etc. - provides a progressively improvable approach to the structure and properties of the nucleon. Each has added insight: for example, we have a qualitative understanding of the nucleon’s magnetic moment from quark models, and of the NAT system from combinations of N , 4 00 and chiral dynamics. Lattice QCD, although capable in principle of answering many important questions about the nucleon, has proved unable to shed light on important and well-posed questions like “What is the gluon contribution to the proton spin?” or “What is the quark orbital angular momentum in the proton?” Certainly no one was able to anticipate the almost complete violation of naive expectations observed when Vernon and his colleagues first measured the nucleon spin sum rule.
82 3. Why the nucleon’s spin?
What attracted Vernon to the nucleon spin problem seems t o have been first the possibility of testing QCD precisely by checking Bjorken’s Sum Rule, and second, the possibility of making a precise measurement of the quark contribution to the nucleon’s spin by measuring the separate proton and neutron spin sum rules. Bjorken’s Sum Rule dates from the Dark Ages of QCD, when quarks were not yet reputable, and field theory was still in eclipse. In his enormously influential 1966 paper on quarks at short distances Bjorken wrote down his famous sum rule (converted to modern notation),
where gI”(x,Q2)and g:”(x, Q 2 ) are the proton’s and neutron’s polarized deep inelastic structure functions. At the time Bjorken was most interested in the fact that the right hand side was independent of Q2 - evidence for scaling. The possibility of measuring g:psenwas so remote that Bj followed his result with a now famous quote that set the stage for Vernon’s work on this subject: “Something may be salvaged from this worthless equation by constructing an inequality. . . ” It is worth examining the theoretical basis of the sum rule. Bjorken assume that ‘the commutators of electromagnetic current operators behaved as in free field theory,
where the operators O(Z) are linear combinations of the unrenormalized currents themselves. At the time this was heresy: Chewian “nuclear democracy” was dominant and hadrons were supposed to be composites only of one another4. Now we know that asymptotic freedom in QCD validates Bjorken’s assumption up to calculable logarithmic corrections. The sum rule follows from broad general properties of QCD plus isospin invariance alone. It relates physics at totally different distance scales: QA is the nucleon’s axial charge measured in P-decay, effectively at zero momentum Q 2 )are measured at asymptotically high momentum transfer, and gIPSen(z, transfer. Such sum rules should give pause to advocates of the modern “effective” approach to field theory. While QCD can be formulated in terms of
83 effective operators defined a t a hadronic scale, you won't discover relations like eq. (1) that way. Bjorken's Sum Rule continues to occupy a special place in QCD. It is now possible to compute corrections t o the sum rule in a threefold series: a) perturbative QCD corrections - a power series in a s ( Q 2 ) 5 1b) target mass corrections - a power series in M 2 / Q 2 , and c) higher twist corrections - a power series in ( F ) / Q 2where , (F)are the matrix elements of more complex operators measuring quark and quark-gluon correlations in the nucleon6. Years of work by theorists is summarized by the 2004 version of the sum rule:
1'
as - -2 43a2 1- (xlQ2)= -6l g gvA 7r 127r2
{
dx gyp-en
+
"1
1
Q2
{9
dxx2 2gyp-en(x, Q 2 )
+ 6g2ep-en(xl
Q2)}
- --Fu-d(Q2) 1 4
(3)
Q 2 27
Sum rules are interesting if both the left and the right hand sides are directly related to experiment and if both have important theoretical significance. Bjorken's Sum Rule relates two strikingly different ways of measuring the (isospin weighted) up and down quark contributions to the nucleon's spin. The parton model provides the simplest interpretation of the left hand side:* In the parton picture the polarized structure function gI(x, Q 2 ) measures the helicity weighted momentum distribution of quarks in a nucleon a t infinite momentum. When an electron scatters from a nucleon with four momentum P , transferring four momentum q , the nucleon structure information is encoded in structure functions that depend on the Lorentz invariants Q 2 = -q2 and x = Q 2 / 2 P . q. The contributions to g1 a t large Q 2 are given by gyP(xc1 Q2) =
e i (Aqa(xl Q 2 )
+ &(x1
Q2))
(4)
a
where Aqa(xlQ 2 ) is the helicity weighted probability to find a quark of type a and momentum fraction x in the polarized proton. (Aq is the same for antiquarks.) These probabilities evolve slowly as the probe resolution, *Subtleties can always be resolved by recourse to the operator product expansion and perturbative QCD.
a4
Q 2 , is increased. When integrated over x we obtain
where Aqa(Q2) has the interpretation of the total contribution of the helicity of quarks and antiquarks of flavor a to the helicity of the nucleon at infinite momentum. The proton-neutron difference that enters the sum rule is proportional to the difference of u and d quark helicities. The right hand side of the sum rule arises more formally. The cross section for deep inelastic electron scattering is proportional to the product of two electromagnetic currents acting at points separated by a light-like interval. This product has an expansion similar to (2), and the particular operator, 0 ,singled out by a) letting Q2 -+ 00, b) taking the p n difference, c) looking for nucleon polarization dependence, and d) integrating over IC, is the isospin weighted axial vector current,
A$ = i i y ” 7 5 ~- &”75d
(6)
So the dominant term on the right hand side of (3) is given by the matrix element of this operator - a very fortunate result: not only is A: the operator that mediates the Gamow-Teller contribution to neutron P-decay, but it is also the (isospin weighted) quark spin contribution to the angular momentum operator. This is actually a slightly subtle subject to which I’ll return at the end of the talk. So, if we define,
AQa ( ~ ~ 1=s ”( ~ s l ~ d ‘ 7lp2 5 ~IPS) a
(7) then we can interpret AQa as the contribution of the spin of quarks and antiquarks of flavor a to the spin of the proton. The renormalization scale p 2 appears because the individual quark axial currents are not conserved and therefore not renormalization group invariant. The isovector combination, A U - A D however, is conserved and is proportional to the nucleon’s axial vector charge, AU
- AD =
( N s l i i ~ ” 7-5 ~d ; ( ” ~ ~ , d l N ~ ) / sg”A = 1.2670 f 0.0030 (8)
Identifying the isospin weighted helicity sum in the infinite momentum frame with the isospin weighted spin contribution in the rest frame, we get Bjorken’s sum rule. This derivation invites one to speculate about the possibility of measuring other flavor weighted quark spin contributions - a possibility that ~ > led ~ to the nucleon spin sum rules was considered in the early 1 9 7 0 ’ ~and often referred to as the Ellis-Jaffe Sum Rules2.
85
The total light quark spin contribution to the proton’s spin can be obtained by adding the contributions from the u, d , and s quarks:+ AX(p2) = AU(p2)
+ AD($) + AS(p2)
(9)
There are serious problems with such a generalization of Bjorken’s Sum Rule: first, this combination cannot be extracted from baryon P-decay data, and second, the famous Adler-Bell-Jackiw triangle anomaly ruins the conservation of the associated flavor-singlet axial-vector currentg>lo, rendering A E renormalization scale (and scheme) dependent as indicated by the p dependence in (9) l. The first problem actually spurred the experimental efforts on polarized deep inelastic scattering in the 1980’s and 1990’s. It certainly attracted Vernon’s interest. First consider baryon P-decay. The operators that mediate weak semileptonic decays of baryons are all flavor changing, either d -+ u or s u, and therefore have no SU(3)flavor-singletcomponents. Thus by taking suitable combinations of nucleon and hyperon @-decays,and using SU(3)flaVorsymmetry, one can measure the flavor non-singlet combinations AU - A D and AU A D - 2AS, but there is no sensitivity to AX. In the standard language of SU(3)flavor,12 ---f
+
(AU - AD) (AU
+ AD - 2AS)
+
F D 3 g A = 1.267 f 0.011 3 F - D = 0.585 f 0.025
t 10)
Neutral weak currents which contribute to elastic neutrino scattering or parity violating electron scattering are sensitive to AX13114,but so far no one has succeeded to use those processes to extract AE. Enter polarized deep inelastic scattering: The integrals over g p ( z ,Q2) and gp“(z, Q2) measure the charge-squared weighted sum of quark axia,l charges, which can be re-expressed in terms of the F, D, and AX,
1 18
= -(3F
Jd
co
1 + D + 2AX(Q2)) = (9F - D + 6AS(Q2)) 18
d z g y ( z , 0’) = 1 18
= -(-20
+ 2AX(Q2))=
1
(6F - 4 0 + 6AS(Q2)) (11)
+The small contributions of heavy quarks can be computed using QCD perturbation theory.13
86
Thus polarized deep inelastic scattering measures AE(Q2), the total quark spin contribution to the spin of the nucleon, or equivalently if you prefer, AS(Q2), the fraction of the nucleon’s spin carried by strange quarks and antiquarks. Back in 1973 Ellis and I speculated that the nucleon contained no polarized strange quarks, and estimated the integrals of gyp and gTn by setting A S = 0. This was before asymptotic freedom, which taught us among other things, that A S is Q2-dependent, so if it were to vanish at one Q2, it could not be zero at a higher scale. Still, the assumption gave experimenters like Vernon something to shoot at. When we set A S to zero we obtained AE = 0.60 f0.05. So even in those benighted times it was clear that quarks’ spin did not account for 100% of the nucleon’s spin. Parenthetically this was the same phenomenon responsible for dropping the value of g A from its non-relativistic quark model value of 5/3 down to its experimental value closer to 4/315. As early as 1974 Sehgal suggested that quark orbital angular momentum made up the other 40%16. The other difficulty with the separate proton and neutron spin sum rules is the fact that the integrals are Q2 dependent. This was not recognized until quite late”. In the absence of the triangle anomaly all the axial currents are conserved up to quark mass terms. This is enough to prove that their matrix elements are renormalization group invariant. So originally the spin sum rules were thought to be on the same theoretical foundation as Bjorken’s Sum Rule. In 1978 Kodaira et a117718showed that the anomaly gave rise to a small (two loop) anomalous dimension and an associated weak Q2 dependence for the flavor singlet axial current and therefore for AX. This allows the quark spin fraction measured in the deep inelastic domain to differ both in value and interpretation from the quark spin “measured” in quark models. This subtlety has spawned hundreds of theory papers, and is still controversial. It won’t be settled soon either, because quark models are not sufficiently well defined to allow one to assign renormalization scale or scheme dependence to the numbers extracted from them. Now, however, is not the time or place to follow this thread of QCD spin physics history further.
4. Testing the spin sum rules
Vernon’s long standing interest in spin physics led him to propose an experiment to measure polarized deep inelastic scattering at SLAC. Others at this meeting have described the how the polarized target and beam were developed and how Vernon fought for the physics, so I will be brief. The
87 first experiment, E80, too crude to test any sum rule, was notable because it demonstrated that polarization persisted in the deep inelastic domain as Bjorken had predictedlg. The first data on polarized DIS is shown in Fig. (3), Despite the quality of the data and the fact that only proton targets
0.8
-
0.4
4
e “
0
-0.4
-0.8
Figure 3. Left: first data on g1/Fl for e p scattering. The old scaling variable w = 1/x was still in use. Right: First attempt to compare polarized DIS with theoretical models.
had been studied, Vernon and collaborators quickly attacked the Bjorken Sum Rule and tried to distinguish among theoretical models. In a 1978 paper entitled “Deep Inelastic e-p Asymmetry Measurements and Comparison with the Bjorken Sum Rule and Models of Proton Spin Structure””, they attempted the first comparison with theory. Their results are shown in Fig. (3) where they compared with some of the models of the day. E80 was followed by a much higher precision experiment, E130, which did allow for a meaningful comparison with theoryz1. The results, which were much discussed at the time, are shown in Fig. (4). The curve was the prediction of a model by Carlitz and Kaur22,consistent with both the Bjorken and Ellis-Jaffe Sum Rules. Clearly a meaningful test of the sum rules required still higher precision data, and in the case of Bjorken’s Sum Rule, data from a “neutron”, ie. deuteron or 3He target. Even as El30 was in process, SLAC was redirecting its polarized electron program to measure parity violating deep inelastic scattering and to the now famous test of the Standard Vernon’s attempts to obtain approval for a followup to E80 and El30 were rejected by the SLAC PAC. After an unsuccessful attempt to interest Fermilab in a polarized muon deep inelastic scattering program Vernon and his group migrated to Europe, where they joined the
88 0.7
0.6 0.5
:0.4 h
0,
0.3 0.2
0.I 0
0 I.*.'
0.2
0.4
0.6 X
0.8
1.0 *"*>A.
Fig 4 Figure 4. Data from El30 compared t o the Carlitz-Kaur model, which was consistent with the Bjorken and Ellis-Jaffe Sum Rules.
European Muon Collaboration, renamed the Spin Muon Collaboration, and helped lead its attack on polarized DIS. The result was confirmation of the Bjorken Sum Rule and a clear signal that something other than quark spin carries a majority of the spin of the proton. The SMC final word on the Bjorken Sum Rule was 0.174f0.005f0.010 measured for the left hand side at Q2 = 5 GeV2, and 0.181 f 0.003 for the right hand side computed from &decay, and perturbative QCDZ4. The world's data on the integrand for the Bjorken Sum Rule are shown in Fig. (5). The SMC data on the proton spin sum rule, shown in Fig. (6), came as quite a surprise to uninitiated, who incorrectly expected 100% of the nucleon spin to be on the quarks' spin, and to the initiated, who expected approximately 60%. Instead the number has settled down somewhere around
89
(World's data in 1998)
Figure 5. The world's data on the integrand of the Bjorken Sum Rule.
25-35%,25
AE(Qg) AU(Qi) AD(Qg) AS(Qg)
= 0.28 f 0.16 = 0.82 f 0.05 = -0.44
f 0.05 = -0.10 f 0.05
(12)
at QE = 5 GeV2. Notice that a relatively small polarized strange quark contribution (-0.10 f0.05) corresponds to a shift of 3 x -0.10 = -0.30 in AX and moves the result from the expected value of NN 0.60 to the observed value of M 0.30. The situation was quite chaotic in 1988 and many theorists wrote things about the spin content of the proton that they would perhaps sooner forget today26. The relation between the quark spin and quark axial charge was not generally understood. Some thought that the quark spin plus the gluon spin had to add up to the nucleon spin, forgetting about orbital angular momentum. The operator description of gluon spin, was worked out by Manohar in 199128,generalizing work by Collins and Soper many years before, which had been forgottenz9. During this period Vernon persistently
90
lo-’
s,’
Figure 6. Left: the SMC data on g;p(z) and d d g 7 P ( z ’ ) . Right: The proton spin sum rules measured by different experiments at different Q 2 .
asked “What is the sum rule for the spin of the proton?”, ie. What are the components of the total angular momentum in QCD, and how can they be measured? His persistent questioning stimulated a series of papers in which the components of the angular momentum were defined and the possibility of measuring them was considered. Perhaps the most notable fallout from this was Ji’s formulation of generalized parton distributions and the elucidation of their role in the spin puzzle. Most of these issues have now been settled, and the principal focus of the community has shifted to the measurement of other components of the nucleon spin, especially the contribution of the spin of the gluons. Groups at RHIC (STAR and PHENIX), at CERN (COMPASS), and at HERA (Hermes) are attempting to measure the gluon contribution, AG(Q2). Abhay Deshpande has described some of these efforts in his talk. It suffices to say that we don’t know if AG contributes significantly. Indeed we don’t even know if it is positive - although initial estimates seem to suggest so. Measuring AG is now the highest priority for the field. 5. So what is the sum rule for the spin of the proton? Vernon’s question: “What is the sum rule for the proton’s spin?” is answered by2?, 1 1 -2 = -AE(Q2) 2 WQ2)L , ( Q ~ ) L , ( Q ~ )
+
+
+
which looks rather obvious: the sum of the spin (AX and AG) and orbital ( L , and L,) contributions of quarks and gluons. However, there is more here than meets the eye. In fact there are two different versions of (13), neither entirely satisfactory.
91
In order to make sense of the total angular momentum one must first recognize that it is not a vector, but instead a rank-2 antisymmetric tensor. In fact it is most fruitfully regarded as the integral over space of the time component of a rank-3 angular momentum tensor density, J k = t k i j d3xMoij, where27
s
MP”‘
=
- z”D’)$
z&cl(x”D”
2
+ ;€PuAu4yuy5$
+ 2Tr {Fpa(z’Du - x”D’)A,} + n(FP’A” F ~ ~ A ~ } + terms that do not contribute to J”’ -
(14)
This conserved tensor (dPMP”’ = 0) is a variant$ of the Noether current associated with Lorentz invariance of which rotations are, of course, a subgroup. The four terms shown are the quark and gluon orbital and spin contributions respectively. The quark spin contribution is the simplest: the components of the rank-3 tensor are proportional to components of the axial current - a great simplification. Sum rules for the proton’s spin follow from considering either the time ( p = 0) or light-cone-time ( p = +) component of MPVX. Here I would like to distinguish between a sum rule and an operator relation. A sum rule expresses the expectation value of a local operator in a state as an integral (or sum) over a distribution measured in an inelastic production process involving the same state. This is the traditional definition of a sum rule, dating back to the Thomas, Reiche, Kuhn Sum Rule of atomic spectroscopy. They are especially powerful because the distribution which is integrated has a simple, heuristic interpretation as the momentum (Bjorken-z) distribution of the observable associated with the local operator. Bjorken’s Sum Rule is a classic example as discussed above. Another, less powerful but still interesting type of relation-sometimes called a sum rule in the QCD literature-arises simply because an operator can be written as the sum of two (or more) other operators, 0 = 01 0 2 . If the expectation values of all three operators can be measured, then this relation, and the assumptions underlying it, can be tested. Such a relation exists for the contributions to the nucleon’s angular momentum 27,30,
+
1 2
-
- = L,
1 + -C + J, 2
$It has been constructed from the symmetrized, “Belinfante” stress tensor.
92
where the three terms can be interpreted as the quark orbital angular momentum, the quark spin, and the total angular momentum on the gluons. Ji has shown how, in principal, to measure the various terms in this relation 30. A sum rule of the classic type also exists for the contributions to the nucleon's angular momentum 31,32733,
2 =
1'
{
dx L,@, Q2)
+ -12A c ( z , Q2) + Lg(x,Q2) + AG(x,Q2)
where the four terms are precisely the x-distributions of the quark orbital angular momentum, quark spin, gluon orbital angular momentum, and gluon spin. However it appears that the distributions L q ( x , Q 2 )and Lg(x, Q2) are not experimentally accessible. So the value of the sum rule is obscure. To extract both the relation (15) and the sum rule (16) polarize the nucleon along the 3-direction in its rest frame and set v = 1,X = 2 in order to select rotations about the 3-direction. The matrix element of M0l2 is normalized in terms of the nucleon's momentum (P= ( M ,0, 0,O)) and spin (SP = (O,O, 0, M ) ) 27. First consider the time component:' M'l2,
i 1 M'l2 = - q t ( Z x f i ) 3 q + - q t c 7 3 q + 2 T r E j ( Z ~ i f i ) 3 A j + T r ( E ~ x(17) )3. 2 2 The four terms look like the generators of rotations (about the 3-axis) for quark orbital, quark spin, gluon orbital, and gluon spin angular momentum respectively. Taking the matrix element in a nucleon state at rest, one obtains 1 1 - = L, -C Lg + A G . (18) 2 2
+
+
There are problems, however. There are no parton representations for i g , Lq, or AG, so it is not a sum rule in the classic sense. We know from the nucleon spin sum rules how to write C as an integral of the helicity weighted quark distribution, but AG is not presented as an integral of the helicity weighted gluon distribution. Interactions prevent a clean separation into quark and gluon contributions. And worse still, Lg and AG are not separately gauge invariant, so only the sum j g = Lg AG is physically meaningful. The most important feature of the relation, eq. (18), is the result derived by Ji, that j , = L,+ic and j gcan, in principle, be measured in deeply virtual Compton scattering 30.
+
93 Turning to the +-component sum rule, we find a much simpler form, 1 z8)3q++ - q l y s q + + 2 T r F + j ( Z x l8)Aj + T r ~ + - ~ j F + z A j 2 (19) in A+ = 0 gauge.§ The four terms in M+12 correspond respectively to quark orbital angular momentum, quark spin, gluon orbital angular momentum, and gluon spin, all about the 3-axis. Each is separately gauge invariantq and involves only the “good”, i.e., dynamically independent, degrees of freedom, q+ and Each is a generator of the appropriate symmetry transformation in light-front field theory. The resulting sum rule, M+12
1
= &(ZX
Al.
1 2
- = L,
1 + -C + L, + AG 2
is a classic deep inelastic sum rule. It can be written as an integral over z-distributions as given in (16). Each term is an interaction independent, gauge invariant, integral over a partonic density associated with the appropriate symmetry generator. AX is the same quark spin contribution that we have seen before. AG is the gluon spin helicity distribution that will be measured over the next decade. However the parton distributions of quark and gluon orbital angular momentum have so far eluded us. We do not know any experiment that can access them. So the experimental answer to Vernon’s question still awaits us. We might be lucky and find that AG together with AX M 0.3 saturate the angular momentum sum rule. More likely, however, orbital angular momentum is important and the challenge of measuring it or relating it to other measurable or calculable quantities remains for Vernon’s descendents, both figuratively - the next generation of experimentalists and theorists studying QCD - and literally, since one of the leaders in this endeavor is another Hughes! References 1. J.D. Bjorken, Phys. Rev. 148,1467 (1966). 2. J. Ellis and R.L. Jaffe, Phys. Rev. D 9, 1444 (1974), erratum 10,1669 (1974).
§This gauge condition must be supplemented by the additional condition that the gauge fields vanish fast enough at infinity. VNote however, that in any gauge other than A+ = 0, the operators are nonlocal and appear to be interaction dependent. The same happens to the simple operators involved in the momentum sum rule, eq. (20)
94 3. N. Makins, Talk given at 8th International Workshop on Deep Inelastic Scattering and QCD (DIS 2000), Liverpool, England, 25-30 Apr 2000. Published in “Liverpool 2000, Deep inelastic scattering”. 4. M. Gell-Mann, in Proceedings of the 13th International Conference on High Energy Physics (University of California Press, Berkeley, 1967). 5. S. A. Larin and J. A. Vermaseren, Phys. Lett. B B259,345 (1991). 6. E. V. Shuryak and A. I. Vainshtein, Nucl. Phys. B B201,141 (1982). 7. A. J . G. Hey and J. E. Mandula, Phys. Rev. D 5,2610 (1972). 8. M. Gourdin, Nucl. Phys. B 38 (1972) 418. 9. S. L. Adler, Phys. Rev. 177 (1969) 2426. 10. J. S. Bell and R. Jackiw, Nuovo Cim. A 60 (1969) 47. 11. R. L. Jaffe, Phys. Lett. B 193,101 (1987). 12. M. Hirai, S. Kumano and N. Saito [Asymmetry Analysis Collaboration], Phys. Rev. D 69,054021 (2004) [arXiv:hep-ph/O312112]. 13. D. B. Kaplan and A. Manohar, Nucl. Phys. B 310,527 (1988). 14. R. D. Mckeown, Phys. Lett. B 219,140 (1989). 15. A. Chodos, R. L. Jaffe, K. Johnson and C. B. Thorn, Phys. Rev. D 10,2599 (1974). 16. L. M. Sehgal, Phys. Rev. D 10, 1663 (1974) [Erratum-ibid. D 11, 2016 (1975)]. 17. J. Kodaira, S. Matsuda, T. Muta, K . Sasaki and T . Uematsu, Phys. Rev. D 20 (1979) 627. 18. J. Kodaira, S. Matsuda, K. Sasaki and T. Uematsu, Nucl. Phys. B 159,99 (1979). 19. M. J. Alguard et al., Phys. Rev. Lett. 37,1261 (1976). 20. M. J. Alguard et al., Phys. Rev. Lett. 41,70 (1978). 21. G. Baum et al., Phys. Rev. Lett. 51, 1135 (1983). 22. R. D. Carlitz and J. Kaur, Phys. Rev. Lett. 38,673 (1977) [Erratum-ibid. 38,1102 (1977)l. 23. Experiments in which Vernon and the Yale group were active participants, C. Y. Prescott et al., Phys. Lett. B 77,347 (1978); C. Y. Prescott et al., Phys. Lett. B 84,524 (1979). 24. B. Adeva et al. [Spin Muon Collaboration], Phys. Rev. D 58,112001 (1998); Phys. Rev. D 58,112002 (1998). 25. These are the final numbers from the SMC. The analysis of spin dependent parton distributions continues to be a subject of considerable interest in anticipation of the new experiments at COMPASS and RHIC. For a recent analysis with qualitatively similar results, see J. Blumlein and H. Bottcher, Nucl. Phys. B 636,225 (2002) [arXiv:hep-ph/0203155]. 26. For a review and critique of early work see Ref. 27. 27. R. L. Jaffe and A. Manohar, Nucl. Phys. B 337,509 (1990). 28. A. V. Manohar, Phys. Lett. B 255,579 (1991). 29. J. C. Collins and D. E. Soper, Nucl. Phys. B 194,445 (1982). 30. X. D. Ji, Phys. Rev. Lett. 78,610 (1997) [arXiv:hepph/9603249]. 31. P. Hagler and A. Schafer, Phys. Lett. B 430, 179 (1998) [arXiv:hepph/9802362].
95 32. S. V. Bashinsky and R. L. Jaffe, Nucl. Phys. B 536,303 (1998) [arXiv:hepph/9804397]. 33. A. Harindranath and R. Kundu, Phys. Rev. D 59, 116013 (1999) [arXiv:hepph/9802406].
THE SPIN STRUCTURE OF THE NUCLEON: A HUGHES LEGACY
GORDON D. CATES Department of Physics, University of Virginia, Charlottesville, VA 22903 More than any other individual, Vernon Hughes can be pointed to as the father of the experimental investigation of nucleon spin structure. Even theoretical development in this area was spurred on by Vernon’s pioneering efforts to make the control of spin degrees of freedom an experimental reality. This talk traces some of Vernon’s work in this area, as well as examining, briefly and not in a complete fashion, some of the other work that can be looked upon as Vernon’s legacy.
1. Introduction
More than any other individual, Vernon Hughes was responsible for initiating and leading the experimental investigation of the spin structure of the nucleon. Vernon embraced the importance of utilizing spin degrees of freedom as a means for testing our understanding of matter. Realizing that such experiments would require a suitable source of polarized electrons, he began work on a prototype in the early 196O’s1i2.As the results of deep inelastic scattering of unpolarized electrons began t o unfold in the late 1960’s, Vernon was poised to begin exploring the underlying spin structure of the nucleon. It is amusing to trace the influence of Vernon’s work in the literature. In 1966, Bjorken wrote the famous paper in which he derived the Bjorken sum rule using current algebra3. In this paper, referring t o spin-polarized cross sections, he states that “ It will be a long time before these cross sections are measured.” Later, in the same paper, he refers to what we now call the Bjorken sum rule as “ ... this worthless equation ...”. Because of Vernon’s work, however, it soon became clear that the study of spin dependent cross sections was not such a far fetched goal. In a paper written four years later titled “Inelastic Scattering of Polarized Leptons from Polarized nucleon^"^ Bjorken starts out in the introduction: “Some time ago, a high-energy sum rule involving electromagnetic scat96
97
tering of longitudinally polarized leptons from polarized protons and neutrons was derived and then dismissed as ‘worthless’. However, it turns out to be interesting to reconsider that negative conclusion in light of the present experimental and theoretical situation.” Later Bjorken states that: “It appears to be possible to produce electron or muon polarized beams which have nearly 100% longitudinal polarization.” and he specifically references a paper by Hughes, Lubell, Posner, and Raith5. In just four years a measurement that had seemed completely impractical had become something worth contemplating quite seriously. It seems unlikely that this change of attitude would have taken place if Vernon had not demonstrated that a source of polarized electrons could indeed be built. Vernon, in his usual way, brought to nucleon spin structure a love for that which is fundamental. He emphasized the value of studying sum rules because by doing so, one could glean the most precise information about the problem. The Bjorken sum rule in its simplest form can be written
where gy and g i are the spin structure functions of the proton and neutron respectively, and they are integrated over the full range of the Bjorken scaling parameter x. The constants g~ and g v are the axial-vector and vector couplings that characterize &decay of the neutron. As Bob Jaffe discusses in these proceedings, the Bjorken sum rule can also be written to include both perturbative and non-perturbative corrections. I often have felt that Vernon was attracted to the Bjorken sum rule because he wanted to launch QCD onto a path of increasingly accurate measurements in much the same way as has been the case in QED. I say this, however, recognizing that Vernon always considered the proton an unfortunately complicated object. Ellis and Jaffe recognized that one could also construct sum rules for the proton and neutron individually6. Here some care needs to be taken because the quantities one encounters are affected by the axial anomaly reference and are sensitive to the factorization scheme and renormalization scale. Still, the formalisms explored by Ellis and Jaffe made it possible, within the naive quark-parton model, to deduce the extent to which the spin of the nucleon comes from quark contributions. To do so requires a measurement of the so-called first moment of the spin structure function of either the proton or the neutron, :?I = J ; gydx or I?; = gydx. I will say more on this later.
Jt
98
2. The early SLAG program
In 1970, Vernon proposed to measure the spin asymmetry in the scattering of polarized electrons from a polarized proton target, an experiment that came to be known as E80. The proposal came at a time when the quark-parton model was still in its nascent period, and was designed to see certain gross features of spin structure that one would associate with the quark-parton model. E80 presented large technical challenges, requiring what would be the first high energy polarized electron beam, and a polarized proton target that went well beyond what had been accomplished previously. The polarized electron source was based on the aforementioned prototype developed at Yale in the 1960’s. Eventually known as PEGGY, it utilized an atomic beam of 6Li that was state selected using hextapole magnets, and photoionized using a pulsed source of ultraviolet light.7. Depicted in Fig. 1, at the time it was built, PEGGY was overwhelmingly the most intense source of polarized electrons ever constructed. During E80 it produced around lo9 electrons/pulse at 120 pulses/sec with a polarization of around 0.5. Following E80 it was established that the polarization was limited by a multistep ionization process. With the elimination of this process, the electron polarization of PEGGY was increased to the impressive level of 0.85.
IWechanical Chopper
Longitudinally polarizing
Figure 1. Illustrated are the major subsystems of PEGGY, the first polarized electron source t o be used on a high-energy accelerator, built by Vernon’s group at Yale.
99
E80 used a polarized nuclear target based on dynamic nuclear polarizatioq (DNP). While E80 was not the first high energy experiment to use a DNP based target, the E80 target broke new ground in certain performance characteristics. It was probably the first such target to utilize a 5 T magnet, something that enabled the use of a 4He refrigerator while still achieving good polarization. With a 4He refrigerator, the E80 target was more tolerant of beam intensity than otherwise would have been the case. The E80 target used butanol beads as a target material, doped with 1.4% porphyrexide. Beam rastering and regular target annealing were used to deal with the effects of radiation damage. Some of the subsystems of the E80 target are shown schematically in Figure 2'.
Figure 2. Illustrated are some of the major subsystems of the Yale/SLAC polarized proton target that was built for use in E80.
The goal of E80 was to determine the spin asymmetry
Al =
*l/2
- *3/2
*l/2
+ *3/2
where ( ~ 3 1 2 )is the total virtual photoabsorption cross section for the nucleon for the case where the total angular momentum of the proton and
100
the virtual photon, when projected onto the direction of the virtual p h e ton, is 1/2 (3/2). In order to determine AI, E80 recorded experimental asymmetries of the form
where dot1 (doTT) is the differential cross section for scattering when a longitudinally polarized electron beam is antiparallel (parallel) to a longitudinally polarized target. The experimental asymmetry Aexpis related to the physics asymmetries A1 and the transverse physics asymmetry A2 by Aexp= D(Al +qAa) where q is a kinematic factor and D , known as the depolarization factor, represents the depolarization of the virtual photon with respect to the polarization of the incident polarized electrong. For the kinematics studied during E80, and indeed most deep inelastic spin-structure experiments using a longitudinally polarized target, Aezp M D A l . The results of E80, the first of their kind, are shown in Fig. 41°. The asymmetries were large and positive, a result that favored the quark-parton model according to a prediction by Bjorken based on his sum rule4.
0.8 0.4
a
t f o \
Q
-0.4
-0.8
Figure 3. Shown are the first spin asymmetries from the scattering of polarized electrons from polarized protons obtained during the SLAC experiment E80.
101
The SLAC program continued with E130, in which several improvements were incorporated1l?l2.The electron polarization was increased substantially to 0.85 from 0.50, and increases in the target polarization were also achieved. For some of the El30 running a new spectrometer was constructed with substantially larger acceptance. With these improvements and additional running time, data on the spin structure of the proton were mapped out over a range of Bjorken z of 0.10 < z < 0.64. This permitted the first crude test of the Ellis-Jaffe sum rule, and under the assumption that the neutron asymmetries would be negligibly small (based on simple quark models), a first look at the Bjorken sum rule.
--
--0
0.2
0.6
0.4
0.8
1.0
X Figure 4. The final results of E80 (open diamonds) and El30 (closed squares) together with several theoretical predictiond2.
The early SLAC spin-structure experiments provided the first information on the spin structure of the proton, and started a new field, but stopped short of making definitive measurements of the Bjorken and Ellis-Jaffe sum rules. If Vernon had had his way, however, the early SLAC program would have gotten quite a bit further. In Fig. 5, the projected errors of a second generation of experiments are shown. Known alternatively as “Son of E130” or E138, the proposal described an experiment whose statistical accuracy is not so bad when compared to the modern experiments that have actually been carried out. Sadly, particularly given the great surprises that were later seen in nucleon spin structure, El38 was not approved. In the late 1970’s SLAC was in hot competition with CERN working to bring the SLAC linear collider, SLC, online. This effort was taxing the lab, and
102
perhaps made the spin-structure program seem like a distraction. In retrospect, however, it is hard not to see El38 as quite a missed opportunity. Luckily, however, there was no way that Vernon was going to drop his dogged pursuit of the physics!
PROTON ASYMMETRY
-0.2 0
0.2
0.4
0.6
X
DEUTERON ASYMMETRY
0.8
1.0
-0.2
0
’
‘
0.2
’
’
1
0.4
0.6
’
I
0.8
’
1.0
X
Figure 5. The projected errors on A1 from the proton and the deuteron from SLAG E138, an experiment known as “Son of E130” that was proposed by Vernon as a follow-on to E80 and El30 but was not allowed to run.
3. The CERN program
With the option of further studies at SLAG cut off, Vernon sought an alternative means to pursue his study of nucleon spin structure. He first joined Fermilab experiment E665 which was studying unpolarized deep inelastic muon-nucleon scattering, hoping to stimulate interest in studying polarized muon-nucleon scattering. While this did not work out, Vernon was subsequently invited to join the European Muon Collaboration (EMC) at CERN, where interest in polarized muon-nucleon scattering was building, and a large volume polarized target was under development. The spinstructure program at CERN proved to be a huge success, with the efforts of EMC being followed by the Spin Muon Collaboration (SMC) of which Vernon was spokesperson. The CERN program produced seminal data that triggered explosive growth in spin-structure studies. To this day the EMC and SMC results have the best coverage in the important kinematic regime of low Bjorken IC.
103
3.1. The EMC spin-structure experiment Using the M2 muon beam at the CERN SPS accelerator, the EMC experiment collected data on the scattering of polarized muons off what was then the largest polarized proton target in existence. With incident muon energies up to 200 GeV, the EMC collected more than a million events over a range of Bjorken x spanning 0.01 < x < 0.7. While the flux of muons was modest, up to 4 x lo7 per pulse every 14 seconds, the polarized target had two cells each of which was 360 mm in length, resulting in a reasonable event rate. The proton polarization was typically between 0.75 and 0.80 and the muon polarization was roughly 0.8, both of which are quite high and contributed to the quality of the data.
Figure 6. Results from EMC on x g1 of the proton as a function of Bjorken x, and the integral of gy as a function of the lower limit of integration.
When the EMC published their results in 198813>14, they pushed our knowledge of spin structure to values of x that were an order of magnitude smaller than had previously been the case in the early SLAC experiments, greatly improving the accuracy with which the first moments of the spin structure functions could be evaluated. In Fig. 6 the EMC results for the spin structure function gy of the proton are shown. The improved
104
coverage at low x is readily apparent. Also shown is the integral of gy as a function of the lower limit of integration. While the full integral requires an extrapolation to x = 0, the plot makes a convincing argument that the integral is converging to a value well below the prediction of the Ellis-Jaffe sum rule, which is also shown on the figure. The EMC result, as presented in their first paper13, was that the integral of gy 1
F ? = J d g?(x)dX = 0.114 f 0.012(st~t.)f 0.026(syst.)
,
(4)
a result that was in strong disagreement with the Ellis-Jaffe (EJ) Sum Rule6, which was quoted in the same paper as predicting that a =
Jd
1
gf(x)dx = 0.189 f0.005 .
(5)
The Ellis-Jaffe sum rule was derived using SU(3) current algebra under the assumption that the strange quark sea was unpolarized. Conversely, it was recognized that if the Ellis-Jaffe sum rule was violated, one explanation was that the strange quark sea is highly polarized. Within the naive quark-parton model (QPM), the first moment of gy has a particularly simple form in terms of Au, Ad and As, where Aqi = (4: - q/)dz is the probability difference for the momentum distributions corresponding to a quark that is aligned or anti-aligned with the nucleon spin. Again within the naive QPM, Aqi is the fraction of the nucleon’s spin carried by the quark helicity of flavor i. Writing the first moment I?; and the Bjorken sum rule out in terms of the Aqi’s, we have
Jt
4 9
1 9
-AU + -Ad
1 + -AS = 2 I?; 9
(6)
A u - A d = - gA gv A u + A ~ - ~ A=s 3 F - D where the third expression follows from SU(3) flavor symmetry. A more theoretical discussion of these matters can be found in Bob Jaffe’s paper in this proceedings. Within this framework, including also first-order QCD corrections, the EMC computed AX = Au Ad As, the fraction of spin carried by all the quarks, to be 0.120 f0.116 f0.234. That is, the fraction
+
+
*A more modern value for the EJ Sum Rule, evolved to a Q2 of 5GeV2, corrected to order a:, and using updated values for the SU(3) couplings F and D would be ry = 0.163 f0.00429.
105
of spin carried collectively by all the quarks is quite small and consistent with zero! The EMC result touched off what at the time was called the “proton spin crisis”, and what some would now call the proton spin puzzle. There was great surprise that so little of the spin of the nucleon was carried by quark spin. The EMC result certainly changed prevailing views of nucleon spin structure, and provided strong motivation for further studies. Experimental efforts were launched at several major laboratorie~l~. At CERN the Spin Muon Collaboration, or SMC, was formed as a follow-on to the EMC with Vernon as spokesman. At SLAC, the very laboratory that had shut down Vernon’s original program, a new set of experiments were undertaken, some of which were led by Vernon’s son Emlyn. And at DESY, the HERMES experiment was formed, a program that continues taking data to this day. In addition to experimental activity, there has also been a huge amount of theoretical progress. Indeed, it is probably fair to say that the effort that went into understanding the EMC result set the stage for many of the more topical subjects in QCD today. At the time of this writing, the paper announcing the EMC result^'^ has been cited roughly 1000 times and nucleon spin structure has grown into a large and rich field.
3.2. The Spin Muon Collaboration (SMC) With the enormous impact of the EMC results, the motivation to continue studying nucleon spin structure at CERN was very high. The Spin Muon Collaboration (SMC) was formed under Vernon’s leadership, and proceeded to collect data from 1992 until 1996 on both the proton and the deuteron. For a Q2 > 1 (GeV/c)2, the SMC collected data down to a value of Bjorken z = 0.003, roughly three times smaller than was the case for the EMC. To improve their statistics, the SMC used a proton/deuteron target comprising two cells, each 60 cm in length, a truly huge polarized target. They also collected data over an impressive length of time. In the end SMC presented data comprising 15.6 million events on the proton and 19.0 million events on the deuteron (after cuts), an impressive increase over the 1.2 million events collected by the EMC. The final papers written by the SMC, published in 1998, included a paper detailing the SMC’s final experimental results16, and a next-to-leading order (NLO) perturbative QCD analysis of the world spin structure data such as it was at that time including the final SMC results17. Then, as is still the case, the SMC experiment had the best coverage at low Bjorken
106
x of any experiment to study spin structure. And despite a limited muon flux, their statistics were also impressive. The SMC experiment gave Vernon a vehicle for pursuing scientific interests that were cut short at SLAC. SMC also formed a vibrant intellectual center for the study of spin structure that helped spur worldwide activity both in experiment and theory. 4. The second generation SLAC nucleon spin-structure
program
When the EMC results were released, which dealt strictly with the proton, it was clear that studies were needed of the neutron. The EMC collaboration itself emphasi~ed’~ “ ... it is of crucial importance to measure the asymmetries from a target containing polarised neutrons ...” In 1989 the first of a new generation of spin-structure experiments was proposed at SLAC to address this need. Dubbed E142, the experiment proposed t o measure the scattering of polarized electrons from a polarized 3He target18t9. Organized and led by Emlyn Hughes, there was amusing irony that it was a Hughes that was bringing the study of spin structure back to SLAC. El42 was a legacy of Vernon’s in more ways than one! While some accelerator-based experiments had previously used gaseous 3He targets, El42 brought the practice to a new level. The target was much larger than those that preceded it, and provided a luminosity approaching 1036Cm-2~-1. El42 was the first of five experiments in a new generation of SLAC spin-structure experiments. It was followed by E143, an experiment that used polarized solid targets containing first hydrogen and then deuteriumlg. El42 and El43 were both run at energies of 29 GeV or less. The energy was limited not by the accelerator, but by the beam lines that transported the beam into End Station A, the area in which the experiments were performed. With an upgrade of the beam line making an energy near 50 GeV possible, a second set of experiments was performed including El54 that again used polarized 3He20921y22, and E15523 and E 1 5 5 ~that ~ ~ ,again used solid hydrogen and deuterium polarized targets. In addition to higher energy, E154, E155, and E155x benefitted from additional improvements, including substantially higher electron polarization due to the use of a “strained” GaAs photocathode. The new generation of SLAC spin-structure experiments, both before and after the 50 GeV beam-line upgrade, were characterized by superb
107
statistics, but took place at significantly lower energies than were available at CERN and consequently had more modest coverage in terms of Bjorken x. The precision of the later SLAC results, however, ensures that they are weighted heavily in any type of global fit of spin-structure data. Because I am mostly familiar with the polarized 3He experiments, I will restrict my detailed comments on the second generation of SLAC experiments to El42 and E154.
4.1. SLAC E l 4 2 El42 was designed to provide a high luminosity study of the spin structure of the neutron at a time when virtually no data on the neutron existed. Polarized electrons were scattered from a polarized 3He target at energies of 19.4 GeV, 22.7 GeV, and 25.5 GeV. Two spectrometers were used at 4.5" and 7.0". The average Q2 of the data was 2GeV2, and data were taken at values of Bjorken x as low as 0.03. Average beam currents were in the range of 1 - 4pA, with an average polarization of 0.38 f 0.02. The target polarization was 0.36 f 0.02 Approximately 300 million events were used in determining gy from E142. While this is substantially more than the 1.2 million events collected by the EMC, the advantage was less pronounced than one might naively conclude. The target and beam polarizations during El42 were about a factor of two lower than in EMC, and the dilution factor (about .11) was about .65 the dilution factor of EMC (about .17). The statistical errors on the two experiments were thus not that dissimilar. And of course, EMC had the clear advantage that their lowest x bin was 0.015 versus 0.030 for E142. Still, the quality of the information that El42 provided was impressive, and at the time, there were no other precision data for the neutron. It is interesting to compare the El42 results for g i to the EMC results for the proton and the early SMC results for the deuteron25 that were being published at roughly the same time. Such a comparison is shown in Fig. 7 taken from the thesis of one of the El42 students26. It is clear that the El42 data were quite precise by any standard, and completely transformed the experimental situation for the neutron. Critical to the success of El42 was the construction of a suitable polarized 3He target. The target was based on the technique of spin-exchange optical p ~ m p i n g ~a ~two-step l ~ ~ , process in which 1) rubidium atoms are polarized by optical pumping, and 2) spin is transferred from the Rb valence electrons to the nuclei of 3He atoms by the hyperfine interaction during
108
.............. 1................ 4.................................................................. L
4.05
I
0
-
1........................................................................
+
9.05
o.05
x&
O
9.05
CC
I
L E-142 Neutron
o.05
xgy
: : :I
a
'
-: : : f 1 SMC Deuteron
@
I
I
+ +
*
w/ :
1:-f. ......................................................................... + + '
"
+
*$ ....... ........ 1
-
............-
I
Figure 7. Shown are data from EMC, SLAC E142, and SMC on the nucleon spin structure function g1(z) such as existed around the time the El42 results were first published.
collisions. At the time it was proposed, it appeared that a polarized 3He target could be built with a luminosity approaching cm-2 s-'. Achieving such a luminosity, however, meant scaling the volume of polarized gas by a large amount over anything that had been done previously. It was not clear to what extent unanticipated problems would be encountered. Spin-exchange optical pumping typically takes place in a sealed glass cell, containing up to around 10 atmospheres of 3He, about 70 Torr of N2, and on the order of 100 milligrams of metallic Rb. The magnitude of the challenge that faced El42 is illustrated in Fig.8 which shows two El42 target cells, ready to be filled with 3He, together with a cell just over 2 cm in diameter which was more typical of samples used for spinexchange optical pumping at that time. The SLAC cells have volumes of around 150 cm3, whereas the smaller cell has a volume around 10 cm3. Targets for use at TRIUMF and Bates with volumes as large as 35cm3 were under development at the time that El42 was proposed, but their
PerP 5. SLAC E154
ormannce had not yetormannce been established. had not yet been established. ormannce had not yetormannce been established. had not yet been established.
ormannce had not yet been established. ormannce had not yet ormannce been established. had not yet been established. 60 1
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also used two new spectrometers, one at 2.75", and one at 5.5". The impact of the experimental improvements is readily apparent in the comparison of El54 data with that of El42 shown in Fig. 9. 0.03
xg: 0.02
0.01
0
-0.01
-0.02
-0.03 lo-'
1
X
Figure 9. Plotted is a comparison of the El54 data with the El42 data on the product of Bjorken x with the longitudinal neutron spin structure function 91".
To this day, El54 provides the most precise data on the spin structure of the neutron over the kinematic range it covered. As a result, the El54 results are heavily weighted in world next-to-leading order perturbative QCD analyses of spin-structure data. With Emlyn at its helm and many of Vernon's former colleagues in other leadership positions, El54 represented an excellent example of Vernon's legacy. 6. Next-to-leading order perturbative QCD analyses
While sum rules involving integrals of the spin structure functions provide a means for accessing remarkably fundamental information, it is a practical reality that the full range of the Bjorken scaling variable, 0 5 z 5 1, is not experimentally accessible. Of particular importance is the region from the lowest value of x at which data are available down to x = 0, since this is a regime in which sea quarks and gluons become increasingly prevalent.
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Probably the most accepted way of coping with this problem is a nextto-leading order (NLO) perturbative QCD analysis. In this approach, the spin structure function is parameterized at low Q2 in a manner that can describe well both the low-x and high-x data. The spin structure function is then evolved to the Q2of interest, and the parameters are iterated to fit the data. In this way a physically reasonable spin structure function with a well defined analytical form is generated that can be integrated over the full range
ormannce had not yet been established. lo-* X
Figure 10. Shown are data on gy from El54 and SMC for the region z < 0.1, together with several fits, as indicated on the plot.
The urgency of needing a well defined prescription is illustrated in Fig. 10 which shows the El54 data on the neutron as well as SMC data on the neutron (from considering the difference of proton and deuteron data) such as existed at the time El54 was published. The data are inconsistent with the simplest Regge theory interpretation that gy is constant at low x. The El54 collaboration considered several alternative possibilities. One was a Regge theory extrapolation with a constrained power-law fit in which it was assumed that 9;" x - ~ ,and -0.5 < Q 5 0. This results in a determination of the first moment of gy of ry = -0.041 f0.004f 0.006, but only fits well the lowest three points. Another was to consider an unconstrained
-
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power law fit, fitting the data for x < 0.1. It was found that Q = 0.9 f0.2 resulting in a determination of r;l.= -0.2, but it is not possible to quote an error on I’;l. because if a = 1 the integral of g1 diverges. A Pomerontype fit was also considered but was not particularly successful. From these considerations, it is clear that the El54 data, taken by themselves, are not sufficiently constraining to yield a reliable low-2 extrapolation, and hence, a determination of r;l.. By employing an NLO pQCD analysis, there is at least a well defined prescription within which to analyze the world body of spin structure data. The evolution of the structure functions with Q2 is handled well, making it possible to combine data from many different kinematic conditions. I worry that there is a certain arbitrariness to the parameterizations that are chosen, but I will leave the consideration of such points to the experts. Many NLO pQCD analyses have been performed. The last such analysis performed by the SMC was published in 199817. There was also an NLO pQCD analysis performed by the El54 collaboration22. Many others exist as well, and some of their results are summarized nicely by Filippone and Ji29. The most recent of which I am aware, which includes the El55 proton data, was published in 200430. One of the quantities that comes out of an NLO pQCD analysis is a value for the first moment of the singlet quark distribution, AX. The analysis must be performed within a particular factorization scheme, which among other things, affects whether or not AC contains a contribution from the gluon spin, AG. In the quark-parton model, AX is the fraction of the nucleon’s spin carried by quark spin. In the MS factorization scheme, in which AX does not contain a contribution from AG, AX is found t o be constrained to the range 0.05 - 0.28 depending on the particular NLO pQCD analysis in question. The original discovery that started the proton spin crisis has certainly held up. It appears that rather little of the spin of the nucleon is carried by quark spin. NLO pQCD fits of the world’s inclusive deep inelastic scattering data are much less definitive regarding AG. While most fits seem to indicate that AG is positive, a reliable determination will need to await new experiments.
7. A large and growing legacy One equation that can be used to discuss Vernon’s legacy with regard to spin structure is the following: -1= - A1X + A G + L , + L g . (9) 2 2
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On the left is the spin of the nucleon, and on the right are the various sources of angular momentum that in principle can contribute. Here the first term represents the angular momentum carried by the quark spin, the second term represents the angular momentum carried by the gluon spin, and the last two terms represent the angular momentum carried by orbital angular momentum of quarks and gluons respectively. The focus of this paper has been measurements of g1 through inclusive deep inelastic scattering. Such measurements predominantly provide information on the first term pertaining to quark helicity. There are many other types of measurements, however, which I cannot hope to enumerate within the scope of this paper. I have essentially ignored A2 and g2, which are important for many reasons. Nor have I discussed semi-inclusive measurements where one detects a hadron in the final state. Such measurements potentially provide more direct measurements of flavor specific spin distributions such as Au, Ad, and As,and have been the focus of some of the current measurements at HERMES. I have also ignored what is arguably the next large push in spin-structure studies, a determination of the second term AG. The COMPASS experiment at CERN and the RHIC Spin program at Brookhaven are both seeking to quantify the degree to which the polarization of gluons contribute to the spin of the nucleon. The contributions to the spin of the nucleon from orbital angular momentum is a fascinating subject in which there have been some interesting developments in recent years. Within the context of Generalized Parton Distributions (GPD’s), it has been suggested that information regarding L, can be gotten from deeply virtual Compton scattering31. Such experiments appear very challenging, and I believe it is still unclear how this will unfold. Before being skeptical, however, it is important to remember the degree to which polarized deep inelastic scattering looked impractical in the late 1960’s. At Jefferson Laboratory there may already be indirect evidence concerning the role of orbital angular momentum. Measurements of the ratio of the electric to the magnetic form factors of the proton have shown a dramatic decrease with Q2, where the naive expectation was that the ratio would be roughly constant32. Explanations of this phenomena have tended to include a non-zero component of angular momentum associated with the quark wave functions33. Several other experiments, including a measurement of A? at high 234,have also seen effects that can be interpreted as evidence of orbital angular momentum. Despite these interesting developments, it is clear that any type of thorough understanding of L, is still at the earliest stage. Nevertheless, the theoretical and experimental
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activity in this area is yet another sign of the richness of the evolving field of spin structure. During my talk, I could not resist pointing out that Vernon’s leadership has indirectly lead to useful technological spin-offs. The EMC results on the proton created a compelling need for better polarized neutron targets. The polarized 3He target that was used for El42 and El54 answered that need, and also represented a large step forward in the use of spin-exchange optical pumping for the polarization of large quantities of noble gas. In a series of experiments that took place immediately following E142, it was demonstrated that polarized 129Xeand 3He could be used for a new type of magnetic resonance imaging35i36. The gases are inhaled, and provide a source of signal for MR images of the gas space of the lungs. A comparison of a 3He image of human lungs with a nuclear medicine scan, the current state-of-the-art, is shown in Fig. 11. The technology that was developed for El42 lead quite directly into MR imaging with noble gases. This is a nice example of an unanticipated spin-off from basic research, basic research that came in part from a field that began with Vernon’s leadership.
Figure 11. Shown are two images off the gas space of human lungs (from different subjects). At left is a traditional ventilation scan in which the subject inhales radioactive gas and an image is made using a gamma camera. At right is an MRI in which the signal source is inhaled nuclear-polarized 3He. Both images were made at UVa.
Fortunately there is another talk in this proceedings that discusses the future of spin-structure studies. Not only are there upcoming experiments such as COMPASS and RHIC Spin, there is also discussion of constructing a polarized electron-ion collider. What started as a field with a handful of people has expanded into a substantial community. Vernon has left us a wonderful legacy, and will be sorely missed.
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References 1. R. L. Long, Jr., W. Raith and V. W. Hughes, Phys Rev. Lett 15, 1 (1965). 2. V. W. Hughes, R. L. Long, Jr., M. S. Lubell, M. Posner and W. Raith, Phys. Rev. A 5 , 195 (1972). 3. J. D. Bjorken, Phys. Rev. 148, 1467 (1966). 4. J. D. Bjorken, Phys. Rev. D 1,465 (1970); Phys. Rev. D 1,1376 (1970). 5. V. Hughes, M. Lubell, M. Posner, and W. Raith, in Proceedings of the Sixth International Conference on High-Energy Accelerators (unpublished). 6. J. Ellis, R. L. Jaffe, Phys. Rev. D 9, 1444 (1974); 10, 1669 (1974). 7. M. J. Alguard et al., Nucl. Instr. Meth. 163, 29 (1979). 8. W.W. Ash in High Energy Physics with Polarized Beams and Targets, ed. M.L. Marshak, Am. Inst. Phys., (New York, 1976), p.485. 9. P.L. Anthony et al. (the SLAC E-142 Collab.), Phys. Rev. D 54, 6620 (1996). 10. M.J. Alguard et al., Phys. Rev. Lett. 37, 1261 (1976). 11. M.J. Alguard et al., Phys. Rev. Lett. 41, 70 (1978). 12. G. Baum et al., Phys. Rev. Lett. 51, 1135 (1983). 13. J. Ashman et al., Phys. Lett B 206, 364 (1988). 14. J. Ashman et al., Nucl. Phys. B328, 1 (1989). 15. E.W. Hughes and R. Voss, Annu. Rev. Nucl. part. Sci. 49, 303 (1999). 16. B. Adeva et al. (The SMC collab.), Phys. Rev. D 58, 112001 (1998). 17. B. Adeva et al. (The SMC collab.), Phys. Rev. D 5 8 , 112002 (1998). 18. P.L. Anthony et al. (the SLAC El42 collab.), Phys. Rev. Lett. 71,959 (1993). 19. K. Abe et al. (the SLAC El43 collab.), Phys. Rev. D 58, 112003 (1998). 20. K. Abe et al. (the SLAC E-154 collab.), Phys. Rev. Lett. 79, 26 (1997). 21. K. Abe et al. (the SLAC El54 collab.), Phys. Lett. B 404 (1997). 22. K. Abe et al. (the SLAC El54 collab.), Phys. Lett. B 405, 180-190 (1997). 23. P.L. Anthony et al. (the SLAC El55 collab.), Phys. Lett. B 463, 339 (1999); Phys. Lett. B 493, 19 (2000). 24. P.L. Anthony et al. (the SLAC E155x collab.), Phys. Lett. B 553, 18 (2003). 25. B. Adeva et al., Phys. Lett. B302, 553 (1993). 26. H. Middleton, Ph.D. thesis, Princeton University, 1994. 27. T. G. Walker and W. Happer, Rev. Mod. Phys. 69, 629 (1997). 28. A. Ben-Amar Baranga, S. Appelt, M.V. Romalis, C.J. Erickson, A.R. Young, G.D. Cates and W. Happer, Phys. Rev. Lett. 80, 2801 (1998). 29. B. W. Filippone and X. Ji, Adv. in Nucl. Phys. 26, 1 (2001). 30. M. Hirai, S. Kumano, and N. Saito (Asymmetry Analysis Collaboration), Phys. Rev. D 69, 054021 (2004). 31. X.D. Ji, Phys. Rev. Lett. 78, 610 (1997). 32. M.K. Jones et al., Phys. Rev. Lett. 84, 1398 (2000). 33. See for instance A.V. Belitsky, X. Ji, and F. Yuan, Phys. Rev. Lett. 91, 092003 (2003) or G. A. Miller, Phys. Rev. C 66, 032201(R) (2002). 34. X. Zheng et al. (JLab Hall A Collab.), Phys. Rev. Lett. 92, 012004 (2004). 35. M. S. Albert, G. D. Cates, B. Driehuys, W. Happer, B. S a m , C. S. Springer Jr., and A. Wishnia, Nature 370, 199 (1994). 36. J. R. MacFall et al., Radiology 200, 553 (1996).
MUON g - 2: THE LAST WORD?
ERNST P. SICHTERMANN, representing the muon g - 2 Collaboration Yale Unversity
P.O. Box 208121 New Haven, CT 06520, USA and Lawrence Berkeley National Laboratory 1 Cyclotron Road Berkeley, CA 94720, USA E-mail: EPSichtermannOlbl.gov In the early 1980's, Vernon W. Hughes initiated a fourth generation of muon g - 2 measurements aiming at an uncertainty well below 1ppm, over an order of magnitude more precise than the results from the famous measurements at CERN. The new experiment has measured the anomalous g values of the positive and negative muon, each t o a precision of 0.7 parts per million (ppm), at the Brookhaven Alternating Gradient Synchrotron. The final results, a,+ = 11659 203(6)(5) X lo-'' and a,- = 11659 214(8)(3) x lo-'' are consistent with the previous measurements. Their average is a,(exp) = 11659208(6) x lo-'' (0.5ppm).
1. Introduction
The anomalous g values, a = (g - 2)/2, of leptons arise from quantum mechanical effects. Their precise measurement has historically played an important role in the development of particle theory. The anomalous magnetic g value of the electron, a,, has been measured to within about four parts per billion (ppb)2,and is among the most accurately known quantities in physics. Its value is described in terms of Standard Model field interactions, with nearly all of the measured value contributed by QED processes involving virtual photons, electrons, and positrons3. Heavier particles contribute to a, only at the level of the present experimental uncertainty. The anomalous magnetic g value of the muon, a,, is more sensitive than a, to processes involving particles more massive than the electron, characteristically by a factor (rn,/m,)2 4.104.4A series of three experiment^^>^ at CERN measured a, to within 7 parts per million (ppm), an uncertainty which is predominantly of statistical origin. The CERN generation of ex-
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periments thus tested electron-muon universality and established the existence of a hadronic contribution to a, with a relative size of 59ppm. Electroweak processes are expected to contribute at the level of 1.3ppm, as are many speculative extensions of the Standard Model7. Theoretical evaluations of the a , were attributed to have a 8ppm uncertainty at the time of the last CERN muon g - 2 experiment, and arose principally from the uncertainty coming from hadronic contributions. As R.W. Williams emphasized in his talk, “Muon g - 2 - the Last Word”’, the theoretical and experimental uncertainties were at the same level and would be hard to improve. Vernon W. Hughes considered pursuing an improved measurement because of the importance of having a precise knowledge of the muon g - 2, despite these observations. In the year 1984 he organized a workshop at Brookhaven National Laboratory (BNL) to initiate a new g - 2 measurement and to work out the general parameters of the experiment (Fig. 1). A letter of intent was submitted to BNL, followed by a proposal in 1985’. N
Figure 1. At Brookhaven National Laboratory, summer 1984. Standing, from left: Gordon Danby, John Field, Francis Farley, Emilio Picasso, and Frank Krienen; kneeling from left: John Bailey, Vernon Hughes, and Fred Combley.
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The goal was an uncertainty well below the electroweak contribution, more than an order of magnitude improvement over the CERN measurements, using a similar concept as the last CERN muon g - 2 experiment and a new superconducting storage ring. The first muon data were collected in 19971°. The long stretch between the letter of intent and the first data reflects on the difficulty of the measurement, as well as on difficulties to secure adequate funds. The new measurements reached an uncertainty of 1.3ppm in a,+ for the positive muon from data collected in the year 199911, followed by 0.7ppm uncertainty from p+ data collected in 200012. Shortly after the Memorial Symposium in honor of Vernon Willard Hughes the collaboration finalized its analysis of a,- of the negative muon once more achieving a 0.7ppm uncertainty13. The focus in the sections below is on some of the many aspects of these last measurements. Vernon W. Hughes had a keen interest in theoretical evaluations of the muon anomalous magnetic g value, and in particular its hadronic contribution. Close relations with the Budker Institute for Nuclear Physics in Novosibirsk were established early on. The Novosibirsk measurements of the hadron production cross section a(e+e- --+ hadrons) have played a lead role in providing improved knowledge of the hadronic contribution to the anomalous moment. At present, the Standard Model expectation for up is known about an order of magnitude more precisely than it was in 1984.
2. Experiment
The concept of the present experiment is similar to that of the last of the CERN experiments5i6and involves the study of the orbital and spin motions of polarized muons in a magnetic storage ring. Protons with energies of 24 GeV from the AGS were directed onto a rotating, water-cooled nickel target. Pions with energies of 3.1 GeV emitted from the target were captured into a 72 m straight section of focusing-defocusing magnetic quadrupoles, which transported the parent beam and naturally polarized muons from forward pion decays. For most of the data taking periods, longitudinally polarized muons of slightly lower energies were injected into a 14.2m diameter storage ring magnet14 through a field-free inflector15 region in the magnet yoke. A fast non-ferric kicker16 located at approximately one quarter turn from the inflector region produced a 10mrad deflection which placed the muons onto stored orbits. Pulsed electrostatic quadrupoles17 provided vertical focusing. The magnetic dipole field of about 1.45T was measured with an nuclear magnetic resonance (NMR) s y ~ t e m relative ' ~ ~ ~ to ~ the free
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proton NMR frequency wp over most of the 9 cm diameter circular storage aperture. Twenty-four electromagnetic calorimeters2' read out by 400 MHz custom waveform digitizers (WFD) were used on the open, inner side of the C-shaped ring magnet to measure the decay positrons and electrons. The WFD and NMR clocks were phase-locked to the same LORAN-C21 frequency signal. Muon decay violates parity, which in the laboratory frame results in a modulation of the number of decay electrons (positrons),
produced with energies above a threshold E. Here, No is a normalization, 64ps is the muon lifetime in the laboratory frame, A 0.4 is an asymmetry factor, 4 is a phase, and w, is the angular difference frequency of muon spin precession and momentum rotation. The muon anomalous magnetic g value is evaluated from the ratio of the measured frequencies, R = w,/wp, according to:
YT
N
N
R
x
a, = - R ' in which X = p,/pp is the ratio the muon and proton magnetic moments. The value with smallest stated uncertainty, X = 3.183 345 39(10)22, results from measurements of the microwave spectrum of ground state m u o n i ~ m and~ theory25. ~ ~ ~ ~ 3. Data Analysis
The proton NMR frequency wp and the muon spin precession frequency w, were analyzed independently by several groups within the collaboration. The values of R = w,/wp and a, were evaluated only after each of the frequency analyses had been finalized; at no earlier stage were the absolute values of both frequencies, wp and w,, known to any of the collaborators. 3.1. The magnetic field frequency The measurement of the magnetic field is based on proton NMR in water. A field trolley with 17 NMR probes was moved typically 2-3 times per week throughout the entire muon storage region, thus measuring the field in 17 x 6 . lo3 locations along the azimuth. The trolley probes were calibrated in dedicated measurements taken before, during, and after the muon data collection periods. In these calibration measurements, the field in the storage region was tuned to very good homogeneity at specific calibration
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Figure 2. Top view of the g - 2 apparatus. The beam of longitudinally polarized muons enters the superferric storage ring magnet through a superconducting inflector magnet located at 9 o’clock and circulates clockwise after being placed onto stored orbit with three pulsed kickers modules in the 12 o’clock region. Twenty-four lead scintillating-fiber calorimeters on the inner, open side of the C-shaped ring magnet are used to measure muon decay positrons and electrons. The central platform supports the power supplies for the four electrostatic quadrupoles and the kicker modules.
locations. The field was then measured with the NMR probes mounted in the trolley shell, as well as with a single probe plunged into the storage vacuum and positioned to measure the field values in the corresponding locations. Drifts of the field during the calibration measurements were determined by remeasuring the field with the trolley after the measurements with the plunging probe were completed, and in addition by interpolation of the readings from nearby NMR probes in the outer top and bottom walls of the vacuum chamber. The difference of the trolley and plunging probe readings forms an inter-calibration of the trolley probes with respect to the plunging probe, and hence with respect to each other. The plunging probe, as well as a subset of the trolley probes, were calibrated with respect to a standard probe with a l c m diameter spherical H2O sample in a similar sequence of measurements in the storage region, which was opened to air for that purpose. The standard probe is the same as the one used in the muonium measurements that determine the ratio X of muon to proton magnetic moment^^^?^^. The leading uncertainties in the calibration procedure
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result from the residual inhomogeneity of the field at the calibration locations, and from position uncertainties in the active volumes of the NMR probes. The ring magnet design14, the inflector design15, and extensive shimming contributed to the overall uniformity of the field throughout the storage ring. Figure 3 shows one of the magnetic field measurements with the center NMR probe in the trolley in the year 2000. A uniformity of flOOppm in the center of the storage region was achieved for the full azimuthal range, in particular also in the region where the inflector magnet is located. Between the data taking periods in 2000 and 2001 the polarity
-
1000
E &sfm
Y
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400 300 200
0
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100
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200
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azimuthal positron [deg] Figure 3. The NMR frequency measured with the center trolley probe relative to a 61.74 MHz reference versus the azimuthal position in the storage ring for one of the 22 measurements with the field trolley during the data collection in the year 2000. The continuous vertical lines mark the boundaries of the 12 yoke pieces of the storage ring. The dashed vertical lines indicate the boundaries of the pole pieces.
of the ring, inflector, and beamline magnets was reversed. After several ramping cycles the field was found t o be of equal uniformity. Figure 4 shows a two-dimensional multipole expansion of the azimuthal average of the field in the muon storage region from a typical trolley measurement in 2001. Since the average field is uniform to within 1.5ppm over the storage aperture, the field integral encountered by the (analyzed) muons is rather insensitive to the precise location and profile of the beam. The measurements with the field trolley were used to relate the readings of about 370 NMR fixed probes in the outer top and bottom walls of the
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storage vacuum chamber t o the field values in the beam region. The fixed NMR probes were read out continually. Their readings were used t o interpolate the field when the field trolley was “parked” in the storage vacuum just outside the beam region and muons circulated in the storage ring.
Multipoles [ppm]
Normal Skew Quad -0.28
0.11
%XI -0.72
-0.45
Octu
0.09
0.01
Decu
1.04
0.38
-4 -3 -2 -1 0 1 2 3 4 radial distance [cm] Figure 4. A 2-dimensional multipole expansion of the azimuthal average of the field measured with trolley probes with respect to the central field value of 1.451 269 T. The multipole amplitudes are given at the storage ring aperture, which has a 4.5cm radius as indicated by the circle.
For the data collection in the year 2001 the field frequency wp weighted by the muon distribution was found to be, wp/(27r) = 61 791 400(11) Hz (0.2ppm)13.
(3)
The uncertainty has a leading contribution from the calibration of the trolley probes and is thus predominantly systematic. The result was confirmed by a second, largely independent analysis, which made use of additional calibration data, a different selection of fmed NMR probes, and a different method to relate the trolley and fked probe readings. The history of systematic uncertainties in the field measurements since 1998 is given in Table 1. The uncertainty in the field measurement was improved by a factor of three over the course of the experiment. A new superconducting inflector magnet and shield, installed between the data collection periods in 1999 and 2000, improved the field homogeneity and further relaxed the demands on the knowledge of the muon beam distribution. Other significant improvements resulted from refinements in the calibration measurements and in the data analysis. The technique is not
123 Table 1. Systematic uncertainties for the wp analysis. The uncertainty "Others" groups uncertainties caused by higher multipoles, the trolley frequency, temperature, and voltage response, eddy currents from the kickers, and time-varying stray fields. Source of errors Absolute calibration of standard probe Calibration of trolley probe Trolley measurements of Bo Interpolation with fixed probes Inflector fringe field Uncertainty from muon distribution Others Total svstematic error on wm
Size [ppm] 1998 0.05 0.3
1999 0.05
0.1
0.10 0.15 0.20 0.12 0.15
0.3 0.2 0.1
0.5
0.20
0.4
2000 0.05 0.15 0.10 0.10
0.03 0.10 0.24
2001 0.05 0.09 0.05 0.07 0.03 0.10 0.17
yet fully exhausted; modest further improvements may result from better measurement of the residual field from kicker eddy currents, and from further refinement in the calibration and analysis. 3.2. T h e muon s p i n precession frequency
The muon frequency w, was determined by fitting the spectrum of arrival times of the decay electrons (positrons) measured with the lead scintillatingfiber calorimeters on the inner side of the storage ring. The calorimeters were read out with waveform digitizers (WFD) which sampled the photomultiplier signals every 2.5ns. The WFD traces were fitted off-line with average pulse-shapes, which were determined for each calorimeter individually from a selection of about lo4 pulses in the energy range 1-3 GeV. The selection was made so as to ensure that transient detector effects had faded away and the traces consisted of detector responses to single electrons (positrons). Two independently determined sets of pulse-shapes were used, as well as two independent implementations of the pulse-finding algorithm. A fraction of several percent of the recordings was found to contain multiple electron (positron) pulses per WFD trace. Extensive studies of the algorithm showed that in such cases each of the pulses was identified and measured correctly, provided that the pulse separation exceeded -3 ns and the pulse energy was larger than -0.3 GeV. Pulses with lower energies escaped reconstruction and pulses separated by less than -3 ns were reconstructed as a single pulse, so called pile-up. Pileup distorts the electron (positron) time spectrum because of miscounting of the number of pulses and misidentification of the energies and times. Since the phase 4 in Eq. 1 depends on the electron (positron) energy and
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correlates strongly with the frequency w, in fits, pile-up potentially causes a sizable error in the fitted value of w,. It is thus advantageous to apply a correction to the data prior to the fitting. The availability of the WFD trace, as well as the fact that the 3ns interval is smaller than the other time-scales in the experiment, allowed us to do so in a way that is based on the data itself and that is self-normalizing1'. The data collection in the year 2000 resulted in a sample of about 4 . lo9 reconstructed positrons with energies greater than 2 GeV and times between 50 p s and 600 p s following beam injection. A slightly smaller sample of electrons was available for analysis from the data collection in 2001. Figure 5 shows their time spectrum after corrections for pile-up and for the bunched time structure of the beam and had been applied.
Figure 5. The time spectrum of analyzed electrons collected in the year 2001, after corrections for pileup and for the bunched time structure of the injected beam had been made.
The main characteristics of the spectrum were that of muon decay and spin precession (Eq. 1). However, additional effects needed to be considered. These effects included detector gain and time instability, muon losses, and oscillations of the beam as a whole, so-called coherent betatron oscillations
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(CBO). The latter were caused by the injection of the beam through the relatively narrow 18(w) x 57(h)mm2 aperture of the 1.7m long inflector channel into the 90mm diameter aperture of the storage region. Their frequencies are determined by the field focusing index n of the storage ring, which is proportional to the electric field gradient, and have been observed directly with fiber harp monitors that were plunged into the beam region for this purpose. Numerically most important to the determination of w, were CBO in the horizontal plane. In the year 2000 the weak focusing storage ring was operated with a field focusing index n = 0.137, a historical setting which is well away from beam and spin resonances. This setting nevertheless formed a considerable complication since it caused the horizontal CBO frequency Wcbo,h 2 7 ~. 466 kHz to be numerically close to twice the frequency w, N 27~.229 kHz. The interference frequency W,-bo,h - w, was thus close to w,, and since the calorimeter acceptances varied with the muon decay position in the storage ring and with the momentum of the decay positron, a small modulation of the time and energy spectra of the observed positrons resulted. This affected the observed asymmetry and phase, and caused a systematic uncertainty in the fitted frequency w, at the level of 0.2ppm. New working points, n = 0.122 and n = 0.142 corresponding to Wcbo,h 2n 419 kHz and Wcbo,h 2 7 ~.491 kHz, were chosen for the data collection in 2001 to move the interference frequency away from w,. The uncertainty was reduced. The muon frequency value for the data collection in 2001 is, N
N
N
w a / ( 2 n ) = 229073.59(15)(5) Hz (0.7ppm)13,
(4)
where the first uncertainty is statistical and the second is systematic. The value was obtained from five largely independent analyses of mostly the same data. The analyses differed in approach and thus gave somewhat different sensitivity to systematic effects. Two of the analyses fitted directly the time spectrum of electrons in the energy range of 1.8-3.4GeV, using slightly different parametrizations. The third analysis was a likelyhood analysis, which used the observed dependence of the asymmetry on the electron energy to maximize the statistical power and to extend the energy range of the analyzed electrons down to 1.5GeV. The fourth and fifth analyses made use of a cleverly devised data-transformation of the time spectrum, which virtually eliminated the dependency on muon decay and on other effects with time scales larger than 7, 4.4p.9. The results of all five analyses agreed to within the expected statistical fluctuations N
126
caused by differences in data selection and in weighting. The frequency in Eq. 4 includes a correction of +0.77(6) ppm for the net contribution to the muon spin precession and momentum rotation caused by vertical beam oscillations and, for muons with y # 29.3, by horizontal electric Table 2. Systematic uncertainties for the wa analysis. The uncertainty "Others" groups uncertainties caused by the Efield and pitch corrections, by beam debunching/randomization, by the fitting procedure and binning, by timing shifts, and for 2000 and 2001 by residual AGS background. Source of errors Coherent betatron oscillations Pileup Gain changes Lost muons AGS background Others Total systematic error on wa Total statistical error on wn.
Size [ppm] 1998 0.2 <0.6 <0.1 0.1 <0.5 <0.2 1 5
1999
0.05 0.13 0.02
0.10 0.10 0.15 0.3 1.3
2000 0.21 0.13 0.13 0.10
2001
0.07 0.08 0.12 0.09
0.09 0.31 0.62
0.11 0.21 0.66
Table 2 shows the progression of uncertainties in the determination of the frequency w,. The largest gain was in the combined statistical uncertainty, which was reduced by an order of magnitude since 1998. The systematic uncertainties were reduced by a factor of about five, largely owing to advances in the analysis of pile-up, to the installation of a sweeper magnet to minimize AGS background in 2000, and to the change of field focusing index before the 2001 data collection. The measurement remains limited by statistics. Future reduction of the systematic uncertainty requires improvements in the stability and monitoring of the calorimeter gains, and a further reduction of muon losses.
4. Results and Discussion
4.1. Experiment The value of the ratio R = w,/wp was evaluated only after the analyses of wp and w, had been finalized, separately and independently. The result for the negative muon, obtained from the data collection in the year 2001,
R(p-) = 37 072 083(26) x 10-l'
(0.7 ppm),
(5)
127
is found to be in good agreement with the combined result for the positive muon from the data collection in the years 1998-2000 (Fig. 6),
R ( p + ) = 37072048(25) x 10-l'
(0.7ppm),
(6)
as expected if CPT is a good symmetry. The overall mean value is:
R ( p ) = 37072 063(20) x 10-l'
(0.5 ppm),
(7)
where the uncertainty accounts for known experimental correlations in the measurements.
R
0.00370722
0.00370720
0.00370718
Figure 6. The ratio of the measured frequencies, R = wa/wp,for the data collection periods of the muon g - 2 experiment at the Brookhaven AGS, together with their average.
The ratio of frequencies, R, and the ratio of muon to proton magnetic moments, A, determine the muon anomalous g value,
R a, =
The values are, = 11659 214(8) x 10-l'
(0.7ppm),
(9)
a,+ = 11659203(8) x 10-l'
(0.7ppm),
(10)
a,-
128
and for p- and p+ combined, a, = 11659208(6) x 10-l'
(0.5ppm))
(11)
in which the uncertainty consists of 5 x 10-l' (0.4ppm) statistical uncertainty and 4 x (0.3ppm) systematic uncertainty. The results are in good agreement with the famous CERN measurements5, which achieved a combined uncertainty of 7 ppm. They remain statistics limited and modest improvement, also in systematic uncertainty, is feasible. 4.2. Theory
The Standard Model expecation for a, receives contributions from QED, hadronic, and electroweak processes, a,(SM) = a,(QED)
+ a,(had) + a,(weak).
(12)
The QED contribution is the predominant contribution, a,(QED) = 11658470.57(29) x
(13)
and has been evaluated perturbatively to O ( a 4 ) 2 8 .Its numerical value seems unlikely to shift in a way that would be significant compared to the present experimental uncertainty in a,, even though a,(QED) continues to be an area of active research3. The weak interaction effect is presently known to two-loop order. The latest evaluation2', a,(weak) = 15.4(2) x
(14)
is in good numerical agreement with the alternative evaluation of Ref.30, which uses a somewhat different approach. The hadronic contribution to a, cannot now be calculated from first principles. Its lowest order contribution has thus far been evaluated from dispersion theory and the measured hadron production cross sections in e+ e- annihilation or, under additional assumptions, from hadronic 7decays. Clearly, this contribution has a long history as new data appeared and analyses were refined. The latest published evaluation^^^*^^ incorporate the reanalyzed and very precise low-energy e+e- annihilation data from the CMD-2 c ~ l l a b o r a t i o n as ~ ~well , as e+e- measurements with substantially improved accuracy in the 2-5 GeV energy region from BES34. The results, a,(had, 1) = 696(7) x 10-l' (e+e- data)31,
(15)
129
and a,(had, 1) = 695(9) x lo-''
(e+e- data)32,
(16)
are based on slightly different treatments of essentially the same data. Significant reduction of the uncertainties requires better measurement of the e+e- cross section, particularly in the region below the p-w resonances. Radiative-return measurement^^^, which are underway at several laboratories, show promise and may provide independent verification of the existing e+e- data. It is unclear at present if the evaluation based on hadronic r-de~ay~~y~~, a,(had, 1) = 711(6) x 10-l'
(T
data)31,
(17)
can be improved much further, or if it is already limited by (in-)adequate knowledge of isospin breaking effects32. Alternative explanations for the systematic disagreement31 between the ef e- and T mr spectral functions may point at experiment, at radiative corrections, or at the assumption that the vector current is conserved. Straightforward combination of the two types of evaluations is presently precluded, even though the numerical difference in a,(had,l) could at face value be considered acceptable. A new theoretical development attempts to calculate lowest order hadronic vacuum polarization on the lattice38. Higher order hadronic contributions include higher order vacuum polarization3', a,(had, 2) = -10.0(6) x
(18)
and hadronic light-by-light scattering. The latter relies on modelcalculation. After the correction for a mistaken sign, its value4' appears to have settled down to: a,(had,lbl) = 8(4) x lo-",
-
(19)
although the uncertainty estimate has come under criticism41 and a 50% larger estimate has very recently appeared on the preprint-~ervers~~. A dependable independent verification, perhaps from lattice QCD, would be highly desirable. In summary, the Standard Model expectation is still in flux,
a,(SM)
_N
11659 180(8) x 10-lo-ll
659200(8) x
lo-''.
(20)
130 4.3. Comparison
The final experimental value of the muon anomalous magnetic g value from the present experiment is, a,,(exp) = 11659 208(6) x lo-''
(0.5 ppm),
(21)
in which the uncertainty consists of 5 x lo-'' (0.4ppm) statistical uncertainty and 4 x 1O-I' (0.3ppm) systematic uncertainty. Standard Model evaluations of a, have been improved substantially since the start of the present experiment. The stated uncertainties have reached a sub-ppm level and are comparable to the present experimental uncertainty. However, systematic disagreement31 between the e+e- and 7 mr spectral functions presently precludes the straightforward combination of evaluations. One should thus consider a range of Standard Model expectations, a,(SM)
21
11659 180(8) x 10-''-11
659200(8) x lo-'',
(22)
which is likely to improve in the near future, in particular with the advent of accurate radiative-return data from the e+e- factories. The range is in agreement with experiment to within one to three times the combined experimental and stated theoretical uncertainties. A conclusive confrontation awaits further improvements in the hadronic contribution to the Standard Model expectation.
5. Concluding remarks
In the early 1980's Vernon W. Hughes initiated a fourth generation of muon g - 2 experiments, aiming for a twentyfold improvement in existing knowledge to a level where the measurements would provide sensitivity to all Standard Model interactions. The experiment collected data at the intense proton beam of the Brookhaven AGS for the first time in the year 1997, and has reached a final uncertainty of 0.5ppm on a,, from data collected in 1998-2001. At this level of precision, the measurement forms a new and stringent benchmark for the Standard Model and for speculative extensions. The fact that about eighty physicists, including more than fifteen PhD students, have spend significant fractions of their lives to perform this experiment is a tribute to Vernon W. Hughes's vision, leadership, and most importantly, his accomplishments in fundamental physics.
131
6. Acknowledgements
I would like t o thank t h e organizers of the Memorial Symposium in honor of Vernon Willard Hughes, in particular Emlyn W. Hughes and Francesco Iachello, for giving me the privilege t o devote a contribution. This work was supported in part by the U.S. Department of Energy, the U S . National Science Foundation, t he U.S. National Computational Science Alliance, t h e German Bundesminister fur Bildung und Forschung, t he Russian Ministry of Science, and t he US.-Japan Agreement in High Energy Physics.
References 1. The Muon g - 2 collaboration (1997-2001): H.E. Ahn15, J. Benante2, E. Benedict', G.W. Bennett2, B. Bousquet12, H.N. Brown2, G. Bunce2, J. Cullen2?+,P. Cushman12, B. Bunker', R.M. Carey', A. Chertov~kikh~, G.T. Danby2, P.T. Debevec', M. Deile15, H. Deng15, W. Deninger', S.K. Dhawan15, A. Disco15, V.P. Druzhinin3, L. Duong12, W. Earle', E. Efstathiadis', K. Endo", F.J.M. Farley15, G.V. Fedotovich3, X. Fei15, J. Geller2, J. Gerhauser7, S. Giron12, V.B. Gobulev3, F.E. Gray', M.A. Green", D. Grigoriev3, M. Gr~sse-Perdekamp'~,A. Grossmann7, U. Haeberleng, M.F. Hare', E.S. Hazen', D.W. Hertzog', H. Hirabayashi", M. Iwasaki14, H. Hseuh', X. Huang', B.J. Hughes', V.W. J.W. Jackson2, L. Jia2, T.D. Jones', K. Jungmann', D. Kawall15, M. K a ~ a m u r a ' ~B.I. , Khazin3, J. Kindem12, S. Kochis2, F. Krienen', I. Kronkvist12, S. Kurokawa", A. Lam', R. Larsen2, D. von Lintig2, Y.Y. Lee2, I. L ~ gas henko'~ A. ~ , Maksimov3, M. Mapes2, R. McNabb12, W. Meng2, Yu. M e r ~ l i a k o v ~ ~J.t , Mi2, D. Miller12, J.P. Miller', Y. Mizumachi13, V. Monich' , W.M. Morse2, D. Nikas2, C.J.G. Onderwater', Y. Orlov4, J. Ouyang', C.S. Ozben2, C. Pai2, J.M. Paley', C. Pearson2, Q. Peng', I. Polk2, C.C. Polly8, J. Pretz15, R. Prig12, G. zu Putlitz7, T. Qian12, S. Rankowitz', S.I. Redin3?l5, 0. Rind', B.L. Roberts', N. Ryskulov3, J. Sandberg2, S. Sedykh', Y.K. Semertzidis2, S. Serednyakov3, P. Shagin12, Yu.M. Shatunov3, R. Shutt2?+, E.P. Si~htermann'~, L. Snydstrup2, E. Solodov3, M. Sossong', A. Soukas', A. St ei nrnet ~'~, A. Stillman', L.R. Sulak', T. Tallerico2, M. Tanaka2It, C. Timmermans", F. Toldo', A. Trofimov', D. Urner', G. Varner', P. von Walter7, D. Warburton2, D. Winn5, K. Woodle2, W.A. Worstell', A. Yamamoto", and D. Zimmerman'', Department of Physics, Boston University, Boston, Massachusetts 02215
* Brookhaven National Laboratory, Upton, New York 11973 Budker Institute of Nuclear Physics, Novosibirsk, Russia Newman Laboratory, Cornell University, Ithaca, New York 14853 Fairfield University, Fairfield, Connecticut 06430 Kernfysisch Versneller Instituut, Rijksuniversiteit Groningen, NL 9747 AA Groningen,
132 The Netherlands Physikalisches Institut der Universitat Heidelberg, 69120 Heidelberg, Germany Department of Physics, University of Illinois at Urbana-Champaign, Illinois 61801 MPI fur Medizinische Forschung, 69120 Heidelberg, Germany lo KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan l 1 Lawrence Berkeley National Laboratory, Berkeley, California 94720 l 2 Department of Physics, University of Minnesota,Minneapolis, Minnesota 55455 l3 Science University of Tokyo, Tokyo, Japan l4 Tokyo Institute of Technology, Tokyo, Japan l5 Department of Physics, Yale University, New Haven, Connecticut 06520 Deceased.
’
’
R.S. Van Dyck et al, Phys. Rev. Lett. 59,26 (1987). T. Kinoshita, these proceedings. V.W. Hughes and T. Kinoshita, Comments. Nucl. Part. Phys. 14,341 (1985). G. Charpak et al, Phys. Lett. 1, 16 (1962); J. Bailey et al, Nuovo Cimento A9,369 (1972); J. Bailey e t al, Nucl. Phys. B510,1 (1979). 6. F.J.M. Farley, these proceedings. 7. A. Czarnecki and W.J. Marciano, Phys. Rev. D 64,013014 (2001). 8. R.W. Williams, in the proceedings of the 1978 Coral Gables conference ”New Frontiers In High Energy Physics”, New York 1978, pages 183-197. 9. A new precision measurement of the muon 9-2 value at the level of 0.35 ppm, AGS Proposal 821, September 1985. V.W. Hughes, spokesman. E. Hazen, C. Heisey, B. Kerosky, F. Krienen, E.K. McIntyre, D. Magaud, J.P. Miller, B.L. Roberts, D. Stassinopoulos, L.R. Sulak, W. Worstell - Boston University; H.N. Brown, E.D. Courant, G.T. Danby, C.R. Gardner, J.W. Jackson, M. May, A. Prodell, R. Shutt, P.A. Thompson - Brookhaven National Laboratory; J.A. Johnson, M.S. Lube11 - City College of New York; A.M. Sachs - Columbia University; T. Kinoshita - Cornell University; D. Winn - Fairfield University; M. Janousch, H.-J. Mundiger, G. zu Putlitz, J. Rosenkranz, W. Schwarz - University of Heidelberg; W.P. Lysenko - Los Alamos National Laboratory; A. Rich - University of Michigan; J.J. Reidy - University of Mississippi; F. Combley - Sheffield University; K. Nagamine, K. Nishiyama University of Tokyo; K. Endo, H. Hirabayashi, S. Kurokawa, T. Sat0 - KEK; K. Ishida - Riken; L.M. Barkov, B.I. Khazin, E.A. Kuraev, Ya.M. Shatunov Institute of Nuclear Physics, Novosibirsk, USSR; J.M. Bailey, S.K. Dhawan, A.A. Disco, F.J.M. Farley, V.W. Hughes, Y. Kuang, H. Venkataramania Yale Unversity. 10. R.M. Carey e t al, Phys. Rev. Lett. 82,1632 (1999). 11. H.N. Brown e t al, Phys. Rev. Lett. 86,2227 (2001). 12. G.W. Bennett e t al., Phys. Rev. Lett. 89,101804 (2002). 13. G.W. Bennett e t al., Phys. Rev. Lett. (2004) (in press). 14. G. Danby e t al, Nucl. Instrum. Meth. A457,151 (2002). 15. A. Yamamoto et al, Nucl. Instrum. Meth. A491,23 (2002). 16. E. Efstathiadis et al, Nucl. Instrum. Meth. A496,8 (2003). 17. Y.K. Semertzidis et al, Nucl. Instrum. Meth. A503,458 (2003). 2. 3. 4. 5.
133
18. 19. 20. 21.
22. 23. 24. 25.
26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.
41. 42.
R. Prigl et al, Nucl. Instrum. Meth. A374, 118 (1996). X. Fei, V.W. Hughes, and R. Prigl, Nucl. Instrum. Meth. A394, 349 (1997). S. Sedykh et al, Nucl. Instrum. Meth. A455, 346 (2000). Superintendent of Documents, LORAN-C User’s Handbook, US. Government Printing Office #050-012-00331-9, 1992. K. Hagiwara et al, Phys. Rev. D66, 010001 (2002). W. Liu et al, Phys. Rev. Lett. 82, 711 (1999). K.P. Jungmann, these proceedings. T. Kinoshita, hepph/9808351 (1998); T. Kinoshita and M. Nio in: Frontier Tests of Electrodynamics and Physics of the Vacuum (eds. E. Zavattini, D. Bakalov, and C. Rizzo), 151 (Heton Press, Sofia, 1998). F. Farley and E. Picasso in: Quantum Electrodynamics (ed. T. Kinoshita), 479 (World Scientific, Singapore, 1990). H.N. Brown et al, Phys. Rev. Lett. D62, 091101 (2000). P.J. Mohr and B.N. Taylor, Rev. Mod. Phys. 72, 351 (2000). A. Czarnecki, W.J. Marciano, and A. Vainhstein, Phys. Rev. D67,073006 (2003). M. Knecht, S. Peris, M. Perrottet, E. De Rafael, JHEP 0211, 003 (2002). M. Davier, S. Eidelman, A. Hocker and Z. Zhang, Eur. Phys. J. C27,497 (2003); ibid. C31, 503 (2003). S. Ghozzi and F. Jegerlehner, Phys. Lett. B583, 222 (2004). R.R. Akhmetshin et al, Phys. Lett. B527, 161 (2002); ibid. B578,285 (2004). J.Z. Bai et al, Phys. Rev. Lett. 84, 594 (2000); J.Z. Bai et al, Phys. Rev. Lett. 88, 101802 (2002). ALEPH Collaboration, ALEPH 2000-030 CONF 2002-019 (2002). See for example, J. LeeFranzini, arXiv:hepph/0403006; M. Davier, arXiv:hep-ex/03 12063. S. Anderson et al, Phys. Rev. D61, 112002 (2000); K.W. Edwards et al, Phys. Rev. D61, 072003 (2000). T. Blum, Phys. Rev. Lett. 91, 052001 (2003). B. Krause, Phys. Lett. B390, 392 (1997); R. Alemany, M. Davier, and A. Hocker, Eur. Phys. J. C 2 , 123 (1998). M. Hayakawa and T. Kinoshita, arXiv:hepph/0112102 (2001); J . B”ijnens, E. Pallante, and J. Prades, Nucl. Phys. B626, 410 (2002); M. Knecht and A. Nyffeler, Phys. Rev. D65,073034 (2002); M. Knecht, A. Nyffeler, A. Perrottet, and E. De Rafael, Phys. Rev. Lett. 88, 071802 (2002); I. Blokland, A. Czarnecki, and K. Melnikov, Phys. Rev. Lett. 88, 071803 (2002). M. Ramsey-Musolf and M.B. Wise, Phys. Rev. Lett. 89, 041601 (2002). K. Melnikov and A. Vainshtein, arXiv:hepph/0312226 (2003).
PAST, PRESENT AND FUTURE OF MUONIUM
KLAUS P. JUNGMANN Kernfysisch Versneller Instituut Rijksuniversiteit Groningen Zernikelaan 25, Groningen, 9747 AA, The Netherlands E-mail: jungmannQKVl.nl Muonium, the atom which consists of a positive muon and an electron, has been discovered by a team led by Vernon W. Hughes in 1960. It is in many respects the most ideal atom available from nature. Due to the close confinement in the bound state muonium can be used as an ideal probe of electro-weak interaction, including particularly Quantum Electrodynamics, and to search for additional yet unknown interactions acting on leptons. Recently completed experiments cover the ground state hyperfine structure, the 1s-2s interval and a search for spontaneous conversion of muonium t o antimuonium. The experiments yield precise values for the fine structure constant, the muon mass and its magnetic moment. The results from these precision measurements have provided restrictions for a number of theories beyond the Standard Model of particle physics. Future precision experiments will require new and intense sources of muons.
1. Muonium
- The Atom discovered by Vernon Hughes
Atomic hydrogen is generally considered the simplest and most fundamental atom in nature. Its role in development of modern physics is outstanding. Our physical picture of atoms, the success of quantum mechanics and the start of quantum field theories such as Quantum Electrodynamics (QED) are just a few examples for insights which go back to careful analysis of what had been observed in this atom. Hydrogen has been exploited in numerous precision measurements to determine fundamental constants and to reconfirm fundamental concepts such as,e.g. the equality of the electron and proton charge units. Unfortunately, the presence of the proton as the nucleus in this one electron atom reduces the possibilities for a complete theoretical description. Precise measurements are at present orders of magnitude more accurate than calculations can be performed. Proton properties such as its mean square charge radius or its magnetic radius or even the dynamics of the 134
135
‘ Y F = O
Figure 1. Energy levels of the hydrogen-like muonium atom for states with principal quantum numbers n = l and n=2. The indicated transitions could be induced to date by microwave or laser spectroscopy. High accuracy has been achieved for the transitions which involve the ground state. The atoms can be produced most efficiently for n=l.
charge and spin carrying constituents inside the proton are not known to sufficient accuracy. High energy scattering experiments have shown for leptons no structure down to dimensions of m. They may therefore be considered ”pointlike”. As a consequence, complications as those arising from the structure of the nucleus in natural atoms and such artificial systems that contain hadrons are absent in the muonium atom (M = p f e - ) , whicl- is the bound state of two leptons, a positive muon ( p + ) and an electron (e) ll2. It may be considered a light hydrogen isotope. The dominant interaction within the muonium atom (see Fig. 1) is electromagnetic. In the framework of bound state Quantum Electrodynamics (QED) the electromagnetic part of the binding can be calculated to sufficiently high accuracy for modern high precision spectroscopy experiments. There are also contributions from weak interactions arising through 2’boson exchange and from strong interactions owing to vacuum polarization
136
loops containing hadrons. The corresponding energy level shifts can be obtained to the required level of precision using standard theory. Precision experiments in muonium can therefore provide sensitive tests of the Standard Model of particle physics and sensitive searches for new and yet unknown forces in nature become possible. Parameters in speculative theories can be restricted. In particular, such speculations which try to expand the Standard Model in order to gain deeper insights into some of its not well understood features, i.e. where the standard theory gives well a full description, but lacks a fully satisfactory explanation of the observed facts. In addition, fundamental constants like the muon mass m, its magnetic moment pp and magnetic anomaly a, and the fine structure constant cr can be measured precisely by muonium spectroscopy. In 1960 a team led by Vernon W. Hughes has observed the muonium atom for the first time '. The details of the exciting circumstances around this discovery and the research in the early years are described in this volume by an eye witness, Richard Prepost '. They are also available from the viewpoint of the leader, Valentin Telegdi, of the very group, which was competing in muonium research with the Yale team of Vernon Hughes for more than a decade 5.
2. Muonium Formation
In the early years muonium research concentrated on measurements that were possible with atoms created by stopping muons in a material and studying them in this environment (see Fig. 2). Besides important work on condensed matter in the framework of muon spin rotation (pSR) there were in particular precision experiments which concerned the ground state hyperfine structure and a search for muonium-antimuonium conversion. In the 1980ies the spectrum of possible experiments could be significantly expanded when methods where developed which allowed to have the atoms in vacuum ll2. All high precision experiments in muonium up to date atom have involved the 1s ground state (see Fig.l), in which the atoms can be produced in sufficient quantities. The most efficient mechanism is e- capture after stopping p+ in a suitable noble gas, where yields of 80(10) % were achieved for krypton gas. This technique was used in the most recent precision measurements of the atom's ground state hyperfine structure splitting A V H F ~ and pp at the Los Alamos Meson Physics Facility (LAMPF) in Los Alamos,
USA
'.
137
Methods of Muoniurn Production
Yields up to 100% Polarization up to 50% (B=O) 100% (B>>l T)
foreign gas effects
Beam Foil
n=2 state populated fast muonium
6+
50%
&+e=
1%
#+ee 0.01%
keV energy
SiO, Powder t h e m 1 Muonium in Vacuo Yields up to 12% Polarization 39(9)%
M(2s) /M(ls) c lo-' velocity 1.5 cm/&
Figure 2. Muonium atoms for precision experiments have been produced by three different methods. Stopping muons in a noble gas gives atoms at thermal energies which are subject to collisional effects. Due to velocity a beam foil technique yields muonium atoms in vacuum at keV energies. Muonium atoms diffuse at thermal velocities in vacuum after being produced by muon stopping in a fluffy SiOz powder.
Muonium at thermal velocities in vacuum can be obtained by stopping p+ close to the surface of a SiOz powder target, where the atoms are formed
through e- capture and some of them diffuse through the target surface into the surrounding vacuum. This process has an efficiency of a few percent and was an essential prerequisite for Doppler-free two-photon laser spectroscopy at the Rutherford Appleton Laboratory of the 1 2 S 1 p - 2 2 S 1 p interval (RAL) in Chilton, United Kingdom 7, which yields an accurate value for m,.
138
Electromagnetic transitions in excited states, particularly the 22S1/222P1/2 classical Lamb shift and 22S1/2-22P3/2fine structure splitting could be induced by microwave spectroscopy, too. Only moderate numbers of atoms in the metastable 2s state can be produced with a beam foil technique. Because furthermore these atoms have keV energies due to a velocity resonance in their formation, the experimental accuracy is now the 1.5 % level which represents not yet a severe test of theory. 899,
3. Muonium Ground State Hyperfine Structure 3.1. The Last LAMPF Experiment
The most recent experiment at LAMPF had a krypton gas target inside of a microwave cavity at typically atmospheric density and in a homogeneous magnetic field of 1.7 T. Microwave transitions between the two energetically highest respectively two lowest Zeeman sublevels of the n=l state at the frequencies v12 and v34 (Fig. 3) involve a muon spin flip. Due to parity violation in the weak interaction muon decay process the e+ from p+ decays are preferentially emitted in the p+ spin direction. This allows a detection of the spin flips through a change in the spatial distribution of the decay e+. As a consequence of the Breit-Rabi equation, which describes the behaviour of the muonium ground-state Zeeman levels in a magnetic field B, the sum of v12 and v34 equals at any value of B the zero field splitting A v ~ p s For . sufficiently well known B the difference of these two frequencies yields the magnetic moment pp. The latest LAMPF experiment has utilized the
-2 -4 -6
-8 Magnetic Field (T) Figure 3. The muonium ground state Zeeman splitting.
139 technique of "Old Muonium", which allowed t o reduce the line width of the signals below half of the "natural" line width Aunat = 1/(27r~,) (Fig. 4)12, where r, = 2.2ps is the muon lifetime. For this purpose an essentially continuous muon beam was chopped by an electrostatic kicking device into 4 ps long pulses with 14 p s separation. Only decays of atoms which had been interacting coherently with the microwave field for periods longer than several muon lifetimes were detected.
10
5
30 20
3 3 .Y
10 m 0
20 10
0
Figure 4. Samples of conventional and "Old Muonium" resonances a t frequency y z . The narrow "old" lines exhibit a larger signal amplitude. The signals were obtained with magnetic field sweep (left column, magnetic field in units of proton NMR frequencies) and by microwave frequency scans (right column).
The magnetic moment was measured to be pp= 3.183345 24(37) (120 ppb) which translates into a muon-electron mass ratio p p / m e = 206.768 277(24) (120 ppb). The zero-field hyperfine splitting is determined t o A v H F S ( e l c p ) = 4463302 765(53) Hz (12 ppb) which agrees well with the theoretical prediction of AvHFs(theo) = 4 463 302 563(520)(34)(<100) Hz (120 PPb).
140 Here, the first quoted uncertainty is due to the accuracy to which m,/m, is known, the second error is from the knowledge of Q as extracted from Penning trap measurements of the electron magnetic anomaly, and the third uncertainty corresponds to estimates of uncalculated higher order terms. Among the non-QED contributions is the strong interaction through vacuum polarization loops with hadrons (250 Hz) and a parity conserving axial vector-axial vector weak interaction (-65 Hz). For the muonium hyperfine structure the comparison between theory and experiment is possible with almost two orders of magnitude higher precision than for natural hydrogen because of the not sufficiently known proton charge and magnetism distributions. The achieved - some six orders of magnitude higher - experimental precision in hydrogen maser experiments can unfortunately not be exploited for a better understanding of fundamental interactions. Among the possible exotic interactions, which could contribute to A V H Fis~muonium-antimuonium , conversion lo. Here, an upper limit of 9 Hz could be set from an independent experiment described in section 6.
1
N
I
vlz-l 897539800 Hz v s . e r e a l Time I
50
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (Sidereal Days) N
100
I 75
v,-2565762965 HzJvs.Sidereal Time
1
II,,,I,IIII,,,,
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Time (Sidereal Days)
Figure 5. The absence of a significant siderial oscillation confirms CPT invariance at the best level tested for muons.
141
3.2. Search for CPT violation
Recently, generic extensions of the Standard Model, in which both Lorentz invariance and CPT invariance are not assumed, have attracted widespread attention in physics. Diurnal variations of the ratio (v12 - V34)/(V12 v34) are predicted (see Fig. 5). An upper limit could be set from a reanalysis of the LAMPF GeV for the Lorentz and CPT violating parameter. In data at 2 . a specific model by Kostelecky and co-workers a dimensionless figure of merit for CPT tests is sought by normalizing this parameter to the particle mass. In this framework AUHFS provides a significantly better test of CPT invariance than electron g-2 and the neutral Kaon oscillations".
+
3.3. The Fine Structure Constant
The hyperfine splitting is proportional to a2 . R, with the very precisely known Rydberg constant R,. Comparing experiment and theory yields a-l= 137.0359963(80) (58ppb). If R, is decomposed into even more fundamental constants, one finds AvHFs = a4m,/h. With him, as de-
Fine Structure Constant a R, & mJh
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142
termined in measurements of the neutron de Broglie wavelength we have 137.0360047(48) (35 ppb). In the near future a small improvement in this figure can be expected from ongoing determinations of him, in measurements of the photon recoil in Cs. A better determination of the muon mass, e.g. will result in a further improvement and may contribute to resolving the situation of various poorly agreeing determinations of the fine structure constant, which is important in many different fields of physics. It should be mentioned that the present agreement between Q as determined from muonium hyperfine structure and from the electron magnetic anomaly is generally considered the best test of internal consistency of QED, as one case involves bound state QED and the other one QED of free particles. 3.4. Future Possibilities for A V H F ~
The results from the LAMPF experiment are mainly statistics limited and improve the knowledge of both A V H Fand ~ pp by a factor of three over previous measurements. This gain could be significantly surpassed with an experiment based on the ”Old Muonium” technique at a future high flux muon source (see section 7). As a useful starting point one would like to have 5 . lo8 p+/s at below 28 MeV/c momentum with typically 1 % momentum width. The beam should be pulsed with lps wide pulses of up to several 10 kHz repetition frequency. One can expect that theory will be continuously improved t o allow the extraction of fundamental physics information from a precision experiment 13.
4. Muonium 1s-2s Two-photon Spectroscopy
In muonium the 1s-2s energy difference is essentially given by the relevant quantum numbers, R, and a reduced mass correction. Therefore, this transition may be regarded ideal for a determination of the muon-electron mass ratio. QED corrections are well known for the needs of presently possible precision experiments and do not play an important role here. Doppler-free excitation of the 1s-2s transition has been achieved in pioneering experiments at KEK l4 and at RAL 15. In all these experiments two counter-propagating pulsed laser beams at 244 nm wavelength were employed to excite the n=2 state. The successful transitions were then detected by photo-ionization with a third photon from the same laser field. The released p+ was then registered on a micro-channel plate detector.
143
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Figure 7. Muonium l s 2 s signal. The frequency corresponds to the offset of the Tisapphire laser from the iodine reference line. The open circles are the observed signal, the solid squares represent the theoretical expectation based on measured laser beam parameters and a line shape model.
4.1. The recent R A L Experiment The accuracy of the early measurements was limited by the ac-Stark effect and rapid phase fluctuations (frequency chirps), which were inherent properties of the necessary pulsed high power laser systems (see Fig. 8). The key feature for the latest high accuracy measurement at RAL was a shot by shot recording of the spatial laser intensity profile as well as the time dependences of the laser light intensity and phase. This together with a newly developed theory of resonant photo-ionization l6 allowed a shot-by-shot prediction of the transition probability as a basis for the theoretical line shape (Fig. 7). The latest RAL experiment yields A ~ 1 ~ 2 ~ ( e x p2)455 = 528 941.0(9.8) MHz in good agreement with a theoretical value A ~ l ~ 2 ~ ( t h e o455 ) = 2528 935.4(1.4) MHz ". The muon-electron mass ratio is found to be m,+/m,- = 206.76838(17). Alternatively, with m,+/m,- as extracted from AVHFS, a comparison of experimental and theoretical values for the 1s-2s transition can be interpreted in terms of a p+ - e- charge ratio, which results as qm+/qe- 1 = -1.1(2.1) . lo-'. This is the best verification of charge
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equality in the first two generations of particles. The existence of one single universal quantized unit of charge is solely an experimental fact and no underlying symmetry could yet be revealed. The interest in such a viewpoint arises because gauge invariance assures charge quantization only within one generation of particles. 4.2. Slow Muons from Muonium Ionization
A new development aims at providing low energy (<1 eV energy spread) muons for condensed matter research. At RIKEN-RAL facility a new muon source is being set-up which bases on the laser photo-ionization of muonium. The atoms are produced from hot metal foils which they leave at thermal velocities. The ionization process involves one-photon excitation of the ls2p transition and subsequent ionization with a second laser. At present the yield is a few p+/s. l8
145
4.3. Future Muonium Laser Spectroscopy
Major progress in the laser spectroscopy of muonium can be expected from a continuous wave laser experiment, where frequency measurement accuracy does not present any problem because light phase fluctuations are absent. For this an intense source of muons will be indispensable (see section 7). which provides at least a factor of 1000 higher flux of (pulsed) surface muons. As a promising starting point one would like to have a pulsed beam 5 . lo8 p f / s below 20 MeV/c with typically 3 % ' momentum width and about 100 Hz repetition rate.
5. Muonium and the Muon Magnetic Anomaly The muon magnetic anomaly a, (see contributions by Francis Farley and Ernst Sichtermann to this volume 19) is given, like in case of the electron, mostly by virtual photon and electron-positron fields. However, the effects of heavier particles can be enhanced by the square of the muon - electron mass ratio m,/m, M 4 ' lo4. At the level of present experimental accuracy there are contributions to the muon magnetic anomaly which are absent in the electron case. For the muon the contributions of the strong interaction, which come in through vacuum polarization loops with hadronic content, can be determined using a dispersion relation and the input from experimental data on e+-e- annihilation into hadrons and hadronic r-decays. They amount to 58 ppm. The weak interactions contributing through W or Z boson exchange give a 1.3 pprn correction. At present standard theory yields a, to about 0.7 ppm. Contributions from physics beyond the Standard Model could arise from, e.g., supersymmetry, compositeness of fundamental fermions and bosons, CPT violation and many other sources. They could be at the ppm level. The experimental values for the magnetic anomaly of p+ and p have been determined very recently by a collaboration headed by Vernon Hughes at the Brookhaven national Laboratory (BNL). It is a "g-2" experiment in which the difference of the spin precession and the cyclotron frequencies is measured. The experimental results for muons of both sign of electric charge are accurate to 0.7 ppm and agree well. Assuming CPT invariance they yield a combined value of a, to 0.5 ppm 20. At this time it is unclear, whether there is a small difference between theory and experiment at the level of 2 to 3 standard deviations due to unresolved issues in the theory of hadronic corrections.
146
+weak
contributions
Figure 9. The spectroscopic experiments on the hyperfine structure of muonium and the 1s-2s energy interval are closely related to a precise measurement of the muon muon magnetic anomaly. The measurements put a stringent test on the internal consistency of the theory of electroweak interaction and on the set of fundamental constants involved.
The microwave and laser spectroscopy of muonium are closely related to the measurement of the muon magnetic anomaly. The fundamental constants such as m,, p p , a and q,+ / q e - are indispensable input for the theory and the experiment on a,. It should be noted that prior to a future significant experimental improvement of a,, such as planned at the Japanese J-PARC accelerator complex 2 1 , an improvement in the knowledge of muon related fundamental constants would be required. Muonium spectroscopy offers a clean way to obtain them. 6. Muonium- Antimuonium Conversion
In addition to the indirect searches for signatures of new physics in the muon magnetic anomaly and in electromagnetic interactions within the muonium atom the bound state offers also the possibility to search more directly for predictions of speculative models. The process of muonium to antimuonium-conversion (M-M)violates additive lepton family number conservation. It would be an analogy in the
147
Figure 10. Muonium-antimuonium conversion in theories beyond the standard model. The interaction could be mediated by (a) a doubly charged Higgs boson A++, (b) heavy Majorana neutrinos, (c) a neutral scalar Q N , e.g. a supersymmetric T-sneutrino D,, or (d) a bileptonic gauge boson X++.
lepton sector to the well known K o - F and B o - F oscillations in the quark sector. Muonium-antimuonium conversion appears naturally in many theories beyond the Standard Model. The interaction could be mediated, e.g., by a doubly charged Higgs boson A++, Majorana neutrinos, a neutral scalar, a supersymmetric r-sneutrino , or a doubly charged bileptonic gauge boson. There have been a number of attempts to observe M-M conversion. The pioneering work was again performed by a group guided by Vernon Hughes already in the 1960ies 22. The early experiments relied on the X-rays which would follow a p--transfer to a heavy element upon contact of with matter as part of their signature. A breakthrough was the availability of thermal muonium in vacuum 24 which led to a significant increase in sensitivity 25. 22723
6.1. The latest
M-M Experiment
at PS I
At PSI an experiment was designed t o exploit a powerful new signature, which requires the coincident identification of both particles forming the anti-atom in its decay lo. The technique had been pioneered by an international collaboration led by Vernon Hughes at LAMPF 25. Thermal muonium atoms in vacuum from a Si02 powder target, are observed for decays. Energetic electrons from the decay of the p- in the atom can be identified in a magnetic spectrometer (Fig. 11). The positron in the atomic shell of M is left behind after the decay with 13.5 eV average kinetic
148
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earn counter photons
Figure 11. The Muonium-Antimuonium Conversion Spectrometer at PSI.
energy. It has been post-accelerated and guided in a magnetic transport system onto a position sensitive micro-channel plate detector (MCP). Annihilation radiation can be observed in a segmented pure CsI calorimeter around it. The decay vertex can be reconstructed. The measurements were performed during a period of 6 months in total over 4 years during which 5.7 lo1' muonium atoms were in the interaction region. One event fell within a 99% confidence interval of all relevant distributions. The expected background due to accidental coincidences is 1.7(2) events (Fig. 12). Depending on the interaction details one has to account for a suppression of the conversion in the 0.1 T magnetic field in the spectrometer. This amounts maximally to a factor of about 3 for V f A type interactions. Thus, the upper limit on the conversion probability is 8.2 . (90% C.L.). The GF,where GF is the weak coupling constant is bound to below 3.0. interaction Fermi coupling constant. This new result, which exceeds limits from previous experiments by a factor of 2500 and one from an early stage of the experiment by 35, has some impact on speculative models. For example: A certain z8 model is ruled out. It had more than 4 generations of particles and where masses
149
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Figure 12. Time of flight (Top) Figure 12. Time of flight (Top) could be generated radiatively with heavy lepton seeding. A new lower limit of 2.6 TeV/c2 x g31 (95% C.L.) on the masses of flavour diagonal bileptonic gauge bosons in GUT models is extracted, which lies well beyond the value derived from direct searches, measurements of the muon magnetic anomaly or high energy Bhabha scattering. Here, g31 is of order unity and depends on the details of the underlying symmetry. For 331 models the experimental result can be translated into 850 GeV/c2 x g31 which excludes some of their minimal Higgs versions, where an upper bound of 600 GeV/c2 has been extracted from an analysis of electro-weak parameters. The 331 models need now to refer to a less attractive and more complicated extensions. In the framework of R-parity violating supersymmetry the bound on the relevant coupling parameters could be lowered by a factor of 15 to A132 . for assumed super-partner masses of 100 GeV/c2. A231 I 3. 6 . 2 . Future Possibilities f o r M-M Experiments
A future experiment to search for M - u conversion could particularly take advantage of high intensity pulsed beams. In contrast to other lepton (family) number violating muon decays, the conversion through its nature as particle-antiparticle oscillation has a time evolution in which the probability for finding a system formed as muonium decaying as increases
150
quadratically in time. This gives the signal an advantage, which grows in time over exponentially decaying background. E.g., with a twofold coincidence as part of a signature: after a time AT = 27, beam related accidental background has dropped by almost two orders of magnitude, whereas a MM-signal would not have suffered significantly at all. An almost ideal beam would have 1 . 1O1O p + / s at below 23 MeV/c with typically 1-2 % momentum width. The beam should be pulsed with up to lps wide pulses of up to several 10 kHz repetition frequency. Such efforts appear well motivated among other reasons through the connection to numerous speculative models involving, e.g., lepton flavour violation in general or a possible Majorana nature of the neutrinos 27.
7. Future Possibilities for Fundamental Interaction Research with Muons It appears that the availability of particles limits at present progress in research with muonium. This includes better fundamental constants as well as the possibility to find very rare processes and to impose significantly improved limits in continuation of the search program of dedicated experiments. Therefore significant measures to boost the muon fluxes at existing accelerator centers and to create future facilities with orders of magnitude higher muon currents is indispensable prior to any significant progress. This requirement matches well with the demand of several communities within physics which request an intense particle accelerator. Such interest exists, e.g., worldwide for a Neutrino Factory and a Muon Collider 26, in Japan for the J-PARC facility and in Europe for EURISOL facility 28. The perspectives for muonium research have beam worked out for such a scenario in some detail 26. Examples of tailored intense muon sources at existing facilities are the x - p converter at PSI, the planned muon production of the planned MECO experiment at BNL or the projected phase rotated intense source of muons (PRISM) 29 in connection with the upcoming J-PARC facility. The design goal for such a new machine should be a minimum of 1 MW proton beam on a production target. This could become a reality at various places including BNL, CERN, GSI and J-PARC.
151
Figure 13. Vernon W. Hughes keeping contact with his colleagues during the Lepton Moments I conference in Heidelberg in 1999. Effective communication is a key to operate simultaneously several challenging large experiments at different research centers around the world.
8. Conclusions
More than 70 years after the muon was discovered 30, its properties still remain puzzling. The mysteries include not less than the reason for the muon's existence, the size of its mass, its charge and the fact of lepton number (and for charged species) lepton family number conservation. All precision experiments to date have confirmed that the muon is a heavy copy
152
of the "point-like" electron. Standard theory appears t o be an adequate description of all measurements, although it cannot answer some of the deeper questions. Searches for a violation of the Standard Model were not blessed with a successful observation yet. However, both the theoretical and experimental work in this connection have led t o a much deeper understanding of particle interactions. One special value of the precision experiments are their continuous contributions towards guiding theoretical developments by excluding various speculative models. The research of Vernon Hughes has most significantly added to shaping our knowledge about nature in this way. Research on muonium has contributed quite some essential facets t o the picture of fundamental particles and fundamental interactions in physics. 9. Final Remarks
a
The author owes his heartily gratitude to Vernon Willard Hughes for a long fruitful collaboration in the framework of a number of international collaborations. The measurements we could carry out together all involved muons. In particular, many of them involved centrally the fundamental atom we could find for our research:
Thank You Vernon for introducing muonium to the scientific community. References 1. V.W. Hughes and G. zu Putlitz, in: Quantum Electrodynamics, ed. T. Ki-
noshita (World Scientific, 1990) p. 822 2. K. Jungmann, in: Muon Science, eds. S.L. Lee, S.H. Kilcoyne and R. Cywinsky (Inst. of Physics Publ., 1999) p. 405 3. V.W. Hughes et al., Phys. Rev. Lett. 5 , 63 (1960) 4. R. Prepost, this volume 5. V. Telegdi, in: A Festschrifi an honor of Vernon W. Hughes, ed. M. Zeller
(World Scientific, 1991) p. 65 6. W. Liu et al.,Phys. Rev. Lett. 82 (1999) 711 7. V. Meyer et al., Phys. Rev. Lett. 84 (2000) 1136
8. C.J. Oram et al., Phys. Rev. Lett. 52 (1984) 910 9. A. Badertscher et al., Phys. Rev. Lett. 52 (1984) 914 and Phys. Rev. A 41 (1990) 93 10. L. Willmann et al., Phys. Rev. Lett. 82 (1999) 49; L. Willmann and K. Jungmann, in: Lecture Notes i n Physics 499 (Springer, 1997) p. 43 aThe author wishes to thank C.J.G. Onderwater for carefully reading the manuscript and his help during formatting.
153 11. V.W. Hughes et al., Phys. Rev. Lett. 87 (2001) 111804; R. Bluhm et al., Phys. Rev. D 57 (1998) 3932; R. Bluhm et al., Phys.Rev.Lett. 84 (2000) 1098 12. M.G. Boshier et al., Phys. Rev.A 52 (1995) 1948 13. M. Eides et al., Phys. Rev. D67 (2003) 113003; S. Eidelman et al., Can. J. Phys. 80 (2002) 1297 14. Steven Chu et al., Phys. Rev. Lett. 60 (1988) 101; see also: K. Danzmann et al., Phys. Rev. A 39 (1989) 6072 15. F. Maas et al., Phys. Lett. A 187 (1994) 247; W. Schwarz et al., IEEE Trans.Instr.Meas. 44 (1995) 505; K. Jungmann et al., Z.Phys.D 21 (1991) 241 16. V. Yakhontov and K. Jungmann, Z. Phys. D 38 (1996) 141; and V. Yakhontov, R. Santra and K. Jungmann, J. Phys. B 32 (1999) 1615 17. K. Pachucki et al., J. Phys. B 29 (1996) 177; S. Karshenboim, Z. Phys. D 39 (1997) 109 and Can. J. Phys. 77 (1999) 241; K. Pachucki and S. Karshenboim, priv. com. (1999) 18. Y. Matsuda et al. J. Phys. G 29 (2003) 2039 19. F.J.M. Farley this volume; E. Sichtermann, this volume 20. H.N. Brown et al., Phys. Rev. Lett. 86 (2002) 2227; G.W. Bennett et al., Phys. Rev. Lett. 89 (2002) 101804 and Phys. Rev. Lett. 89 (2002) 129903; G.W. Bennett et al, hep-ex/0401008 (2004), accepted for publication by Phys. Rev. Lett. 21. R.M. Carey et al., J-PARC Letter of Intent L17 (2003) 22. J.J. Amato et al., Phys. Rev. Lett. 21 (1968) 1709 23. T.M. Huber et al., Phys. Rev. D41 (1990) 2709; B. Ni et al., Phys. Rev. Lett. 59 (1987) 2716 24. K. A. Woodle et al., Z. Phys. D 9 (1988) 59; A. C. Janissen et al., Phys. Rev. A 42 (1990) 161 25. B.E. Matthias et al., Phys.Rev.Lett. 66, (1991) 2716 26. Alsharo’a et al, Phys. Rev. ST. Accel. Beams 6 (2003) 081001; J . Aysto et al., hep-ph/01092 17 27. M.A. Perez et al., hep-ph/0402156 ; A. Gusso et al., J. Phys. G 30 (2004) 37; S Huber, Nucl. Phys. B 666 (2003) 269; T.E. Clark and S.T. Love, Mod.Phys.Lett. A19 (2004) 297 28. D. Ridicus et al., DAPHNIA-SPHN-2000-59 29. Y. Kuno, High Intensity Muon Sources, ed. Y. Kuno and T. Yokoi (World Scientific, 2001) 30. P. Kunze, Z. Phys. 83 (1933) 1
PARITY NONCONSERVATION IN ELECTRON-ELECTRON SCATTERING EMLYN WILLARD HUGHES Division of Physics, Math and Astronomy, California Institute of Technology Pasadena, CA 91125
Low-energy precision measurements of fundamental parameters in the electroweak theory provide information on new physics at high mass scales, beyond the reach of present-day colliders. We report on a first measurement of the electroweak mixing angle from the observation of a parity-violating asymmetry in the scattering of high energy polarized electrons by unpolarized electrons in a liquid hydrogen target. The parityviolating asymmetry is very small, on the order of 100 parts per billion. The experiment was performed in the fixed target progam at the Stanford Linear Accelerator Center. We also compare the results to other low energy tests of the electroweak theory and summarize the status of this field of study. The present experiment gives sensitivity to new physics at the TeV energy scale.
1. Introduction Only a year and a half ago many of us were present at Yale celebrating my father’s 80” birthday and reviewing his many contributions to physics. It is much too soon to be back discussing his research again. But, I am grateful to Yale for organizing this wonderful symposium and honoring my father.
I would also like to thank Yale for the support that it has given to my father over the years. My father was at Yale just shy of fifty years. That he remained and never wavered from his aggressive focus on physics research is a testament to the tremendous backing that Yale provided for him. For my father, Yale was a resource, and he used it incessantly in research and beyond. I would like to give one personal recollection involving my father, Yale and me. When I was eight years old, I approached my father with determination and told him that I wanted to be a heart surgeon. My father sat thoughtfully for a moment and then asked for my reasons. I told him that I believed it would be an exciting career and that I would be helping people. After pondering this situation a bit longer, my father responded that it is important before making such important decisions that one consults with others in order to get different views. Although he acknowledged my interests and recognized the importance of heart surgery, he said that I should also speak with someone who also had wanted to be a heart surgeon at an early age, but later decided to study physics instead. Shortly after this conversation, he took me to a faculty party at Yale and introduced me to this “prospective-heart-surgeon-turned-physicist”, and I found 154
155 myself talking alone to Alan Bromley. Honestly, I do not remember one word of what Alan said to me that day. All I know is that when our conversation was over, my career as a heart surgeon was finished. The point, of course, is that my father used the resources that Yale offered, in a variety of creative ways. Yale was his family, and for this, I also thank Yale. My topic today, a recent SLAC electron-electron scattering parity violation experiment (SLAC E158) [ 11, builds upon my father's early pioneering research on polarized electron scattering [2-31. In particular, the first observation of parity violation in electron scattering, SLAC Experiment E122, provided conclusive evidence for the mixing between the electromagnetic and weak interactions [3]. The description of this experiment has been covered previously by Charles Prescott at my father's 70" birthday celebration [4], and much of what I will describe in the next section is a synopsis of Prescott's article. However, since the techniques and philosophy developed in the SLAC El22 experiment had an enormous impact on the SLAC El58 experiment, it is worth reviewing again this first SLAC parity violation measurement.
*
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Figure 1 . Schematic setup of a high-energy electron scattering parity experiment.
SLAC Experiment El22 At leading order, the electroweak theory predicts a non-zero spin-dependent cross section asymmetry for all cases in which a polarized electron scatters off any unpolarized object. The asymmetry originates from an interference between two Feynman diagrams, one being photon exchange and the other being Z-boson exchange. The Z boson diagram violates parity. For the early parity experiment, SLAC Experiment E122, the unpolarized objects were quarks, and the regime was deep inelastic scattering. For the experiment discussed today, SLAC Experiment E158, the unpolarized objects are electrons contained within a liquid hydrogen target.
156
As shown schematically in Figure 1, SLAC Experiment El22 involved scattering a high current (-10 pA) 40% polarized electron beam produced from a GaAs source off a 30 cm long liquid hydrogen target. The beam energy of the electrons was 16, 19 and 22 GeV, which scanned the highest energy range that SLAC could produce at the time. The scattering angle in the experimental hall was chosen to be 4 degrees, producing a high enough scattering rate to measure a -4
relative small parity-violating asymmetry, -10 , and yet was kinematically within the deep inelastic scattering regime. Both a lead-glass calorimeter and a threshold Cerenkov counter were used as detectors in the spectrometer and integrated the full blast of scattered electrons for the asymmetry measurement. Tracking of the electrons on a particle by particle basis was not performed, except for background studies at low beam current. Data collection occurred in 1978, and the full SLAC machine was dedicated to the experiment during this period.
Oplical Revorsai Schema
Figure 2. Polarized Electron Source Optics setup for SLAC Experiment El22
The El22 Experiment was a collaboration primarily between Group A at SLAC, under the leadership of Charles Prescott, and my father’s group at Yale. My father had developed the first polarized electron source used in an electron scattering accelerator experiment, and Prescott’s group pioneered the development and implementation of the GaAs source technology. The GaAs source was necessary to attain the high beam current, allowing for the
157
determination of the small parity-violating asymmetry arising from electroweak mixing. Systematic control over the helicity-dependence of the electron beam production and transport was a extremely important for the experiment. The spin direction of the electrons was flipped on a pulse-by-pulse basis at 120 Hz by reversing the helicity of the source laser light using a Pockel cell. Figure 2 shows a schematic of the optics setup. A slow reversal implemented every few runs was performed in order to check for false asymmetries. Figure 3 presents the results of the asymmetry measurements versus time, where the effects from the slow half-wave plate reversals are evident. In Figure 4 the result of this reversal is averaged over the experiment. One sees clearly a ten standard deviation parity-violating asymmetry for data taken over the full experiment; and the asymmetry reverses cleanly with the half-wave plate rotation. 90 Polarized Beam ;ii'
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One additional important, and convincing, systematic check for false asymmetries came from an independent helicity reversal by performing the parity-violation measurement at different beam energies, namely 16, 19 and 22 GeV. After the longitudinally polarized electrons were accelerated to the end of the SLAC linear accelerator, the beam was bent by 24.5 degrees at the beam switch yard and then directed into the experimental hall. During the 24.5 degree bend, the electron spins underwent a 8-2 precession. As demonstrated in Figure 5, a 16 to 19 to 22 GeV energy measurement reverses the overall parity-violating asymmetry for each 3 GeV change. The clear asymmetry reversal from energy changes was a powerful systematic check for false asymmetries. Although a number of beam parameters change with energy, the parity-violating asymmetries appear to be stable, indicating that the overall measurement is robust with respect to any small unmeasured variations of the beam parameters.
158 20
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Figure 4. Parity-violating asymmetry versus prism orientation averaged over the experiment.
The final integrated parity-violating asymmetry from SLAC Experiment E122, 2 2 5 normalized to the average Q , was found to be A/ Q = (-9.5 ~ 1 . 6 )x 10(GeV/c)'2. Using the Standard Model and the measurement of A from the El22 2 experiment, a value for the electroweak mixing angle is found, namely sin 8, = 0.224+ 0.020. It is noteworthy that today's world average determination of 2 sin 8, from high-precision electron-positron collider asymmetry measurements is 0.2245 ? 0.00017. Within uncertainties, the El22 result remains precisely on today's prediction. More importantly, the El22 experiment was performed during a time when many atomic physics measurement of electroweak mixing and parity violation were coming out with null results. These atomic experiments were extremely challenging both experimentally, since they were measuring a level asymmetry, and theoretically, since they used large multi-electron atoms (e.g. bismuth). The conversion of a parity-violating asymmetry back to the electroweak mixing parameter was plagued by difficulties 2 stemming from atomic theory calculations. The theoretical values for sin 8, typically varied by a factor of two. The result from SLAC Experiment El22 represented a triumph for the Standard Model. For us today, it*laid the philosophical groundwork for handling systematic effects in a high energy electron scattering parity violation experiment.
-
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Figure 5. Parity-violating Asymmetry versus beam energy averaged over the experiment.
SLAC Experiment El58 SLAC Experiment El58 is an electron scattering experiment that involves the elastic scattering of a high-energy high-current polarized electron beam off the electrons in a large liquid hydrogen target [4]. The Moller scattered electrons are chosen kinematically by a spectrometer that selects specific scattering angles and energies. By detecting scattered electrons in a forward integrating calorimeter, a right-left asymmetry, A=, in the Moller scattering cross sections is found, where ARL=
O R- O L
, and CTLand O R correspond to the scattering
O R+ c T L
cross sections for left and right handed polarized electrons, respectively. At the tree level, the relationship between Am and sin%, is given by
160
where rn is the mass of the electron, E is the beam energy, G, is the Fermi coupling constant, and 6 is the center of mass scattering angle between the beam and target electrons. There are some interesting features of this formula that have direct impact on the experiment. First, the Fermi constant G, is small, and this sets a scale for the measurement, namely that the asymmetry is extremely small. In fact, the expected electroweak prediction for the raw value of Am is -lo-’ (100 ppb). Secondly, Am increases with beam energy. This implies that one needs a high-energy electron beam (-50 GeV) to have a sufficiently large asymmetry for the electron-electron scattering process. A lower beam energy experiment would imply an even smaller asymmetry. Finally, the asymmetry measurement provides a direct determination of the difference between sin2€), and 0.25. This detail is important. It turns out fortuitously that sin2€), has a value very close to 0.25 (sin2€), 0.23). The relationship between the uncertainty on AA RL ARLand the uncertainty on sin2OWis simply ‘w . This implies,
-
ARL
1
- - sin28,
4 for example, that a 10% relative measurement of Am determines the difference between sin2€), and 0.25 to a precision of lo%, namely that sin2€), is found to a precision of f 0.002. In fact, including higher-order radiative corrections, the relationship between Am and sin%, becomes even more favorable for the extraction of sin2€), by approximately a factor of two. In the Moller experiment we are aiming to measure Am to a precision of -10% of its central value, which determines sin2€), to an absolute precision of approximately *O.OO 1, (formally in the proposal f0.0009, including statistical and systematic uncertainties).
In summary, we are measuring a very small asymmetry, but only to a precision of about 10% of its value. One nice consequence of the rather large relative uncertainty on the ALRmeasurement is that we do not require, for example, precision beam polarimetry. The El58 Moller polarimeter will determine the beam polarization to -3% on AAmR/Am. This differs from the SLD experiment, which required a high precision measurement of the beam polarization (less than 1% on AARL/Am). On the other hand, the small asymmetry places a high demand on electron beam control and requires high statistics. This implies a high beam current, a large target, a large acceptance spectrometer recording events at very small scattering angles and high resolution for our beam monitors. Any broadening of statistical distributions coming from degraded beam monitor resolutions will increase the overall statistical uncertainty. This is an important consideration, since the statistical uncertainty is expected to be the dominant
161
uncertainty for the experiment. The El58 systematic uncertainty goal is more stringent than, but similar to a previous parity violation measurement performed at Bates [ 5 ] . The El58 experiment was conditionally approved in autumn of 1997 and collected data over three run periods in 2002 and 2003. The El58 collaboration consists of approximately 60 physicists from ten institutions in the US and France. Seven graduate students (Klejda Bega (Caltech), Waled Emam (Syracuse), Mark Jones (Caltech), Peter Mastromarino (Caltech), David Relyea (Princeton), Imran Younus (Syracuse) and Antonin Vacheret (Saclay) have or will soon earn their PhD working on the experiment. Results from the first two run periods are presented in this paper. The measurement of such a small asymmetry, -100 ppb, brings about numerous challenges. These can be categorized into four classes: 0 0 0
Statistics Beam monitoring and resolution Beam systematic effects and false asymmetries Backgrounds
Obviously, to make a 10% relative measurement on a asymmetry means that RL one needs to have enough events to measure A to The primary means to maximize the statistics for the experiment was to collect data with the maximum beam current that SLAC could deliver, build and operate an extremely long hydrogen target and collect all Moller scattered electrons into a full acceptance azimuthally symmetric detector. The details work out as follows. With SLAC operating at 10 pAmps (same beam current as SLAC Experiment E122), using a 1.5 meter long liquid hydrogen target, the rate of scattered Moller electrons into 7 our detector was on the order of 10 per pulse. The repetition rate of the 9 5 accelerator was 120 Hz, resulting in 10 electrons per second. There are 10 14 seconds in a day, giving 10 electrons per day. And, the experiment collected 16 data for a total of approximately 100 days. So, approximately 10 scattered electrons were recorded, which is the number needed for a lo-* asymmetry measurement.
162
Figure 6. Schematic setup of SLAC Experiment E158.
Since the experiment was designed for a very small scattering angle, the experimental setup looked like a long beamline. Figure 6 shows the layout of the equipment to scale. It is evident that the equipment occupies the entire 60 meter long experimental hall. The beam enters from the left and interacts in the target. Moller electrons appear from the target with a range of energies. So that electrons are not double counted, only scattered electrons with energies between 12 and 24 GeV survive through the spectrometer optics. The spectrometer consists of a chicane of three dipole magnets that separate electrons of different energies and is followed by four quadrupoles which serve to focus the Moller electrons onto the detector at the back end of the experimental hall. A scheme of high power collimators are built inside the spectrometer package to shield against neutral particles, charged particles with too low energy and against scattering off collimator slits. At the rear of the experimental hall is a segmented donut shaped, cylindrically symmetric total absorption calorimeter made out of copper and high radiation quartz fibers. The calorimeter is divided into four donut-shaped rings. The innermost and outermost rings are segmented into 10 identical pieces azimuthally, and the middle two rings are segmented into 20 identical pieces azimuthally. Each segment has one photomultiplier which provides one signal per beam pulse. The segmentation is extremely important for studying and characterizing beam systematic effects, since often they do not cancel out per detector channel. At a smaller scattering angle located at the rear of the experimental hall is a luminosity monitor that also serves as an important check for beam systematic studies.
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Figure 7. Correlation scatter plot between neighboring beam monitors. Each point represents a contributionfrom one beam pulse.
In an ideal experiment, if there is absolutely no jitter in the beam position, angle, intensity or energy and the calorimeter electronics have a high resolution, the statistics accumulated in the experiment would simply follow l/dN counting statistics. However, in reality, the beam intensity jitters by -1/2 %, and there is significantjitter in the angle, position and energy. This jitter has to be taken out and corrected for with beam monitors. Figure 7 presents correlations between various beam position monitors and beam toroids, which determinethe beam change. observcd left-right nsymme8ry distribution 14w 12w
Bw MXI 400 200 0
Figure 8. Change in the left-right asymmetry distributionfrom the raw result in one phototube to the final analysis, summing over all phototubes and correctingfor beam fluctuations.
One sees an extremely high correlation between various measurements, and if these correlations are not taken out, then the full spread of the beam appears in the data, which blows up the statistical uncertainty by widening the event and
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asymmetry distributions. Figure 8 presents the changes in these distributions as one systematically incorporates some correction to the beam jitter data. A major focus in the El58 analysis was the task of taking out beam correlations and beam jitter. The third challenge for the experiment was to ensure that there were no false asymmetries. Figure 9 presents the upgraded polarized source optics used for Experiment E158. A tremendous effort went into building multiple feedback units
I
Figure 9. Schematic setup of the polarized source optics for SJAC Experiment E158.
to correct for beam changes [ 6 ] . The basic philosophy was to measure the helicity-dependentbeam conditions (e.g. charge and position) imme diately after production, in the 1 GeV section of the accelerator, and then correct with Pockel cells the laser beam helicity to null out any wandering of the beam from its nominal setting. As Figure 9 demonstrates, a sophisticated optics setup was developed incorporating numerous Pockel cells and a piezo-electric mirror feedbacks, which were continually adjusted. In the end, the primary means to check for false asymmetries.used the same philosophy as SLAC Experiment E122, namely making the asymmetry measurement by inserting a half-wave plate and by collecting data at two different beam energies, 45 and 48 GeV. Results from the El58 asymmetry measurement versus time are presented in Figure 10. An asymmetry reversal occurs whenever the wave-plate is inserted or removed or whenever the beam energy is changed. An average of the results from the various run conditions are given in Figure 11 with the final measured asymmetry.
165
I
Run1
Run11 I
0
5
10
Figure 10. Parity-violating asymmetry versus time for different run conditions. Units for the asymmetry are given in parts per billion (ppb).
The last concern in the experiment pertained to the understanding of backgrounds. The important issue for the asymmetry measurement is to fold in the dilution from background that contaminates the event sample and to subtract out the asymmetry which that particular background contributes to the main Moller signal. For example, if one particular background only contributes
a
90
Jw
-150 M&r
-109
30
0
Aymnstrg(ppb)
Figure 11. Parity-violating asymmetry versus averaged over the 2002 data collection period for different beam conditions (half-wave plate setting and beam energy settings).
166
2% to the total sample but has a ten times larger asymmetry than the Moller asymmetry. The impact of that background, if not corrected is that it will change the relative asymmetry by 20%, if one does not correct for it. In fact, for our experiment, the largest uncertainty came from exactly such a contamination from radiative inelastic electron-proton scattering. These are events which, for example, radiate a photon by Bremmstrahlung and produce a lower energy beam 2 electron which then scatters deep inelastically off a proton at high x (or large W 2 > 3 GeV ). These events come from deep inelastic scattering and have a large asymmetry, even though they only contaminate the total event sample by a few percent. Figure 12 presents a measurement of this large ppm level asymmetry in our outer ep detector. The asymmetry behaves well, reverses cleanly and even provides a smaller asymmetry at lower energy, consistent with what is expected theoretically. The largest fractional background comes from radiative elastic scattering of the beam electrons by the hydrogen protons. Although the elastic electron-proton background was quite large (-6 % of the total event sample), the asymmetry is essentially identical to the Moller scatter asymmetry. So, it does not result in a large systematic uncertainty after the correction is applied.
Figure 12. Deep inelastic electron-proton scattering asymmetry measured in the SLAC El58 outer ring detector. The asymmetry reverses with wave-plate and energy reversals as expected.
It is hard to imagine that such a concept as a ‘humerous’ background could exist in a difficult parity experiment, but one did, indeed, appear in our experiment. As one of the systematic checks performed for the experiment, we collected data with a transversely polarized electron beam incident upon the liquid hydrogen target. Our expectation was that the asymmetry measured in this process would
167
be small and negligible. However, when the measured asymmetry plotted versus detector channel was recorded, the result was a large value which changed with azimuthal angle. Figure 13 presents the asymmetry versus detector channel number. One observes asymmetries ranging from zero to the 1 ppm level. This was, indeed, physics. It turns out that there is a two photon diagram that gives a positive azimuthally dependent asymmetry in the scattering of a transversely polarized electron by an unpolarized electron [7]. The asymmetry does have a sin+ dependence, where 4 is the azimuthal angle corresponding to the detector channel viewed with respect to the central unscattered electron beam. For our experiment, this effect is not important, since we scattered only longitudinally polarized electrons, with a negligible transverse component, and since our final result is averaged over all the detector channels, summing around the ring. Nevertheless, when observed, it was a surprise to us all.
Figure 13. Right-left asymmetry versus azimuthal channel number in the main El58 calorimeterfor a transversely polarized electron beam. This effect comes from a two-photon electron-electron scattering process.
The final experimental results fell short of our proposed goals, but the experiment appears to have worked well, not something that was obvious when we proposed it in 1997. Figure 14 presents the integrated number of beam spills versus time, merging the three data collection periods. Results presented in this paper come from the first two periods taken in 2002, a bit more than half of the total data sample. The asymmetry can be converted into a value for the electroweak mixing angle. 2 From the 2002 data, we find that sin 8 , = 0.2308 ? 0.0015 (stat.) & 0.0014 (syst.) f 0.0006 (theor.) in the MS scheme evaluated at the Z mass. Radiative
168 corrections from various sources [8-91 have been combined to take into account different effects that are specific to our experiment, such as the target length, for example. Results from the Run I data sample, which constitutes approximately one-quarter of the total data collected, have been published [ 101.
Figure 14. Number of spills collected for the experiment versus time in days. Results from this paper only include up to the first 500 million spills.
Figure 15 presents our result compared to other similar precision low energy tests of the electroweak theory coming from atomic parity violation [ l l ] and from neutrino-nucleon scattering [ 121. The neutrino data is, interestingly, three standard deviations from the Standard Model prediction, whereas the atomic parity violation experiment and our experiment agree with the Standard model within experimental uncertainties. However, it should be noted that the atomic parity violation measurement’s value has changed significantly with time due to the application of numerous atomic physics theoretical corrections to the multielectron atom of cesium [13-141. The bottom line today is that more precise low energy measurements of the Standard Model are needed to clarify the situation and establish whether this is or is not ripe ground for the discovery of new particles or new interactions. A number of future measurements are presently being planned. An experiment, similar to SLAC Experiment E158, exists at Jefferson Laboratory. The experiment, called Qweak [ 151, will measure parity violation in elastic electronproton scattering at 1 GeV. If successful, this experiment should be able to determine the electroweak mixing parameter with a precision of a factor of two
169
better than the El58 experiment. In a Letter of Intent submitted to SLAC [ 161, an experiment has been proposed to perform a precision measurement of the deep inelastic parity violation experiment similar to SLAC experiment E122. The goal would be to do a sub 1% asymmetry measurement using a 30 GeV longitudinally polarized electron beam scattering at 10 degrees off a liquid deuterium target. The asymmetry is very large, on the order of lob3,but the challenge is to do precision beam polarimetry, measuring the beam polarization to Ap / p 0.3%. Unfortunately, due to limited funds, the experiment has not been approved, but some version of this effort could be performed at the new 12 GeV facility soon to be built at Jefferson Laboratory [ 171.
-
0.242
NuTeV
0.24
El58 0.238
0.236
0.234
Atomic 0.232
-..,
0.2:
10‘
1on
10’
10’
.
,
.
. ..
id
2
Figure 15. Low energy measurements of sin €Iw versus average four-momentum transfer Q, given in units of GeV/c.
In conclusion, it has been a long time since my father’s creation of the first polarized electron beam for spin-dependent electron scattering experiments to study both the nucleon spin structure functions, discussed by Professors Gordon Cates and Robert Jaffe in this book, and parity violation. However, the field is still active, as new results continue to appear and new experimental efforts continue to be proposed and built.
I, more than most, will miss my father’s calm temperament, his brilliant, deep, unwavering and mysterious mind and his shy smile. But, with regard to his physics, we have only just begun.. .
170 References 1. R. Can et al., “A Precision Measurement of the Weak Mixing Angle in Moller Scattering”, SLAC-Proposal-E-158, July 1997. 2. M.J. Alguard et al., Phys. Rev. Lett. 37 (1976) 1258; 1261. 3. C.Y. Prescott et al., Phys. Lett. B77,347 (1978); B84,524 (1979). 4. See article by C. Y. Prescott, A Festschrifr in Honor of Vernon W. Hughes, (World Scientific, New York, 1992), ed. M.E. Zeller. 5. P.A. Souder et al., Phys. Rev. Lett. 65,694 (1990). 6. B. Humensky, Nucl. Instr. Meth. 521A, 261 (2003). 7. L. Dixon and M. Schreiber, “Radiative Corrections to the Azimuthal Asymmetry in Transversely Polarized Moller Scattering”, SLAC-PUB10345 (Feb. 2004). 8. A. Czarnecki and W.J. Marciano, Phys. Rev. D53,1066 (1996); Int. J. Mod. Phys. A15,2365 (2000). 9. J. Erler, A. Kurylov, and M.J. Ramsey-Musolf, Phys. Rev. D68, 016006 (2003). 10. P.L. Anthony et al., “Observation of Parity Nonconservation in Moller Scattering”, accepted for publication in Phys. Rev. Lett. (2004). 11. C.S. Wood et al., Science 275, 1759 (1997). 12. G.P. Zeller etal., Phys. Rev. Lett. 88,091802-1 (2002). 13. M. Yu. Kuchiev and V.V. Flambaum, Phys. Rev. Lett. 89,283002-1 (2002). 14. A. I. Milstein, O.P. Sushkov, and I.S. Terekhov, Phys. Rev. Left. 89, 283003-1 (2002). 15. D. Armstrong et al, “The Qweak Experiment: A Search for New Physics at the TeV Scale via a Measurement of the Proton’s Weak Charge”, Jefferson Laboratory Proposal E02-020, December 2001. 16. J.R. Arrington et al., “DIS-Parity:Search for New Physics through Parity Violation in Deep Inelastic Electron Scattering”, SLAC LOI-2003-1, May 2003. 17. D. Abbott et al., “The Science Driving the 12 GeV Upgrade at CEBAF’, February 200 1.
EXPLORING THE NUCLEON SPIN THE NEXT DECADE ABHAY DESHPANDE Department of Physics, SUNY Stony Brook, Stony Brook, NY 1I974 RIKEN BNL Research Center, BNL, Upton, NY 1I973
Abstract I review aspects of the physics case for a polarized electronproton collider including present plans and layout of the collider at BNL. Investigations of spin with such a collider in the next decade will be a iogical extension of the RHIC spin physics now being pursued at BNL. In describing the physics case, I will highlight the topics that were of particular interest to Vernon W. Hughes in whose memory this article is written.
Vernon W. Hughes and the Polarized e-p Collider Most of the physics included in this article exists because of the early efforts by Prof. Vernon W. Hughes to explore the physics frontiers of a polarized electron proton collider. His interest in a polarized collider arose from the results of the experiments that he led in the mid 1990s at CERN. At the time the message from experiments, the Spin Muon Collaboration (SMC) at CERN[ 11, the series of experiments El42 to E155X at SLAC[2] and the HERMES experiment at DESY[3] was clear: the largest uncertainties in our knowledge and understanding of the origins of the nucleon spin came from the lack of measurements of the spin structure function at low x: below x 0.003 (from SMC). Vernon noted that historically, exploration of lower x and increasing the Q2 of the measurements in deep inelastic scattering always resulted in significant new findings that had fundamentally changed our way of thinking about the strong interactions: the EMC effect [4] or the violation of Ellis-Jaffe Spin sum rule[5] in polarized DIS, and unexpected rise of the unpolarized structure function F2 at low x [6] were his favorite examples. Vernon believed that the potential for new and fundamental physics to be discovered with spin was high. It was only natural that the next step for polarized DIS was indeed an experiment at higher center of mass energy, possible with a polarized collider. From Vernon’s point of view, HERA at DESY was ideal if its proton beam could be polarized[7].
-
171
172
At HERA, there existed a polarized -27 GeV/c electron beam, and a -820 GeV proton beam resulting in center of mass energy of -300 GeV. Additionally there existed two large, functional, hermetic, almost full acceptance detectors, HI and ZEUS, along with the physicists who were experienced in their operation. Only the polarization of the proton beam was missing. From about 1995 to about 2002, Vernon held on to the hope that “polarized HEM”would eventually be realized. Towards this goal his efforts were limitless. Not only did he co-lead the series of “Future Physics at H E W workshops related to the polarized proton beam development at DESY[8], but he also tried his best to build and setup a “polarized proton beam group’’ at DESY to deal with the accelerator issues. I was fortunate enough to be with Vernon at this time. I saw him at work with his legendary passion and zeal in spite of his advanced age. Developing the polarized collider at DESY also meant a need for high energy proton beam polarimetry which was not developed at the time. For this, Vernon and his group at Yale plunged in to the ongoing effort on this topic at BNL. The proton-Carbon Coulomb Nuclear Interference (CNI) polarimeter concept developed in experiment E950 at the AGS[9] is now being used for the RHIC Spin program[lO] for proton polarimetry[ 111. Although Vernon never joined the RHIC Spin Program at BNL’, he supported all efforts to learn how to handle the polarized high energy protons. As such, he supported RHIC Spin and did what he could to enhance this program. One can not only see Vernon’s physics, exploring the nucleon spin, advance at RHIC, but also, his presence is felt indirectly through the large number of students and post docs that Vernon trained, who are now carrying on the investigations of nucleon spin at RHIC. I have no doubts that this will also be true for the main topic of this article: the electron ion collider at BNL (eRHIC), which Vernon supported whole-heartedly and hosted one of the early workshops at Yale[l2]. Seeing the activities on eRHIC gain momentum through 2001-2002 at BNL, Vernon was optimistic that, unlike HERA,
For Vernon, proton-proton scattering was much too complicated a way to explore properties of the proton.
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eRHIC will be realized and allow for a precision study of nucleon spin in the next decade. The electron ion collider at BNL: eRHIC The Relativistic Heavy Ion Collider (RHIC) at BNL has been operational since 2001. It has successfully stored and collided polarized protons and unpolarized gold nuclei at 200 GeV center of mass energy. The success of polarized protons collisions at center of mass energies of 200 GeV required many notable achievements [ 131: successful transfer of polarized protons from AGS to RHIC (at approx. 24 GeV/c), successful operation of Siberian Snake magnets, which maintain the polarization of the protons in RHIC at the injection energies and preserve the polarization through the acceleration of the protons to 100 GeV/c. It also implies stable and reliable operation of two RHIC polarimeters based on coulomb nuclear interference in single spin proton-Carbon scattering [l l ]. All these are state of the art today and have been developed at RHIC. The principle aim of the RHIC program is to discover and study the Quark Gluon Plasma [14], while that of the RHIC Spin program [lo] is to understand the origins of proton spin in particular to investigate the polarized gluon distribution. Polarized RHIC will explore the polarized gluon distribution using a variety of proton-proton probes, and it will also explore the flavor separation of quark spin from virtual W production in the next 5-7 years through 2010. The addition of a high intensity, polarizable electron/positron beam facility to the RHIC complex such that it could collide with the existing RHIC heavy ion and polarized proton beams, will allow for a precision study of nucleon spin and nuclear matter that before now was not possible. The facility has been called eRHIC[15]. The eRHIC project has been discussed extensively amongst the nuclear physics community in the last few years. It will for a to study of fundamental and universal aspects of QCD, in a unique environment. In this article I will focus only on certain aspects of it, mostly on the spin variables and associated investigations, as they were of most interest to Vernon. For an overview of the rest of the eRHIC physics program the reader is referred to Ref. ~51.
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The design requirements of eRHIC are shaped by three decades of experimental work carried out with fixed target high-energy physics facilities at SLAC, CERN, DESY, and Fermilab. In addition, a significant amount of effort was expended at DESY to investigate future polarized electron - proton (e - p)[8] and unpolarized electron - ion (e - A) [16] options. The inherent limitations of these facilities point to the need for a facility with the following characteristics: Collider geometry with polarized electron-proton and electronnucleus collisions Wide range of center of mass energies, with an emphasis on large energies High luminosity L(ep) = at least 1033cm-2s-' per nucleon, Polarization of electron and proton and possibly light ions Nearly hermetic detectors with good tracking, particle identification, and both electromagnetic and hadronic calorimetry Collider geometry offers two major advantages over fixed target electron-protonhon (e - p/A) studies. First, the collider delivers vastly increased energy to the collision, providing a greater range for investigating partons with small momentum fractions (x) and their behavior over a wide range of momentum transfers
(p).
Figure l a and Fig. l b show the x-@ range possible with the eRHIC and compares that range to the presently explored kinematic region. The beam energies assumed for the eRHIC are: 0
0
0
100 GeVhucleon for nuclear beams as they exist at RHIC 50-250 GeV for polarizedhn-polarized proton beams possible at RHIC 10 GeV/c for polarized electron and positron beams although it should also be able to provide a 5 GeV beam and at least a few alternate energies with minimal loss in polarization and luminosity
The only electron-proton collider in existence is H E M , which is limited to polarized electron or unpolarized proton collisions. Thus, the
175
electron-nucleus and polarized electron-polarized nucleon collisions at eRHIC are both entirely new territories. Q2 (GeV2) I
Figure 1: The x-Q2 Range of the proposed eRHIC facility is compared with previously measured ranges. The figure on the left is for polarized lepton - nucleon DIS, while the figure on right is for unpolarized lepton-nucleon and lepton - nucleus DIS, where leptons can be electrons or muons. Note that the H E M coverage (right) is for e - p scattering only while the fixed target and the eRHIC regions also include DIS off nuclear targets.
Secondly, the collider geometry allows for the examination of final states of interactions. If one wishes to examine the final state fragments from the struck nucleon or nucleus in fixed-target geometry, it is necessary to use a thin target so that the fragments can escape the target and be detected. The thin target makes acquisition of adequate number of events a serious problem. This could be overcome in a future collider with high luminosity. The boost acquired by target fragments in the collider mode would makes them readily available for detection when separated from the beam. High luminosities of the order of L(ep)=l 033cm-*s-' for electron-nucleon scattering, are a necessary and crucial requirement for eRHIC. It corresponds to observing -86 pb-' per day. Previous studies have established that significant results could be attained with a polarized collider with -0.5-2 fb-', integrated luminosity [ 151. Therefore the statistical precision required for significant physics should be easily within the reach of eRHIC.
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This luminosity can be achieved with either of the two accelerator scenarios presently under consideration for eRHIC: a ring-ring configuration, and a ring-electron linac configuration [ 171. Each has its own advantages and limitations discussed later in this article. Achieving the proposed luminosities requires electron cooling of the ion beams (except at the highest proton energies) and intense electron beams of about 450 mA. While challenging, the intense electron beams are already available at the presently operating B-factories (SLAC and KEK B). The electron linacs (one for cooling the ion beam and another providing high-energy electrons in the collider) require full-energy recovery following the model of the full-energy recovery 50 MeV linacbased free electron laser at Thomas Jefferson Laboratory. Figure 2 shows the unique parameters of the eRHIC in the context of existing and planned lepton scattering facilities worldwide. The eRHIC facility will have higher energies than any existing polarized fixed target experiment and two order of magnitude higher luminosity than the existing HERA collider. In addition the possibility of DIS off nuclei in collider mode would be unique for the foreseeable future.
1
10
lo2 CM Energy (GeV)
Figure 2: The center-of-mass Energy vs. luminosity of eRHIC relative to other facilities.
177
The Scientific Fronters of eRHIC at BNL: While a broad physics program to investigate the structure of matter and that of its spin are possible with eRHIC, I will focus only on the spin related measurements that were of most interest to Vernon. With the experimental facility described above along with a hermetic ‘‘47~’’ detector, the scientific frontiers open to eRHIC fall in the following major categories: 1.
2.
3. 4.
5.
Unpolarized and polarized quark and gluon distributions in the nucleon using inclusive and semi-inclusive deep inelastic scattering with good particle identification in the detector Correlations between partons: Measurements of DVCS and other such measurements leading to Generalized Parton Distributions (GPDs) to understand the spatial structure of the nucleons and in the future the orbital angular momentum of partons The role of quarks and gluons in nuclei: structure functions of the nuclei Hadronization in nucleon and nuclei: the process of formation of nucleons starting from a high energy collisions in which the partons are presumably free Study of partonic matter under extreme conditions: Discovery and a detailed study of high density gluonic matter if it exists in large nuclei at high energies
For detailed discussion on each of these topics the reader is referred to the eRHIC Whitepaper 2002 [ 151 and the references therein. Nucleon Spin Studies in the Next Decade Since RHIC will be able to provide different species of hadrons for collision and since the electron and light hadron beams will be polarized, it should be a powerful tool for exploring the spin properties of nucleonic matter. This section and the rest of the article describe some of the important opportunities that would be afforded by eRHIC with polarized beams.
178
Measuring the polarized structure function, g , (x,@), of the proton and neutron using either deuteron or 3He beams would be one of the unique sets of measurements possible with eRHIC. The spin structure function at low x is interesting not only because of its relevance to the spin sum rules, but also because the pQCD analyses at NLO made very dramatic predictions for the low x behavior of the structure functions. These lowx predictions, based on the fits to existing data, indicate that below the present lowest measured x value (0.003), gp and g: become large and negative. The physical origin of this dramatic decrease is due to the large and positive polarized gluon distribution. Presently, uncertainties on gluon distributions are too large to draw definitive conclusions.
1. Y
L
Q2= 2 GeVZ Q2= 10 GeVZ Q2= 20 GeVZ
3 ir
.5
t
10
~ . . . ~ . . ~ " - ~ ~ . - ~ . ~ . ~ '. . - - ~ I
1oJ
103
102
1'1.111
in.*
Figure 3: Statistical accuracy of gp (x).This figure shows the statistical accuracy with 400 pb-' luminosity with the eFUIIC (- 1 week of data) assuming 250 GeV polarized protons and 10 GeV polarized electrons. The curves a the best fit to the world's data set evaluated at different Q'.
Figure 3 shows the dramatic behavior predicted from a pQCD analysis of the spin structure functions as a function of x for different values of @ (2,10,100 GeV2) [ 181. The projected eRHIC statistical uncertainties correspond to 400 pb-' luminosity for e - p scattering with an almost 471. acceptance detector such as ZEUS or HI in HERA at DESY. Clearly, the measurements possible with the eRHIC can easily distinguish between the QCD calculations at different scales and establish a pQCD
179
evolution of the spin structure function and the parton distribution in this kinematic region. Note that the luminosity used to estimate the statistical uncertainty, 400 pb-‘ is rather small for eRHIC, which is expected to provide -86 pb-’/day at full luminosity. In a typical eRHIC run of “one year 2one can expect ten times the statistical significance shown in Figure 3 . 66
The neutron spin structure function [19] could be measured by circulating polarized deuteron (p+n) or doubly charged helium (2p + n) in the eRHIC, resulting in e - d and e - He collisions. If the hadronic proton fragments are tagged, an exclusive measurement of the spin structure function of the neutron can be performed. This would allow an accurate measurement of the neutron spin structure function for the first time below a few times lo”. The variation of the spin structure function of the neutron will be very different from the proton case since at very small x, g f a n d gr should be approximately equal, while in the currently available kinematic regime g,P = -gr . An accurate measurement would be an essential test of pQCD at low x. Combined data on spin structure functions of the proton and the neutron will provide a precise test of the Bjorken sum rule. It is estimated that a statistical accuracy of the order of 1-2% [19] could be expected for such measurement in a rather short running time. Systematic uncertainties due to polarization measurements would be dominant in such measurement and would need careful attention. The present uncertainty (-5-10%) associated with the Bjorken sum rule is dominated by the lack of data at low x,after 30 years of experiments.
Assuming ten weeks of proton running a year,
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Polarized Gluon Distribution A G(x,Q*)
The polarized gluon distribution, AG(x,@), appears at NLO in the pQCD analysis of the spin structure function. To determine this function experimentally, one needs to analyze the world’s available data, assuming certain initial conditions for the polarized parton distributions, and then fit them to the data using the DGLAP evolution equations and the pQCD coefficient and splitting functions evaluated at NLO. The results of these analyses are a set of parton distribution functions, particularly the gluon polarization distribution function, AG(x,@), and its first moment. The first moment determined in one analysis [11 is:
AG(Q’
+ I .2+0.4+1.4
= lGeV ’) = 1 .O-0.3-0.2-0.5
The first uncertainties are statistical, the second are systematic experimental uncertainties and the last are uncertainties from the theoretical sources/inputs (e.g., the assumption of the functional form of the parton distribution function at the initial scale, the value of the strong interaction coupling constant as(Q2), and higher order corrections). The dominant uncertainties arise from the unmeasured low x region. These uncertainties can be reduced by at least a factor of -5 with data from eRHIC[ 181.
Polarized Gluon Distribution from Photon Gluon Fusion Process:
The other ways to determine the polarized gluon distribution involve semi-inclusive and inclusive measurement of processes where the gluon appears at leading order. The process that is most powerful in measuring the gluon polarization is Photon-Gluon-Fusion (PGF). The Feynman diagram for such a process is shown in Figure 4(a). The two quark lines in the final state may materialize as quark-jets if the interaction occurs at high enough energies (Di-Jet Analysis), or the jets may hadronize which can be observed as oppositely charged leading hadrons (High pt Hadron Track Analysis). The fundamental physics at the vertex is the same in each case. The experimental background in Photon Gluon Fusion measurements is shown in Figure 4(b). This is called the QCD Compton (QCD-C) diagram.
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Figure 4: Photon Gluon Fusion Process and QCD-Compton Process Photon Gluon Fusion process (left, a) is the principal means for accessing the polarized gluon distribution in the nucleon. The QCD - Compton process (right, b) that contributes as background.
This background can be reduced to less than 10% [20], by choosing the kinematics of the events appropriately. It is estimated that the data obtained at eRHIC for about a week of running, can determine the first moment of the polarized gluon distribution to a precision of (+/- 0.3). This method of determining the polarized gluon distribution function does not include assumptions about the functional form of the parton distribution function, as is the case for the NLO pQCD analysis. Therefore, the shape of the gluon distribution function is highly constrained. 0.8
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182 A variant of this method in which one takes the highest p-t hadron (leading hadron) from the jet was used to access gluon polarization by the HEFWES [21] and SMC[22] Collaborations in fixed target mode. This could also be done at eRHIC. One advantage of having two analyses is that they use different detection components in a collider detector. As such, the same quantity AG would be accessed with mutually exclusive detector systems. It was noted in such a study presented at a polarized HERA workshop [23] that about 60% of the events detected in the di-Jet analysis also showed up in a high-pt hadron track analysis. Thus, a “common” dataset can be analyzed in both ways, providing an important crosscheck for understanding uncertainties in different experimental systems. A pQCD analysis of g, (x) and the di-Jet asymmetries probe the same gluon distributions. If a combined analysis of the two is performed, it is expected that the gluon distribution could be determined with an overall smaller uncertainty. This type of analysis was carried out in detail for polarized HERA studies [24] and shows that such a global analysis does indeed reduce the uncertainties in the gluon distribution. A similar analysis for eRHIC [18] indicates that the effect of combined analyses reduces the uncertainty of the polarized gluon distribution by about a factor of -3 or more.
Photo-production In the photo-production limit, i.e. in the region where the intermediate photon virtuality is small, the e - p cross-section can be approximated as a product of a photon flux and an interaction cross section of the real photon with the proton. Measurements at H E M in this photoproduction region led to significant improvement in our knowledge of the structure of the photon and the proton, and a better understanding of the transition from a virtual to a real photon. At the Yale-eRHIC workshop many of these issues were explored assuming high-energy eRHIC polarized proton and electron beams. Only the most attractive and unique topics are discussed below. Other interesting topics such as
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open charm production, Drell-Yan processes, large pt photon and inelastic J / y production have been considered for polarized HERA studies [S]. The high luminosity at the eRHIC would provide for substantially better measurements over those possible at H E M . A detailed study was performed [25] of the physics with 1-2 jets or highpt tracks originating from photon gluon fusion diagrams. It shows that this would be a significant probe of the polarized gluon distribution, and would be sensitive to the polarized parton distributions inside the photon, Aqy. The measurements of the photon structure function would be unique, as well as fundamental and groundbreaking, without competition for a long time to come. The only comparable measurements of any significance would be made at a gamma-gamma collider now under consideration for construction towards the end of the next decade.
Photo-production and Drell-Hern-Gerasimov Spin Sum Rule The H1 and ZEUS detectors at DESY routinely take data using “electron taggers” situated in the beam pipe 6 - 44 meters away from the end of the detectors. They detect the scattered electrons from events having very low @ and scattering angles. If electron taggers were included in eRHIC, similar measurements could be performed [26]. The @ range of such measurements at eRHIC is estimated to be lo-*GeV2, in the center-of-mass region of 30-70 GeV. These measurements would be directly relevant to the Drell-Hearn-Gerasimov (DHG) spin sum rule, which relates the real photon-proton cross sections when the photon and proton are aligned and anti-aligned:
In this expression K is the magnetic moment of the proton and a is the electromagnetic fine structure constant, or coupling constant. This measurement can be made in the vrange of 600 GeV to few TeV. Although the contribution to the DHG sum rule from this region is small, the information from the eRHIC would be valuable. All other experimental measurements are performed in the v range of 10-20 GeV.
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It is necessary to extrapolate to high v to obtain the complete integral, and to do this it is necessary to assume a certain shape of the crosssection coming from the Regge type of behavior in this region. No other accelerator facility will be able to check this experimentally. It would be an important input for other measurements, presently underway around the world, to acquire these data points and constrain the extrapolations that are now based on unverifiable assumptions. Flavor Decomposition of Quark Spin Structure
Significant insights into the nucleon’s spin and flavor structure can be gained by using semi-inclusive scattering in which hadrons produced in a photon-quark reaction are detected in coincidence with the scattered lepton. Knowledge of the identity of these hadrons and their kinematic correlation with the momentum and energy of the virtual photon will allow separation of the contributions from the different quark flavors involved in the scattering event. In combination with polarized targets and beams, the spin contribution of the individual flavors can be determined as well. The spin contribution of the strange quarks is especially important; their role in nucleon structure is one of the most poorly understood aspects of the nucleon spin. In fixed target experiments, Lorentz boost of the beam produces the socalled current hadrons at forward angles in the laboratory frame. This region is difficult to instrument adequately, especially since the luminosity is increased to gain significant statistical accuracy. In addition, almost all of the fragments of the target nucleon are lost at small energies and large angles. Correlation of these target fragments with the hadrons directly produced would enhance the power of the semi-inclusive scattering technique. A polarized ion-electron collider has the ideal geometry to overcome the shortfalls of the fixed target experiment for semi-inclusive studies. The collider kinematics open up the final state into a large solid angle in the laboratory, which, using an appropriately designed detector, would allow for complete identification of the hadronic final state both in the current and target kinematic regions of fragmentation phase space. At eRHIC energies the current and target kinematics are well separated, thereby
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greatly improving the reliability of the application of the factorization theorem to the fragmentation processes. Parity Violating Structure Function gs
Because high @ measurements are possible with a high-energy eRHIC, it also will be possible to access the parity violating spin structure functions gSw+’-’ through the charged current interactions. The events in the case of W exchange are characterized by a large transverse momentum imbalance caused by the inability to detect neutrinos from the event. The charge of the W boson is dictated by the charge of the lepton beam used in the collision. Using the data from such charged current events, the parity violating spin structure functions, g5, are expressed as: A W= do: do:
-dog +do:
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(+/-)bgy +agT aFy(+/-)bF:
N-
gy Fy
where a and b, kinematic factors associated with the kinematic variable y and W and includes W(+’-). The spin structure functions, g5, are combinations of polarized u, c , d and S quark distributions.
+ ds Au g,”- = Au + Ac - Ad g,”’ = A d
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A Monte Carlo study, including the detector effects, showed that the measurement of the above asymmetry and the parity violating spin structure function is feasible at eRHIC. Figure 5(a) shows the asymmetry vs. log (x) and 5(b) shows the spin structure function g5 vs. log (x) calculated for W- with 2 fb-’luminosity [27]. Similar estimates exist for w‘ but would require measurements with a positron beam. The curves assume Gehrmann-Sterling spin structure functions for the values of the asymmetries and the spin structure functions, where it is assumed that FIwwould be measured well at HERA by the time this measurement is performed at eRHIC. The simulated data shown in the Fig. 5 are for @ > 225 GeV2. Standard assumptions used by HI collaboration regarding the scattered electrons for good detection were applied. The results could be obtained (including machine and detector inefficiencies) in a period of little over one month at the eRHIC luminosity.
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It is possible that only one or both of the electron-proton and positronproton collisions could be performed, depending on which design of the accelerator is finally chosen. In the linac-ring design, it would be impossible to have positron-proton collisions because there may not be a strong enough positron source. Even if this is the case, there is no foreseeable measurement of the parity violating spin structure function gSw-anywhere in the world. Therefore the eRHIC could provide a unique and important measurement that could otherwise be performed only if the HERA proton beam is polarized in the future. 0.35
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Figure 6: Statistical Uncertainty of the Asymmetry of A(W-) and g,(W-)Figure (a) is the projected statistical uncertainty on the asymmetry that can be measured with the EIC operating at high center-of mass energy. Figure (b) assumes that the structure function xF3 will be measured by the time the EIC takes data, the spin structure function g5 could be measured with this accuracy.
Hard Exclusive Deeply Inelastic Processes & Hadron Structure In recent past there has been a surge of theoretical and experimental studies of large @ exclusive processes: DES or Deep Exclusive Scattering including production of photons, and Deeply Virtual Compton Scattering, DVCS:
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Deeply Virtual Compton Scattering (DVCS) e +N
0
+ e + y + Baryon(N,A, Nz),
Deep Exclusive Scattering - DES e +N
+ e + Meson + Baryon(N,A, N n , A)
One also can consider the processes, where a few mesons, a baryon or an antibaryon are produced instead of a meson [ 3 6 ] . The GPDs, which describe DCVS and DES, can be qualitatively interpreted as the amplitudes for removing a parton with given quantum numbers from the nucleon and putting another quark back into the system with a different light-cone fraction at the same impact parameter. Therefore, they provide a new highly localized way to probe baryon wave function that is referred to as the “micro-surgery” of baryons. Depending on the process and Bjorken x, the dominant contribution originates from the quark or the gluon exchanges. These processes allow for an investigation of the parton structure of nucleons and a comparison to that of A - isobars, hyperons, and Nz . In addition, these processes provide a way to address a novel question about short-range parton correlations in nucleons. In addition, these processes address a number of key questions regarding high-energy QCD including the determination of the maximum transverse color separations in high-energy strong interactions that are dominated by pQCD, and how far down in x one can use linear QCD evolution equations.
A characteristic feature of these processes is that the final state contains a particle or even a few particles that have small momenta in the target rest frame. This is a challenging, though not impossible, task for the highenergy fixed target experiments. Detection of these reactions in the collider kinematics is expected to be easier than at fixed target kinematics, since the particles that are slow in the target rest frame fly along the beam direction. It is also much easier to select coherent interactions with nuclei. Detailed studies of various available generators for DVCS processes that could be measured in future at eRHIC are now underway.
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The status of the eRHIC project & prospects: The eRHIC recently appeared in the US DOE’S list of “28 must-do” scientific initiatives to be constructed or completed the next 20years[28]. It is expected that eRHIC will be presented formally to NSAC in the 2005/6 long-range planning exercise after which we will proceed to complete the Conceptual Design Zero (CDO) and formally start the project. The roughly estimated time-line puts the construction of eRHIC to begin between 20 10 and 20 12. Recently (March 2004) the electron beam design ideas along with the interaction region design concepts were presented to the experimental physics community in a Zeroth Design Report (ZDR) [17]. The collaboration of institutes that led this effort were BNL and MIT/Bates with close cooperation with DESY, Budker Institute and Jlab. The detector design studies are beginning with a view that a preliminary design consistent with the interaction region presented in the eRHIC ZDR might also be ready by the beginning of the NSAC long range review process in late 2005. Presently, the main design options for the eRHIC proposed in the ZDR are the following [171: 1. The Ring-Ring Design The electron ring will be about 1/3 the RHIC size and could sit north of the RHIC ring at IP12. A 10 GeV linac located inside the electron ring would feed the electron ring. 2. The Linac-Ring Design A 10 GeV energy recovery linac would be located inside or outside the RHIC ring and could collide with the RHIC hadron beam. Variants of this proposal include having a beam in the RHlC tunnel which would allow multiple interaction regions. The Ring-Ring Design seems to satisfy the design luminosity and polarization goals within a factor of two or smaller. This is presently considered as the main design line, and is the baseline from which future initiatives towards luminosity enhancement are being launched. One of the conditions for this design included a conservation, but ambitious R&D program using well-understood techniques. For the most part this
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proposal if approved could be built in a short time and without disrupting the existing RHIC annual running program. Hence the advantages of this design are: 1. Minimal R&D and short construction 2. Both electron and positron beams with high intensity and polarization possible The disadvantages include possibly only one interaction region allowed by the ring-ring geometry. The Linac Ring design is somewhat more ambitious in its luminosity reach, which would take longer for completion because of the amount of R&D that would be required. The design includes a 10 GeV energy recovery linac next to the RHIC ring. Having one interaction is trivial but if the second detector does not need high luminosity nor polarization, the electron beam could be transported to the next IP (RHIC Ips) and another detector could be situated there to collect unpolarized low luminosity data. Such a possibility is being explored with people interested in low x low Q2 physics. In a more ambitious layout out of the linac-ring version the 10 GeV energy recovery linac might sit inside the RHIC ring north of the STAR detector (for example), the electron beams could enter the RHIC tunnel on the east of STAR and westhorth of PHENIX and be in the tunnel to collide with the hadron beam of the RHIC at potentially four different IPS (IP10, IP12, IP2 and IP4). The advantages of linac ring design are several: 1. Larger luminosity 2. Multiple interaction regions (at higher costs) 3. Electron beam energy upgrades technically straight forward The disadvantage includes no possibility of positron beams, which might be useful for some electronweak physics and DVCS measurements. Other issues include an extended R&D program: including demonstration of energy recovery at the high intensities and energies of eRHIC, and the development of high intensity electron gun. A rough expectation is that this design is about 3-5 years behind the Ring-Ring version. Not knowing when the eRHIC funding for construction might get underway, it is prudent to pursue both options at this time. The linac as well as the ring versions, and make the design and technology decisions at a later time.
190 References
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
15.
16. 17. 18. 19. 20. 21. 22. 23. 24. 25 26. 27. 28
B. Adeva et al., Spin Muon Collaboration, PRD58 (1998) 12001 & 112002 El43 Collaboration, PRD58 (1998) 112003; E. W. Hughes & R. Voss, Ann. Rev. Nucl. Part. Phys. 49 (1999); P. L. Anthony et al., SLAC-El55 Collaboration, Phys. Rev. B493 (2000) 19 A. Airapetian et al, HERMES Collaboration, Phy. Lett. B442 (1 998) 484; ibid B404 (1997) 230 J. Ashman et al., Phys. Lett. B206 (1988) 364; ibidNucl. Phys. B328 (1989) 1 J. Ellis & R. L. Jaffe, Phys. Rev. D9 (1974) 1444; D10 (1974) 1669 A. De Roeck, Review of Physics at HERA, AIP Conf. Proc. 531 (2000) 122 V. W. Hughes & A. Deshpande, Nucl. Phys. B, Proc. Suppl., 79 (1999) 579, Proceedings of DIS99 Conference, DESY Zeuthen A. Deshpande, Proceedings Workshop on Polarized Protons at High EnergyAccelerator Challenges and Physics Opportunities, 1999, hep-ex/990805 1 J. Tojo et al., AGS-E950 Collaboration, PRL 89, 052302 (2002) G. Bunce et al. Ann. Rev. of Nucl. & Part. Sci. 50 (2000) 525-575 I. Alekseev et al., RHIC pC CNI Polarimeter, SPIN2002 AIP Conf. Proc. 675 (2003) 817 Proceedings of eRHIC workshop at Yale, BNL Report 52592 T. Roser et al., RHIC Spin Run 11, Proc. Of EPAC 2002 Conference See set of review articles: “Quark Gluon Plasma 2”, Ed. R. C. Hwa (U. of Oregon), World Scientific publishers; also, Phys. Rev. Focus http://focus.aps.org/story/v8/st34;K. Adcox et al., PHENIX collaboration, Phvs. Rev. Lett.. 88. (2002) 022301 A White Paper on eki-IIC, Editors; A. Deshpande, R. Milner & R. Venugopalan, BNL-Report No. 68933 L. Frankfurt and M. Strikman, Nucl. Phys. Proc. Supp. 79 (1999) 671 eRHIC ZDR, http://www.agsrhichome.bnl.gov/eRHIC/index.htmI A. Deshpande & V. W. Hughes, Proc. Of eRHIC Workshop at Yale, BNLReport-52592 A. Deshpande & V. W. Hughes and G. Igo & T. Sloan, BNL Report-52592 G. Radel & A. De Roeck, Proc. Of eRHIC Workshop at Yale, BNL-Report 52592 A. Airapetian et al., HERMES collaboration, Phys. Rev. Lett. 84 (2000) 2584 B. Adeva et al., SMC collaboration, accepted for publication PRD; hepex/04020 10 A. De Roeck and T. Gehrmann, Physics with Polarized Protons at HERA, DESY-97-233; hep-ph/971 I512 A. De Roeck, A. Deshpande, V.W.Hughes, J. Lichtenstadt, & G. Radel, Euro. Phys. J. C6 (1999) 121 M. Stratmann and W. Vogelsang, in BNL-Report 52592 and BNL-Report 68933 S. Bass and A. De Roeck paper on GDH spin sum rule J. Contreras and A. De Roeck in BNL-Report 52592 and BNL-Report 68933 Facilities for the Future of Science, A twenty-Year Outlook, http://www.sc.doe.gov/Sub/Facilities_for-future/facilities-future. htm
REMARKS AT THE SYMPOSIUM BANQUET HONORING VERNON HUGHES
D. ALLAN BROMLEY Sterling Professor of the Sciences
The New Haven Lawn Club November 12,2003
Miriam, Emlyn, Ladies and Gentlemen: We have come together to celebrate the life and accomplishments of a late husband, father and colleague, Vernon Hughes, and in memory of a remarkable man, scientist and educator. This evening I will not attempt to recite any details concerning Vernon’s lifelong love of fundamental physics and his continuous search for precision. Those of you who have spoken today and who will speak tomorrow are much better qualified than I am to do this. But Vernon and I shared over forty years in physics. I arrived at Yale just as Vernon was taking over the Chairmanship of the Physics Department, and on my first day here, Bob Beringer, who had brought Vernon to Yale from Pennsylvania, told me, “There have been some changes since you were hired; we have a new Chairman, Vernon Hughes, and in his first faculty meeting he told us that any expansion of nuclear physics at Yale would be over his dead body!” As you can imagine, we had some vigorous discussions on this matter, but we emerged from them friends and respected colleagues.
In my career, I have interacted with a great many scientists, both here and abroad, but I never met one with more energy or more dedication than Vernon. He spent a lot of time over 30,000 feet on his way to and from SLAC at Stanford, LAMPF at Los Alamos, Bates at MIT, CERN in Geneva, Fermilab and Brookhaven --- although in the case of Brookhaven he was lucky to get over 3,000 feet. 191
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He had a worldwide reputation as a leading figure, both in atomic physics and in particle physics, and his contributions to both were major. He will be much missed in the international science community. But he will be even more missed here at Yale, where his leadership, drive, and insistence on excellence contributed enormously to the spirit and reputation of our department. Let me thank all of you who have come, many from long distances, to pay tribute to Vernon’s memory. It is not our intention to have many speeches this evening, although many have volunteered. Vernon’s close friend and colleague over many years, Gisbert zu Putlitz, Professor and former Rector of the University of Heidelberg, was scheduled to join us, as noted in your program, but unfortunately a serious family illness has made that impossible. He has provided us with the text of the talk that he would have given and has asked that I read a short excerpt from it. I shall also read short messages from Professor Alexander Skrinsky, Director of Russia’s largest research laboratory in Novosibirsk and from Yuri Orlov, a good friend of both Vernon and Miriam. It is a pleasure for me now to be able to introduce you to The Honorable Jack Marburger. Former President of the State University of New York at Stony Brook, then Director of the Brookhaven National Laboratory and now Science Advisor to the President of the United States: Jack Marburger. Let me then introduce an old friend of Vernon’s and one of the world’s leading atomic physicists, Dan Kleppner of MIT: Dan Kleppner. Next 1 would call on Nick Samios, longtime Director of Brookhaven National Laboratory and an internationally recognized leader in elementary particle physics: Nick Samios. Finally, let me introduce Vernon’s son, of whom he was justifiably proud, now professor of physics at Caltech, where he is carrying on the Hughes tradition: Emlyn Hughes. That, ladies and gentlemen, concludes this evening’s activities but please let me again thank all of you for being here. We look forward to seeing as many of you as possible at 9:OO A.M. in the same location in the Sloane Physics Laboratory for the second day of this Symposium in Vernon’s honor.
VERNON WILLARD HUGHES A text prepared for the Banquet Speech at the symposium in honour of him by GISBERT ZU PUTLITZ
Dear Miriam, Dear Family, Dear Friends and Colleagues, Dear Students and Collaborators of Vernon Hughes!
In reflection of the different contributions to this symposium I was made again aware of the richness of the scientific life which Vernon Hughes has carried out over more than five decades, a time span, during which physics progressed from electrons and nucleons towards quarks and leptons and the unification of several of the known fundamental interactions. Vernon, educated in the Rabi school to address fundamental questions and tackle them both experimentally and theoretically, contributed to the stepwise development of physics ever on the forefront, e.g., are the charges of the electron and the proton equal, can the finestructure of triplett He and of positronium measured to a precision to test the newly developed quantum electro dynamics QED, or could there be an anisotropy of the inertial mass. Questions like these were answered by his experiments at a high level of precision. Moreover, new effects were observed and explained by Vernon like the first observation of a two quantum transition (in the microwave quadrupole transition in RbF) or the narrowing of spectral lines beyond the limit of the natural lifetime of states by selection of longer lived states through coherent observation. In 1960 muonium was discovered by Vernon and his students. Richard Prepost has given an account of this breakthrough and its implications. Ever refined experiments have been performed in collaborations with an international group of researchers, notably from the United States, Germany, England, Switzerland, China and Canada. Klaus Jungmann will report on these experiments on Saturday. The group carried the life of gypsies wandering from accelerator to an even better accelerator, from Nevis at
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Columbia to SREL at Newport News, to LAMPF at Los Alamos, SIN in Switzerland and the Rutherford Lab in the UK. Vernon’s contribution was not only to guide us younger colleagues to the best places to work world wide, he also pushed strongly for better muon sources, notably at LAMPF, an accelerator, where to the conceptual design he also significantly contributed. Our work at LAMPF deserves a special comment. The bolo tie with the Hopi overlay bear claw was in his case not an expression of world wide travel experience, which he had more than any of us, but rather because of a deep involvement in America’s past, the American Indian Culture, the Pueblo Indian people, where he was a well known friend and supporter over decades. It was my privilege and that of my family to share this experience with him and Inge and Miriam. In his scientific autobiography Vernon recalls the many physicists from Heidelberg after my first entry into his laboratory at Yale in 1967 and the continuing collaboration, satisfaction and fun in our common enterprises. In his autobiography he wrote: “Gisbert and I, as well as our families, have been close friends for over 30 years. Our collaboration and friendship have been among the better experiences in my life”. How true this is even more for me! Vernon was my colleague, also my scientific father and teacher, my closest scientific partner. I am full of gratitude for every day and year I could be together with him. Muonium was Vernon’s life atom, his personal possession, tied to his name forever. The most precise measurement was a stringent test of QED and searches for exotic interactions. And it served in a larger context as one of the important corner stones for Vernon’s last big enterprise, the g-2 experiment in Brookhaven, a very demanding, technically difficult set up with the world’s largest superconducting coils, an unprecedented precision in magnetic field technology, carried out by an international team of physicists and engineers and technicians. Vernon enjoyed the result of fifteen years of investment, of talent, skill and labor two years ago when the first number on (g-2) of the positive muon was published. The latest news you will hear from Ernst Sichtermann at this meeting, after Francis Farley has prepared the stage today already I could go on from here to many other areas of physics, particularly the long lasting effort of Vernon to explore the inside of nucleons and the role of quarks and gluons in nuclear spin and magnetism. Indeed, it is interesting and educational that the tools indispensable for this research grew out of Vernon’s early work in atomic physics and nuclear magnetic resonance, resulting in beams of polarized electrons and highly polarized
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proton targets. The highly successful research in this area will be presented by his son Emlyn and by his former student Gordon Cates. Vernon was in command of different fields in physics and could utilize them in a true interdisciplinary way like not many other physicists. Let me, at the end, make a few remarks about Vernon as a teacher. In the beginning of his time on the Yale faculty Vernon worked hard towards a modern curriculum. Later his incoming colleagues joined him. Vernon was a dedicated and convinced university man. In his opinion the best way to educate students was to let them participate in research, identify in a systematic way fundamental questions and invent experiments to find answers to these questions. Such spirit can be expressed not better than in the words of Karl Jaspers, the late Heidelberg philosopher, who wrote in his essay “The idea of the university” that the basic principle of the university is ‘(tosearch in the community of the teaching and the learning for truth”. Vernon lived to such a principle in the most honest way. We admire in Vernon Hughes a very gifted man whose leading role in physical research and his advice to us was inspiring and encouraging, critical but with active interest, open for discussions but also bringing problems and decisions to the point, often by his famous phrasing “Don’t you think we should . . .” . We mourn Vernon Hughes passing away from us so quickly. We embrace you, dear Miriam, and your family. We will miss Vernon very much, his devotion and inspiration. But let us be thankful also that we had the privilege and enjoyment to have Vernon with us for such a long time. He will live on in what we have inherited from him. We will carry on his style in science in the spirit he had taught us. Let it live on. It stands for the purest symbol of human dignity.
JOURNAL OP PAcsrCsG:NUCL~AR AND PARTICLE PHYSICS
I N s m OP PHYSICS pusllsrwo
PIk S0954-3899(03)55619-5
J. Phys. 0:NUCl. Pm. Phys. 29 (2003)181-188
Tests of CPT for muons Vernon W Hughes Yale University, New Haven. CT, USA
Received 30 October 2002 Published 17 December 2002 Online at stacks.iop.org/JPhysG/29/181
Abstract The status of tests of CPT invariance for muons is reviewed, These tests involve energy levels of muonium. The the g-values of p+ and p- and the *man earliest experiment of a clock comparison type is discussed. Invarianceof physical observables under the combined transformation of charge conjugation, parity inversion and time reversal is a findmental theorem in local quantum field theory [ 1,2]. However, in stringtheory, where the gravitational interaction together with the quantum electrodynamics,weak and strong interactions are unified, violation of CPT may occur [3]. The principal tests of CF'T invariance as given in the particle data book [4] are listed in table 1. These quantities are the properties of particles and antiparticles. which should be equal according to the CPT theorem. From a very natural viewpoint, the sensitivity of a test is taken to be the differencebetween a property of a particle and its antiparticledivided by the mean value of this property. Note that the sensitivity obtained from the measurement of the mass differencebetween KO and its antiparticle is the greatest, being In this shortpaper, I review the present status of tests of for muons and indicate some advances that are expected soon. In addition to the standard tests of the equality of a property for a particle and its antiparticle expressed as their difference divided by their mean value, tests of CPT invariance based on an extension of the standard model which allows for CPT violation are discussed. Also the earliest test in the spirit of this extended theory is recalled. As table 1 [4] shows the most sensitive test for CPT violation for muons involves their This result is g-values. Thecurrent value for (g(p+)- g(p-))/gaw, = -(2.6f 1.6) x provided by the last of the famous CERN 'g - 2' experiments [5]. A new g - 2 experiment at BNL has improved the precision of the CERN result by about a factor of 10. The approach of this experiment is basically the same as that of the CERN experiment. It involvesmeasurements of the difference frequency between the spin precession and orbital cyclotron frequencies of polarized muons in a magnetic ring. Figure 1 is a photograph of the muon storage ring at BNL.The ring diameteris 14 m, the B field is 1.5 T and the stored muons have a momentum of 3.1 GeV/c. A result for g(p+)from this experiment has been reported [6]:
wo
g(p+) = 2[1
+ 11659204 (8.6) x lo-"].
Data have been obtained for p- of comparable precision and are now being analysed. Hence soon the equality of g(p+)and g(p-) will be tested at the level of low9. 0954-3899/03/010181+30.00
0 2003 IOP Publishing Ltd Printed in the UK
Paper previously published in Journalof Physics G: Nuclear and Particle Physics Vol. 29 (2003) pp. 181-188 (www.iop.org/joumaJs.jphysg)and reproduced here courtesy of Institute of Physics Publishing.
196
181
197 V W Hughes
182
lbbk 1. Test of conservation laws. CPT in*
-0.002 f 0.007 <8 x CL = 90% <4
10-3
(-0.5 f 2.1) x lo-'' (2 f 8) x (-2.6 f 1.6) x (2 f 5) x lo4 (6 f 7) x (-0.6 f 1.8) x (0.1I f om)% (s = 1.2) (-0.5 0.4)% (0.8.1 1.2)%
*
<10-'8
(2.9 f 2.7) x (-0.8 f 3.1) x lo-' (-0.1 f 0.6)' <s x 10-7 (-9 f 9) x 10-1'
<s x (-2.6 f 2.9) x 10-3 (9 f 5 ) x 10-5 (-0.1 f 1.1) x lo-' 0.04 f 0.09 (-0.6 f 1.2) x lo-'
(S
= 1.6)
0.014 f 0.015 (1.1 2.7) x 10-4
*
0.02 f 0.18 +O.Ol f0.05 (-1 f 8) x -0.002 f 0.040
Some years ago Kostelecky and co-workers [7-101 developed an extension of the standard model based on spontaneous symmetry breaking of Lorentz and CFT symmetry in an underlying theory without gravity. There low-energy effective theory provides a theoretical basis for establishing quantitative bounds on CPT invariance. This extended theory is done in the context of conventional relativistic quantum mechanics and quantum field theory in four dimensions and retains the usual gauge structure and renormalizability. The Lorentz and CFT-violating additions to the standard model Lagrangian are highly suppressed to remain compatible with the established experimental bounds. The underlying viewpoint of this theory is that our present standard model represents a breakdown of physics at the Planck scale Characterized by the small perturbative parameter mp/mnad = Particle masses in the standard model are regarded as unknowns which should be calculable from a general theory of physics at the Planck scale. The postulated CPT-violating terms are regarded as a small perturbation of the standard model of similar magnitude. The theory with CPT and Lorentz violation involves spatial components in a celestial frame of reference, and, since the laboratory rotates with the earth, these celestial components vary with time, and, consequently the experimentally observed quantities may oscillate about
198 183
Tests of CPT for muons
Figure 1. The muon g - 2 storage ring at Brookhaven National Laboratory.
-2 -4 -6 -8
0 0.25 0.5 0.75
1
1.25 1.5 1.75 2 2.25 Magnetic Field (T)
Flgure 2. The Breit-Rabi energy level diagram of ground-statc muonium At high fields, the indicated transitions, U I and ~ u ~are , essentially muon spin flip mnsitions.
a mean value at the eaxth's sidereal frequency SL = 2n/23h - 56m. No such signal would be obtained from the standard model. For muons there are two observables whose time variation can be studied [ 111. These are the Zeeman energy levels in ground-state muonium and the spin precession frequency of polarized muons in a magnetic field. The most relevant terms in the extension of the standard model are those in the QED limit, involvingonly muons, electrons and photons. The additional terms in the Lorentz-violating Lagrangian lead to a modified Dirac equation and are given by
- b ~ $ e ~ ~-~iH$$euuB+e ' + ~ + kic$$eyuDp+e + iid$$tysy'DB+t. The lepton fields are denoted by Li = e-, p- and iD, = ia, - qA, where q =-]el. L = -a:$ey'+t
All terms are Lorentz violating, while a and b are CFT odd, and H, c and d are CPT even. As applied to muonium these CPT-violating terms shift the Zeeman energy levels in ground-state muonium (figure 2). The transition frequencies ulz and u~ observed in a strong magnetic field are changed by the amountsSulzand Suwdue to the new terms in the Lagrangian. These can be calculated using perturbation theory and relativistic two-fermion techniques.
199 V W Hughes
184
,.,..,..,.I,,..
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Time (Sidereal Days)
v,,(t)
-
+ bv,, sin(Znt+cp,)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Time (Sidereal Days)
Flgore 3. lWo yem of Qm on VIZ a d v34 are shown binoed versus sidereal time and l l for ~ a possible siausoidal variation.The amplitudes are consistent with zero.
For the strong field transitions dominantly only muon spin flip occurs so that these energy shifts are characterized by the muon parameters alone of the extended theory. This results in sw12
= -SUM = &/Jr
where 8; = br + d&m, + HG are laboratory frame parameters. High precision experiments on muonium can measure or set limits on the parameters of these symmetry-violating terms, which are sensitive at the Planck scale level [ 121. Predictions of the values of v12 and v~ from standard theory4ominantly the QED terms-require values for many atomic constants including m,, p, and Aw as well as the calculation of higher order QED radiative corrections. The relevant constants and calculations are not known to as high accuracy as the experimental determinations of w12 and WM.Indeed several of these constants-Aw and pr/pp-are obtained from the muonium experiment [ 121. Comparing predictions for w12 and ws (based on independent determinations of the required atomic constants) with the experimental results results in poor sensitivity to the non-standard model energy shifts Sv12 and SVM. The precision measurements of v12 and w~ taken in 1995 and 1996 are plotted as a function of a sidereal day, where 12 points at g 2 h intervals are plotted and the vertical scale is in hertz (figure 3). The data for 1112 and w j q were fit separately by the functions wij(t) + Swij(sin2rt + 4;)) where I is the time in sidereal days, and the fit parameters are (wij). the amplitude of the possible time variation 6vg and the phase &j (where no phase relation was assumed between v12 and v ~ ) . The amplitudes for 6 ~ and 1 S~V M are consistent with zero, -4 f 13 Hz and - 13 f 15 Hz, respectively. As stated above, the theory being tested requires S w l 2 = -SUM. A plot of u 1 2 - w ~ also indicates no variation with time at about the same level of sensitivity. Systematic errors were carefully considered.
200 185
Test8 of CPT for muons
Transformation from the laboratory frame quantity 5; to the non-rotating celestial frame quantities 6: is done taking into account the direction of the laboratory magnetic field at Los Alamos where the experiment was done relative to the equatorial axes P, 2) where 2 is oriented along the earth's rotational North pole. The data exhibit no variation with time within f 2 0 Hz with a l a confidence level and establish the limit
(x,
d
m < 20Hz
or 2 x
GeV.
Comparison of theory and experiment thus establishes a limit to the magnitude of the CPTviolating terms in the extended theory. The theory introduces many parameters in the overall Lagrangian for the standard model associated with the known particles. Comparison of the sensitivities established for these terms is not well established. For the muonium case considered above it is suggested that a figure of merit is
This figure of merit is consistent with the viewpoint that the standard theory including particle mass values will be understood from a more general theory at the Planck mass scale. The additional CPT/Lorentz violation terms to the standard theory should be characterized by a perturbation parameter of order of the new energy term divided by the known particle mass, just as the standard theory is characterized by the ratio of a particle mass to the Planck mass. For the muon magnetic moment, in addition to the test for CPT invariance that g(p+) = g(pL-),time variation of the anomalous precession frequency o, (the difference between spin and cyclotron frequencies) would be predicted by the theory with CPT/Lorentzviolating terms. The time-dependent term is [ 131 tioz*
= 26;* cos x
+ z@$*cos at + 6;* sin at)sin x
1
where b';* = f$ + m,dJo + E J K L H K L . The angle X is the geographic co-latitude at the experiment, i.e. the angle between the vertical direction of the laboratory frame and the earth's axis. From the oscillation amplitude of 0:' or o f a combination of model parameters can be extracted.
Since w. is proportional to the magnetic field the test has to be performed at constant B. Appropriate time-dependent data are available for both p+ and p- from the recent BNL experiment [6] and the analysis to search for time variation is in progress. We note finally that the parameter 6;. which is not tested in the muonium experiment, is bound at the level of lo-" GeV by the measurements of w$* and wz- at CEFW 151 and BNL [6]. One of the earliest measurements or searches for the sidereal time dependence of a physical observable arising from the rotation of the earth relative to celestial axes was done in the spirit of Mach's principle to search for an anisotropic component of the inertial mass of a body [ 14,151. The viewpoint of Mach's principle is that an inertial frame of reference is determined by the mass distribution in the universe, that the inertiol force on a body is the gravitational interaction of distant matter on the body and that the inertial mass of a body is determined by all the matter in the universe. With this view one can ask whether an anisotropic distribution of matter in the universe has the consequencethat inertial mass itself has a directional dependence or is anisotropic.
201 V W Hughes
186
centre of galaxy
Flgure 4. The principal axes for inertial mass tensor for a model of mass distribution with the galactic mnss Mo at the cenm of mass of the galnxy and the remaining mass of the universe isonopically distributed.
If the angular dependence is expressed as a series of Lagrandra polynomials, the simplest allowed anisotropic term is AM Am = - P ~ ( c o s ~ ) rv in which AM is an element of mass m the universe, 0 is the direction of acceleration with respect to the direction r' frombody m to body AM in which we take 0 < u < 1. More generally the usual Newtonian law is replaced by Fi = m;pj in which the mass mu is a symmetric tensor. If all the mass in our galaxy is located at the centre of mass of our galaxy (figure 4) and all the rest of the mass in the universe is distributed uniformly throughout all space, then the mass tensor can be diagonalized so that mrz = mo + Am where Am is due to the point mass Mo in our galaxy and m,~is due to the rest of the mass in the universe and z is the direction from m to MO. Cocconi and Salpeter suggested [16] that the effect of mass anisotropy on the atomic Zeeman effect may bemeasured with great sensitivity. An atomic electron with nonzero orbital angular momentum will move in different directions with respect to an external magnetic field in different substates, and, hence if the mass depends on the direction of motion, the energy difference between different magnetic substates will depend on the mass anisotropy. Thus for an atom with a single electron in a P-state figure 5 shows the &man energy levels and resonance lines for a P3/2 electron as perturbed by mass anisotropy. The contribution of the mass anisotropy to the energy of a particular magnetic substate is Am AE=-t~ ( C O eS )
mo
where t i s the mean kinetic energy of the electron and &(cos 0) is the expectation value of P~(COS 0) in a particular magnetic substate. There will be three different lines in the Zeeman spectrum. If the effect of mass anisotropy were too small to be resolved, the three lines would appear as a broadened line with an increased width 4 Am AW = --. 5 mo An experiment has been done to ldok for this effect [ 143. A much more sensitive search for Am based on the same idea can be made with the nuclear Zeeman effect because the nuclear mass energy is so large compared to the nuclear Zeeman energy. In particular For 8 'Li3 nucleus (f = 3/2) the nuclear structure according to the nuclear shell model can be considered as n single P3p proton moving in a central nuclear
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Flgum 5. &man energy levels and resonance lines for a 3 1 2 electron ns perturbed by mass nnisouopy. Tbe width of a n m a l &man line is noted as W.and the width of the unresolved lines associated with mass B"iS0uopy is W + (4/5) (Am/m)F. This figure is nlso applicable to the nuclear energy levels and reaonana lines for a nucleus with spin I = 3/2.
potential. The nuclear Zeeman effect is observed by nuclear magnetic resonance (NMR). Since the perturbed energy levels depend on the direction of the laboratorymagnetic field with respect to the direction to the centre of our galaxy, the energy levels change w i 9 the rotation of the earth. The standard frequency was taken to be a hydrogen maser using the H h f s and thus independent of the earth's rotation. This is a most sensitive way to search for a mass anisotropy Am. The first such experiment established A m / W < lo-*' obtained by setting v=o.
Recent high precision measurements [ 171have increased the sensitivity by about a factor of lo5 to 10'. These measurements are now considered as clock comparison experiments which test Lorentz invariance. I am grateful to have been asked to contribute a paper in honour of Albert0 Sirlin. His extensive theoretical work on the electroweak interaction has established a very high standard of excellence and has been most influential on experimental physics.
Acknowledgment This work was supported in part by the US Department of Energy.
References [I] Lee T D 198 IPam'cle Physics and Inrmduction to Field mory (New York: H a n v o o d Academic) [2] Weinberg S 199.5 Ihe Quantum Theory ofFields vol I (Cambridge: Cambridge University Press) 131 Omen B 1999 The Eleganr Universe (New York:Rnndom House) 141 Bartcls J. Haidt D and Zicbichi A (ed)20 Review of panicle properties The E m Phys. J. C IS 1-4 (51 Bailey J er ol 1979 Nucl. Phys. B 150 1
203 188
[6] Bennett 0 W er a1 2002 Phys. Rev. Len. 89 101804.1 [7] Kostelecw V A and Potting R 1991 N u d Phys. B 359 545 Kostelecks. V A and Potting R 19% Phys. Len B 381 89 [8] C o W y D and Kostelecw V A 1997 Phys. Rev. D 55 6760 Colladay D and Kostelecw V A 1998 Phys. Rev. D 58 116002 191 Kosteleckf V A (ed)1999 CPTund Lorem Symmmy (Singapon: World .$cientific) [ 101 Kosteleckj, V A (4)2001 CPTund Lorenh Symmetry If (Singapore: World Scientific) [Ill Bluhm R, Kostdecw V A and LaneC D2OOO Phys. Rev. Len. 84 1098 1121 Hughes V W erul2001 Phys. Rex Len. 87 111804-1 [ 131 Deile M er a f 2001 in [lo] p 305 [ 141 HuV W, Robinson H 0 and Beluan-LopezV 1960 Phys. Rev. Len. 4 504 Drever R W P 1961 Phil. Mag. 6 683 [ 151 Hughes V W 1964 Gmvirarion and Refativity (New York Benjamin) p 106 [ 161 CoccoN 0 and Salpeter E E 1958 Nuovo Cimento 10 646 Cocconi 0 and Salpeter E E 1960 Phys. Rev. Len. 4 176 [ 171 Restage J D er af 1985 Phys. Rev. Len. 54 2387 Berglund C I er of 1995 Phys. Rev. Lerr. 75 1879
V W Hughes
VERNON WILLARD HUGHES May 28, 1921-March 25, 2003 BY ROBERT K. ADAIR
V
ERNON WILLARD HUGHES, Sterling
Professor Emeritus and senior research associate at Yale University, died on March 25, 2003, at the age of 81 at Yale-New Haven Hospital from medical complications after an operation for an aneurysm, Hughes began research in physics in 1942 when he worked on radar at the MIT Radiation Laboratory. During his terminal stay in the hospital, he wrote letters of recommendation for a postdoc working with him on a major experiment. Thus, Hughes worked at physics researchlargely at the cutting edge of atomic, nuclear, and elementary particle physics-for 61 years. Born in Kankakce, Illinois, on May 28, 1921, Vernon Hughes was raised in the Morningside Heights sector of New York City by his mother, Jean Parr Hughes,who was a librarian at Teachers College of Columbia University. His father, Willard Vernon Hughes, died when Vernon was three years old. As a New York City boy of his time Hughes played stickball in the streets-he later told his sons Gareth and Emlyn that he had been a very good stickball player-and he played tennis on the local Columbia University courts, His sons recounted with amused affection that when he played tennis against them in later years, he gave no quarter. 204
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Entering Columbia in 1938 as a freshman pre-law student with the intention, he wrote, “of doing good things for the world,” Hughes took enough time from his studies to play on the tennis team and work on the school newspaper, Columbia Spector. He wrote later that while he found some of the Columbia core courses in humanities and contemporary civilization valuable, the mathematics and physics courses were more interesting to him, and he decided to direct his efforts toward mathematics, physics, and engineering. Growing up in modest circumstances during the Great Depression years of the 19.30~~ he tells of his concerns about a choice of schooling that would result in a job after college. Gfter completing an especially heavy academic schedule with excellent grades in only three years and winning the Van Buren Math Prize, he graduated from Columbia as a physics major in the spring of 1941just after his twentieth birthday. Looking for a new environment, Hughes enrolled as a graduate student at Caltech that fall. A picture from that time shows Hughes atop Mt. San Gorgonio in California along with fellow students Pief Panofsky, Bill Eberhardt, and Ed Deeds. Hughes writes that at Caltech he found Smythe’s course in electricity and magnetism, which consisted largely of blackboard presentations by the students of problems assigned from Smythe’s book, especially challenging, but he wrote that the acceptance of his work was helped by his “being an acceptable tennis partner for Professor Smythe.” After receiving his M.Sc. degree from Caltech in 1942, with the country at war, Hughes went back east to work on radar at the MIT Radiation Laboratory. Here he joined a group directed by Burton Chance that was especially concerned with accurate time measurements-at the microsecond level-of the reflected radar pulse and thus target range
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information. He was later coauthor with Chance and others of the Radiation Laboratory volume titled Waveforms (1949). After World War 11, in January 1946, Hughes returned to Columbia for graduate study with the goal, he writes, of doing his thesis work with I. I. Rabi. While he found the theoretical work of Yukawa on nonlocal field theories and Selig Hecht’s biophysical investigations of vision interesting, he settled on a research topic in molecular beams with Rabi. A decade later Rabi wrote that Hughes “was one of the best students I ever had.” With molecular-beam electronic-resonance apparatus that he “built from scratch” Hughes and Lou Grabner measured nuclear electric quadrupole interactions. His thesis for the Ph.D. degree he received in 1950 was based on those measurements. In the course of that work he and Grabner discovered the first clear two-photon transition in their molecular beam electric resonance studies, and Hughes worked out the theory. Hughes commented later that “at that time at Columbia the theoretical course work was extensive and one was expected to handle the theory relevant to one’s experiment.” After receiving his PhD in the fall of 1950 Vernon Hughes married Inge Michaelson. German-born Inge had left Germany in 1938 with her family as refugees from the Nazi racial laws. Vernon had met Inge when she was a student in a summer class in mathematics he taught. Inge, who had just graduated from Barnard, took the course in preparation for graduate work in biology. Later Inge received her Ph.D. in biology from the University of Pennsylvania. Their son Gareth was born in 1955 and their son Emlyn in 1960. After Inge’s death in 19’79Hughes married Miriam Kartch, who teaches at the Mannes College of Music. He had known Miriam when he was a student at Columbia. They first met in 1947 when Miriam was assigned as the teacher when the
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26-yearsld Hughes enrolled as a beginning piano student. He is survived by Miriam, his sons, and four grandchildren. During a two-year period as a postdoc at Columbia, Hughes, always deeply interested in fundamental matters, found by measuring deflections in an atomic beam that the electron-proton charge difference, Iq,q I < 10-l3 e, and the P neutron charge, Iq,l < e, supportmg the view that e w a s indeed a fundamental quantity. Thirty years later, with his students, he reduced the limits by a factor of lo6 using atomic measures of these quantities though bulk measures on the charge of gases were by then somewhat more sensitive. In 1953 Hughes left Columbia for a position at the University of Pennsylvania and then joined the Yale faculty in 1955. While much of Hughes’s work w a s on the properties of atoms, he regarded atoms primarily as laboratories for the study of the fundamentals of electromagnetism and preferred to consider simple atoms ”where the theory was adequate.” Thus he concentrated on studies of the helium atom, on the electron-positron atom, positronium, the simplest of atoms, and then-arguably his most nearly unique contribution to physics-on muonium, the atom made up of a muon and an electron. His extensive work on helium from 1950 to 1980,largely using atomic beam methods where Hughes and his colleagues did the experiments and Hughes the theoretical calculations, provided rigorous tests of modern quantum electrodynamics (QED) for two-electron systems and a precise value of a,the fundamentally important dimensionless ratio of the square of the electric charge to the product of Planck’s constant and the velocity of light. With Martin Deutsch discovered the electron-positron atom, positronium, in 1952,Hughes began studies of that simplest of atoms with C. S. Wu, again emphasizing connec-
208
tions with QED. At Columbia, with Wu, he made a measurement of Av, the interval between the states l%, to l%&, that was somewhat more precise than Deutsch’s pioneering measurement, His later high-precision measurements at Yale gave a result about three standard deviations from theory, a discrepancy that has not yet been resolved. After the discovery of parity nonconservation by Wu, Ambler, and others, Hughes withJack Greenberg measured the longitudinal polarization of the electrons emitted from Co60 as a function of their momentum using Mott scattering as an analyzer and found that the polarization was accurately proportional to the electron velocity, p, a result in accord with the Yang-Lee model of weak interactions. Hughes noted that it was his work on this experiment that kindled his interest over two decades in the design of polarized electron beams. H e focused his efforts to create a polarized electron source on the photoionization of a polarized beam of alkali atoms, especially 39Kand “I;i. Ten years of work culminated in 1972 with a source that produced a 1,5ps pulse of a 20 pA current of polarized electrons. That source was then used to produce a high-energy polarized electron beam at the Stanford linear accelerator. About 1960, elaborating on a suggestion by Cocconi and Salpeter, Hughes used nuclear magnetic resonance methods to study the isotropy of mass. Mach considered that the mass of an object should derive from the distribution of distant matter-far-off galaxies-and thus its inertial mass might be slightly different when accelerated in different directions even as the mass of the universe might be slightly anisotropic. Hughes set that anisotropy for the psl2 proton outside of the closed shell in the lithium nucleus as Am/m < lo-**, which from Mach’s principle meant that the Universe was isotropic to about one part in lo2*.
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Hughes with his colleagues McColm, Prepost, and Ziock “discovered”the electron-muon atom named muonium, M, in 1960 by observing its characteristic Larmor precession frequency. His following 40 years of experimentation on that atom, concentrating on ever more accurate measurements of the 13S, to llS,interval, Av, the Lamb shift in the 11x2 state, and the 1s-2stransition, verified to high precision that the muon is indeed a “heavy electron,” gave us new avenues into the experimental study of quantum electrodynamics and created a tool to probe the highest energy scales of elementary particle physics. Aside from this “conventional” physics Hughes established important limits on the muonium-antimuonium transition rate, again testing fundamental concepts. In 1967 Gisbert Zu Putlitz, later rector at Heidelberg, who had just completed his Ph.D. at Heidelberg came to Yale and worked w i t h Hughes for nearly two years before returning to Germany. Hughes wrote that their collaboration, largely on muonium physics, and their friendship and personal association, which continued until Hughes’s death 35 years later, was “among the better experiences in my life.” Hughes also wrote of the importance of his close association with Val Telegdi to the muon work that engaged them both in the decade beginning in the late 1960s. In his atomic physics experiments Hughes worked unceasingly to increase the accuracy of his measurements. Quantities such as the magnetic moment of electrons and muons stem primarily from the elementary electric charges of these elements as observed statically. Then there are “corrections” that represent effects at very small distances or complementarily at very high energies. These modifications to the static result connect the simple leptons with all other particles, including the strongly interacting quarks. Thus, the measurements of very small corrections to the simple
210
model of leptons approaches very much the same kind of physics as cruder measurements of the interactions of the leptons at very high energies. Hughes looked in both directions. A colleague famous for an important breakthrough once said admiringly that Vernon Hughes was the only physicist he ever knew who would mount an experiment to improve the precision of some fundamental measure by a factor of two.But Hughes’s attack went on unceasingly, with improvements by two, and two, and two, and two,which added up to new insights. As early as 1958, Hughes, along with Wheeler, Beringer, and Gluckstern at Yale, began a serious design study of a proton linear accelerator “meson factory.” This machine was meant to place a 1 mA beam of 800 MeV protons on a target to produce meson and muon fluxes a thousand times greater than those then available. Such a meson factory, the Los Alamos Meson Physics Facility, based largely on the Yale design was built, but not at Yale.(Hughes later wrote that Rabi advised him: “If you can’t beat them, join ‘em. . . Its a wonderful place to spend the summers with your family.” Indeed Hughes did s t a r t going to Los Alamos in the mid1960s to help develop the muon facility there.) Those summers were wonderful and led to Hughes’s longtime friendship with the San Idlefonso Indians neighboring Los Alamos and a special appreciation of their remarkable art-especially their pottery and sand paintings. With his wife, Inge (and after Inge’s death and his remarriage, with Miriam), Hughes amassed a collection of that art that gave the comfortable living rooms of their home in New Haven some of the ambience of a charming museum set. Hughes’s close association with Los A m o s and the Los Alamos Meson Physics Facility (LAMPF) continued until
.
21 1
1996, when LAMPF was shut down. During that time his major program directed toward the properties of muonic atoms was conducted there. In particular, Hughes’s group measured Avand the ratio of the magnetic moments of the muon and proton, pp/pp,with ever increasing accuracy. As he did always and everywhere, Hughes worked intensively at LAMPF. In 1988 the director of LAMPF wrote an unsolicited letter to the Yale department chair saying that Hughes, then 67 years old, “was still absorbed in physics, indifferent to fashion, and is a true inspiration to younger scientists. . . He insists on taking the 4:OO AM shift [the experiments on accelerators always ran three shifts, 24 hours a day, every day] so that he can still put in a full working day in addition to taking a shift.” Hughes’s development of polarized electron ion sources was fundamental to the use of polarized electrons in highenergy accelerators beginning in 1963, when he developed the first polarized source for the Stanford two-mile accelerator. That vision led to the observation of parity nonconservation in deep inelastic electron scattering and in electron-positron scattering and to measurements of the spindependent structure of the proton. After the groundbreaking Stanford linear accelerator experiment led by Friedman, Kendall, and Taylor identified partons, with quark-like properties, as point-like physical constituents of nucleons, Hughes became deeply interested in measuring the spindependent structure of the proton. Thus, he began in 1972, with Peter Schiiler, Kunita Kondo and his group from the University of Tsukuba, and a Stanford linear accelerator (SLAG) group led by Dave Coward, measurements of the deep scattering of polarized electrons by polarized protons. The large asymmetrieselectrons and protons with their spins opposed scattered more than those with their spins parallel-that were mea-
.
212
sured over the next five years supported the general quarkparton model of the nucleon. Following a suggestion by Charles Prescott, the group also investigated the parity-violating scattering of longitudinally polarized electrons by unpolarized protons. Initial measurements, using the Yale polarized electron source, showed no effects at a sensitivity level of lW3. However, with the development at SLAC of a higher-intensity polarized electron source, the group did see effects at a level of that were in accord with the electro-weak theory of Glashow, Salam, and Weinberg. Hughes had hoped to continue work with polarized electrons and protons at SLAC and his initial proposals were received positively. SLAC decided, however, to go in other directions at that time. His disappointment was ameliorated somewhat when 10 years later, SLAC resumed measurements of polarized electron scattering with a very successful program led by Vernon’s son, Emlyn Hughes (now a professor at Caltech). In spite of the termination of the SLAC program Hughes was still deeply interested in polarized lepton-nucleon scattering; he was therefore pleased to accept an invitation by Erwin Gabathuler of Liverpool for the Yale group to join the European Muon Collaboration (EMC) at the European Organization for Nuclear Research (CERN). The collaboration had previously discovered a change in the nuclear structure function when the nucleon is in a nucleus (the EMC effect) and most of the EMC collaborators were much more interested in that effect than in polarized muon-nucleon scattering. With the Liverpool group and the Lancaster group lead by Sloan,Hughes with his Yale collaborators directed a portion of EMC efforts toward polarized muon-nucleon scattering in a kinematic region that had not been explored by the previous SLAC experiments.
213
The results of that work were very interesting. It was known that the spin of the nucleons was generated by the spins of the constituent quarks together with the orbital angular momentum of the neutral charged gluons coupled to the quarks. The charged muons interacted only with the charged quarks and thus measured the portion of the nucleon spin held by the quarks. That portion turned out to be much lower than expected (by the Ellis-Jaffe sum rule); the quarks carry only a small portion of the nucleon spin-a result called the “spin crisis” or “spin puzzle.” After this result a new group was formed in 1987 (the spin muon collaboration), with Vernon Hughes elected as spokesperson. That group, with about 150 physicists from European, American, and Japanese institutes, as well as strong internal CERN contributions, began taking data in 1992 and continued through 1996. The results were in very good agreement with general QCD (quantum chromodynamics) models (the Bjorken sum rule) but strongly violated the conventional view of the nucleon quark structure (the EllisJaffe sum rule) supporting, with more extensive and more accurate data, the previous spin-puzzle results. Hughes continued to work on designs for more extensive and powerful experiments and was planning a trip to Europe to meet with his collaborators at his death. Over about the same time span Hughes conceived of and led an experiment to improve the measurement of magnetic moment of the muon by a large factor. The deviation of the magnetic moment, g, from the elementary Dirac value of 2, in natural units, thus (g-2)p,serves as a benchmark for the testing of new ideas in particle physics. The precession rate of muons moving in a magnetic field is proportional to the product of the field and (g-2lp.Hence, an accurate measure of the anomalous magnetic moment
214
of the muon, (g-2)p,requires very precise determinations of both the magnetic field and the precession frequency. A previous major experiment at CERN had established the value of (g-2)pto the remarkable accuracy of 7 ppm (parts per million). That value was in agreement with the theoretical value-also the product of a massive effortthat was considered accurate to 8 ppm, where much of the error reflected uncertainties in the hadron physics contribution to the moment. Thus, that nominal theoretical uncertainty could be reduced by improved hadron experiments, in particular by improved measurements of the production of hadrons in high-energy positron-electron collisions. A result as accurate as that reached at CERN, and in agreement with theore tical results calculated assuming conventional physics, already served to exclude many interesting and plausible extensions of that conventional physics. Hughes understood that a significantly better measurement of (g-2)pcould place even more rigorous limits to the character of the extensions of the conventional models of elementary particles that were required and that a better experiment could be conducted at the Brookhaven National Laboratory AGS accelerator, which by 1980 generated beam intensities, and then muon fluxes, superior to that available at CERN. Hence, beginning in 1982 Hughes began serious studies of methods that might lead to a more accurate measurement. Then in 1984 he began to assemble a group of experienced physicists, many with leading roles in the previous CERN experiment, who were prepared to design and conduct the experiment. Aside from significant contributions from the Brookhaven National Laboratory and CERN,major contributions were made by groups from KEK in Japan and the Budker Institute for Nuclear Physics in Novosibirsk.
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A highly accurate measurement made at Novosibirsk of the hadron production crosssection by electron-positron collisions was of major importance, because that measurement served to accurately set the hadron contribution to the anomalous moment and thus significantly reduced the theoretical uncertainty. By 2002 the collaboration had reached an accuracy of better than 0.7 ppm and the theoretical calculations were accurate to about the same level. The values differed but not quite beyond chance. Somewhat more accurate results were still possible, but as of 2003 government fiscal constraints on Brookhaven physics seemed to have precluded further measurements. At his death Hughes (at 81) was still playing a major role in two international groups, one working on the large muon (g-2), experiment at Brookhaven and another on the design of an experimental program to further study nucleon spin constituents and the problem with those constituents that he had been instrumental in uncovering. Although he spent his youth in physics very much in the trenches building the equipment for his thesis work “from scratch,” his early years at Columbia, Pennsylvania, and Yale usually found him in the laboratory or on the accelerator floor with his hands on his apparatus. In the course of time Hughes found himself occupied more with the tasks of organization and leadership. Over the decades Hughes had worked on the frontiers of physics, and the complexities of experiments had increased greatly. Along with that increased complexity came increased monetary costs and, sociologically most important, a significant increase in the scientific effort required to conduct an experiment. While Hughes’s early experiments involved two, three, and four scientists with a few technicians and typically one or two scientist-years of effort,
216
there are 60 authors on the final Brookhaven paper, representing 11 laboratories from 4 different countries. The paper, describing an effort of more than 100 scientist-years of work, was published 20 years after Hughes had begun working on the problem. And there were 142 authors from 24 institutions from 15 countries on the last SMC publication. With so many participants in experiments that are so complex, the organization of effort is important and only a physicist who is knowledgeable about all experiment details and has the trust and confidence of everyone can exercise leadership. Vernon Hughes was special in his broad knowledge of the experiment and singular in how he held the confidence of his colleagues. This confidence and special breadth led Hughes into leadership positions. (He was usually a senior spokesman for the experimental groups he worked with.) In those positions Hughes often represented his collaborations in the presentations before laboratory program committees, the committees that effectively accepted or rejected a proposed experiment. With his energy and interests-both deep and broad-he was usually involved in several rather different programs, and the program committees were often concerned with the division of his time; committee members wondered whether Hughes was really going to work personally on the experiment he was advocating. With this concern in mind, when Hughes appeared before a European committee addressing a proposal to support an experiment on deep electron-proton scattering (which would be supported by the U.S, Department of Energy budget for elementary particle physics) and knowing that Hughes had heavy commitments on the (g-2), experiment at Brookhaven (also supported by the U. S . Department of Energy elementary particle physics budget), the committee chair asked Hughes what portion of his time would he spend on the
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experiment he was advocating. Hughes answered, “50 percent,” noting that he would spend the other 50 percent on the Brookhaven experiment. One of the committee members then said, ”but what about your LAMPF experimental programs at Los Alamos?” Hughes answered, slightly affronted, “But that’s nuclear physics!” (LAMPFwas supported by the Department of Energy nuclear physics division). But all was well; the committee recognized that all his life Hughes had worked at a 150 percent level. While his researches in physics took the highest priority, Hughes was ever sensitive to the goals of his youth, to do “good things for the world,” and lent his weight and substance to social goals that he found meritorious; thus, Hughes worked hard and effectively on administrative tasks that he found worthwhile. With the impact of the radar that Hughes worked on at the MIT Radiation Laboratory, which was sometimes said to have won World War 11, and the neutron chain reaction bombs, which could be said to have ended the war, the level of financial support of research in physics and other science at major universities increased so greatly as to change forever those universities. The newly configured institutions became -research universities,” with research money from the government that reached a level near or in excess of the instruction budget. While Yale continued to emphasize undergraduate education (at Yale College) more than many other universities, it had to follow other schools in shifting its institutional priorities sharply toward scientific research and graduate education. With its historic emphasis on the humanities, not science, Yale was not well placed to make that change in general, and not well set in physics, in particular. In the late 1950s Yale president Whitney Griswold became aware that in an era of great physics, Yale was not
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playing a major role and asked J. Robert Oppenheimer, then director of the Institute for Advanced Study at Princeton, to review the department and report back to him and the corporation. Oppenheimer’s critical report w a s devastating, perhaps to the point of being unfair. Yale had considerable strength in experimental nuclear physics-with Schultz, Beringer, and Bockelman, and the strong effort in nuclear theory by Gregory Breit-but by 1958 many of the more fundamental questions in nuclear physics had been answered, and nuclear physics itself was sliding behind the frontiers of physics. Though the low-temperature work of C. T. Lane and Henry Fairbank was also first rate, Oppenheimer recognized only the work of Hughes as lying at the cutting edge of physics. Hence, at Oppenheimer’s urging Hughes was appointed department chair in 1962 and with special resources from the university was given the task of bringing the Yale department into the first ranks. Hughes served in that office for the university’s statutory limit of two terms, or six years. During that tenure he moved aggressively and effectively, bringing in many new faculty members and new programs while constraining some of the roles of older faculty members. Hughes’s changes had consequences: In the decade of 1961-70 the average number of students receiving the Ph.D. in physics per year at Yale rose to about 20, giving Yale then by that measure the country’s eighth largest graduate school in physics. Of course, the changes that Hughes instituted did not come without costs in personal relations. Hughes was perhaps Gregory Breit’s best friend among the senior faculty, and they had established a tradition of having lunch together each Saturday at a popular campus restaurant. Greatly displeased by Hughes’s actions as chair in taking theoretical physics outside of Breit’s personal control and broadening its intellectual base, Breit stopped speaking to Vernon
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for a time, but as Hughes later told a friend bemusedly, they continued to meet Saturdays for a silent lunch. Hughes’s very rare clashes with his peers were always without personal animus on his part. While he strongly disagreed with Breit on department matters, his deep respect for Breit’s accomplishments in physics was untouched. In 1999, when Hughes was 78, he organized a symposium at Yale on Gregory Breit’s lifework in physics to mark the 100th anniversary of Breit’s birth. Hughes also contributed administratively by serving on the Board of Trustees of Associated Universities, Inc., for more than 40 years, from 1962 until his death. An independent organization created by scientists and administrators from nine northeastern universities, including Yale, Associated Universities established Brookhaven National Laboratory in 1947 and the National Radio Astronomy Observatory 10 years later. Hughes was elected to the National Academy of Sciences in 1967. In 1978 he was awarded the Davisson-Germer Prize in Atomic Physics and in 1990 the Tom R. Bonner Prize in Nuclear Physics, both from the American Physical Society.
SELECTED BIBLIOGRAPHY 1949
With others. Waveforms. MIT Radiation Laboratory Series, vol. 19. New York: McGraw-Hill. 1950
With L. Grabner. The radiofrequency spectrum of Rb85F and Rb87F by the electric resonance method. Phys. Rev. 79314. 1951
With L. Grabner. Further evidence for a two quantum transition in molecular spectroscopy. Phys. Rev. 82:561. 1954
With G. Weinreich. Hyperfiie structure of helium3 in the metastable triplet state. Phys. Rev. 95:1451-59. 1955
With S. Marder and C. S. Wu. Static magnetic field quenching of the orthopositronium decays: angular distribution effect. Phys. Rev. 98:1840. 1957
Experimental limit for electron-proton charge difference. Phys. Rev. 105:170-81. 1960
With H. G. Robinson and V. Beltran-Lopez. Upper limit for the anisotropy of inertial mass from nuclear resonance experiments. Phys. Rev. Lett. 434244. With J. S. Greenberg, P. P. Malone, and R. L. Gluckstern. Mott scattering analysis of longitudinal polarization of electrons from Corn.Phys. Rev. 120:1593-1405. 1963
With others. A very high intensity proton linear accelerator as a meson factory. In International conference on Sector-Focused cycle220
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trons and Meson Factories, ed. F. T. Howard, p. 365. Geneva: N. Vog t-Nielson. 1966 Muonium. Annu. Rev. Nucl. Sci. 16:445-70. 1968 With others. Muonium-antimuoniumconversion. Phys. Rev. Lett. 21:170912. 1970 With S. A. Lewis and F. M. J. Pichanick. Experiments on the 23P state of helium. 11. Measurements of the Zeeman effect. Phys. Rev. A 2:86-101. 1976 With B. E. Zundell. Precise measurement of electronic gj value of helium, gj(4He,29S,).Phys. Rev. Lett. 59A381-82. 1980 With others. First observation of the ground-state hyperfine structure resonance of the muonic helium atom. Phys. Rev. Lett, 45:148386. 1984 With M. W. Ritter, P. 0. Egan, and K. A. Woodle. Precision determination of the hyperfine-structure interval in the ground state of positronium. V. Phys. Rev. A 30:1331-38.
1987 With others. First observation of a negative muon ion produced by electron capture in a beam foil. Phys. Rev. A 35:3172. 1990 With others. Measurement of parity violation in the elastic scattering of polarized electrons from 12C. Phys. Rev. Lett. 65:69497.
222 1992
With others. Muon production of J/w and the gluon distribution of the nucleon. 2.Phys. C 56:21-28. 1994 With others. Measurement of the polarization of a high energy muon beam. N u d . Instnun. Methods A349:34. 1997
With others. Next to leading order QCD analysis of the spin structure function gl. Phys. Rev. D 58112002-1-14. 1999
With others. High precision measurement of the muonium ground state hyperfine structure and the muon magnetic moment. Phys. Rev. Lett. 82711. 2000
Various researches in physics. Ann u. Rev. Nucl. Part. Sci. 5O:i-xxxvii.
2001 With others. Test of CPT and Lorentz invariance from muonium spectroscopy. Phys. Rev. Lett. 87:I 118041-6.
2002 With others. Measurement of the positive muon anomalous magnetic moment to 0.7 ppm. Phys. Rev. Lett. 89:101804-1-6.
Publication List Vernon W. Hughes
1. Ultrasonic Delay Lines, I. B. Huntington, A. G. Emslie, and V. W. Hughes of the Franklin Inst. 245, 1-23 (1948). 2. Generation of Triangular Waveforms, V. W. Hughes and R. M. Walker, pp. 254-288; Pulse-Recurrence-Frequency Division. A. H. Frederick, V. W. Hughes and B. F. MacNichol, Jr., pp. 567-601; Electrical Delay Lines, V. W. Hughes, pp. 730-750; Supersonic Delay Device, V. W. Hughes and H. B. Huntington, pp. 751-765, ed. by B. Chance, V. W. Hughes, B. F. MacNichol, D. Sayre and F. C. Williams, Massachusetts Institute of Technology Radiation Laboratory Series, 19, (McGraw-Hill Book Co., New York, 1949). 3. The Radiofreqeuncy Spectrum of Rbs5F and Rbg7F by the Electric Resonance Method. V. w . Hughes and L. Grabner, Phys. Rev. 79, 314-322 (1950). 4. Energy Levels, Selection Rules, and Line Intensities for Molecular Beam
5. 6. 7. 8.
9.
10. 11. 12.
13. 14.
Electric Resonance Experiments with Diatomic Molecules, V. W. Hughes and L. Grabner, Phys. Rev. 79, 829-836 (1950) The Radiofrequency Spectrum of K.F by the Electric Resonance Method L. Grabner and V. W. Hughes, Phys. Rev. 79, 819-828 (1950). Further Evidence for a Two-Quantum Transition in Molecular Spectroscopy L. Grabner and V. W. Hughes, Phys. Rev. 82, 561 (1951). Effect of Nuclear Structure on the Hyperfine Structure of He3 V. W. Hughes and G. Weinreich, Phys. Rev. 91, 196-197 (1953). The Magnetic Moment of the Helium A t o m in the Metastable Triplet State. V. W. Hughes, 0. Tucker, E. Rhoderick and G. Weinreich, Phys. Rev. 91, 828-841 (1953). Relativistic Contributiorth to the Magnetic Moment of 3Si Helium. W. Pen and V. W. Hughes, Phys. Rev. 91 842-852 (1953); Phys. Rev. 89, 886-887 (1953). Hyperfine Structure of Helium-S in the Metastable Traplet State, 0. Weinreich and V. W. Hughes, Phys. Rev. 95, 1451-1460 (1954). Hyperfine Structure of Helium-S in the Metastable Traplet State, W. B. Teutsch and V. W. Hughes, Phys. Rev. 95, 14 61-1463 (1954). Static Magnetic Field Quenching of the Orthopositronium Decay: Angular Distribution Effect, V. W. Hughes, S. Marder and C. S. Wu, Phys. Rev. 98, 1840-1848 (1955). Two-Quantum Transition i n the Microwave Zeh’eman Spectrum of Atomic Oxygen, V. W. Hughes and S. Geiger, Phys. Rev. 99, 1842-1845 (1955). Effect of a n Electric Field o n Positronium Formation in Gases: Experimental, S . Marder, V. W. Hughes, C. S. Wu and W. Bennett, Phys. Rev. 103, 1258-1265 (1956).
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224 15. Effect of a n Electric Field o n Positronium Formation in Gases: Theoretical, W. B. Teutsch and V. W. Hughes, Phys. Rev. 103, 1266-1281 (1956). 16. Experimental Limit f o r the Electron-Proton Charge Difference, V. W. Hughes, Phys. Rev. 105, 170-172 (1957). 17. Electron g Value in the Ground State of Deuterium, J. S . Geiger and V. W. Hughes, Phys. Rev. 105, 183-188 (1957). 18. Positronium Formation in Gases. V. W. Hughes, J. Appi. Phys. 28, 16-22 (1957). 19. Hyperfine Structure of Positronium in Its Ground State. V. W. Hughes, S. Marder and C. S. Wu, Phys. Rev. 106, 934947 (1957). and Asymmetry of e in 20. Information Obtainable on Polarization of u Muonium Experiments. G. Breit and V. W. Hughes, Phys. Rev. 106, 12931295 (1957). 21. Considerations of Depolarization of Positive Muons in Gases; Eflect of Molecular Ions. V. W. Hughes, Phys. Rev. 108, 1106-1107 (1957). 22. Magnetic Moment of Helium in Its 35- Metasiable State. C. W. Drake, V. W. Hughes, A. Lurio and J. A. White, Phys. Rev. 112, 1627-1637 (1958). 23. Electron Magnetic Moment and Atomic Magnetism. V. W. Hughes, Recent Research in Molecular Beams, ed. by I. Estermann, (Academic Press, Inc., NY, 1959) pp. 65-92. 24. Microwave Zeeman Spectrum of Atomic Oxygen. H. B. Radford and V. W. Hughes, Phys. Rev. 114, 1274-1279 (1959). 25. Atomic and Molecular Beams Spectroscopy. P. Kusch and V. W. Hughes, Handbuch der Physik, Vol. 3711, ed. by S. Fliigge, (Springer-Verlag, Berlin, 1959). 26. Considerations on the Design of a Molecular Frequency Standard Based on the Molecular Beam Electric Resonance Method. V. W Hughes, Rev. Sci. Instr. 30, 689-693 (1959). 27. Hyperfine Structure of the Metastable Triplet State of Helium Three. J. A. White, L. Y. Chow, C. Drake and V. W. Hughes, Phys. Rev. Lett. 3,428-429 (1959). 28. Molecular Beam Electric Resonance Method with Separated Oscillating Fields. 3. C. Zorn, C. B. Chamberlain and V. W. Hughes, Quantum Electronics, ed. by C. H. Townes, (Columbia Univ. Press, NY, 1960) pp. 156-159. 29. Narrow Linewidths for Decaying States by the Method of Separated Oscillating Fields. V. W. Hughes, Quantum Electronics, ed. by C. H. Townes, (Columbia Univ. Press, NY, 1960) pp. 582-587. 30. Upper Limit f o r the Anisotropy of Inertial Mass f r o m Nuclear Resonance Experiments. V. W. Hughes, H. G. Robinson and V. Beltran-Lopez, Phys. Rev. Lett. 4, 342-344 (1960). 31. Production and Detection of a Polarized Deuteron Beam Using the Atomic Beam Magnetic Resonance Method. V. W. Hughes, C. W. Drake, Jr., D. C. Bonar, J. S. Greenberg, G. F. Pieper, Proceedings of the International Symposium on Polarization Phenomena of Nucleons, ed. by P. Huber and K. P. Meyer, (Birkhauser Verlag, Basel, 1960) pp. 89-107, 435.
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225 32. Formation of Muonium and Observation of Its Larmor Precession. V. W. Hughes, D. W. McColm, K. Ziock and R. Prepost, Phys. Rev. Lett. 5, 63-65 (1960). 33. Atomic g j Values f o r Neon and Argon in Their Metastable 3P2 States; Ewidence for Zero Spin of loNeZo.A. Lurio, C. Weinreich, C. W. Drake, V. W. Hughes and J. A. White, Phys. Rev. 120, 153-157 (1960). 34. Mott-Scattering Analysis of Longitudinal Polarization of Electrons from Co60. J. S . Greenberg, D. P. Malone, R. L. Gluckstern and V. W. Hughes, Phys. Rev. 120, 1393-1405 (1960). 35. Experimental Limits f o r the Electron-Proton Charge Difference and for the Neutron Charge. J. C. Zorn, C. B. Chamberlain and V. W. Hughes, Proceedings of the 1960 Annual International Conference on High Energy Physics at Rochester, ed. by E. C. C. Sudarshan, J. H. Tin-lot, A. C. Melissionos, (_Universityof Rochester, NY, 1960) pp. 790-792. 36. Positronium V. W. Hughes Encyclopedia of Sciences and Technology Vol. X, ed. by Daniel N. Lapides, (McGraw Hill, NY, 1960) pp. 524525. 37. Observation of the Hyperfine Structure Splitting of Muonium b y Use of a Static Magnetic Field. R. Prepost, V. W. Hughes and K. Ziock, Phys. Rev. Lett. 6, 19-21 (1961). 38. Production and Detection of an Accelerated Beam of Completely Polarized Deuterons. C. W. Drake, D. C. Bonar, R. D. Headrich and V. W. Hughes, Rev. Sci. Instr. 32, 995-996 (1961). 39. Microwave Zeeman Spectrum of Atomic Fluorine. H. B. Radford, V. W. Hughes and V. Beltran-Lopez, Phys. Rev. 123, 153-160 (1961). 40. Atomic Processes Involving Muonium and Anti-Muonium. V. W. Hughes, D. McColm, K. Ziock and R. Prepost, 2nd International Conference on the Physics of Electronic and Atomic Collisions, (W. A. Benjamin, Inc., NY, 1961) pp. 166-169. 41. Theoretical Values for Magnetic Moments of Mu-Mesonic Atoms. K. W. Ford, V. W. Hughes and J. G. Wills, Phys. Rev. Lett. 7, 134-135 (1961). 42. A Polarized Ion Source Using the Atomic-Beam Magnetic ResonanceMethod. C . W. Drake, D. C. Bonar, R. D. Headrick and V. W. Hughes, International Conference on High Energy Accelerators, ed. by M. H. Blewett, (Division of Technical Information, U.S. Atomic Energy Commission, Brookhaven National Laboratory, NY, 1961) pp. 379-384. 43. Hyperfine Structure of Muonium. K. Ziock, V. W. Hughes, R. Prepost, J. Bailey and W. Cleland, Phys. Rev. Lett. 8, 103-105 (1962). 44. Hyperfine' Structure of Muonium. J. Bailey, W. Cleland, V. W. Hughes, R. Prepost and K. Ziock, International Conference on High Energy Physics at CERN, ed. by J. Prentki, (CERN, Geneva, 1962) pp. 473-476. 45. Muon Resonance. V. W. Hughes, International Conference of Paramagnetic Resonances, ed. jy W. Low, (Academic Press, NY, 1963) pp. 382-396. 46. Theoretical Values for Magnetic Moments of Mu-Mesonic Atoms. K. W. Ford, V. W. Hughes and J. C. Wills, Phys. Rev. 129, 194-201 (1963) 47. Experimental Limits for the Electron-Proton Charge Difference and for the Charge of the Neutron. J. C. Zorn, C. E. Chamberlain and V. W. Hughes, Phys. Rev. 129, 2566-2576 (1963).
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226 48. A Very High Intensity Proton Linear Accelerator as a Meson Factory, E. R. Beringer, W. A. Blanpied, R. L. Gluckstern, V. W. Hughes, H. B. Knowles, S. Ohnuma and C. W. Wheeler, International Conference on Sector-Focused Cyclotrons and Meson Factories, ed. by F. T. L. Howard and N. Vogt-Nilsen, (CERN, Geneva, 1963) pp. 365-371. 49. Photoproduction of Negative and Positive Pions from Carbon at Forward Angles. W. A. Blanpied, J. S. Greenberg, V. W. Hughes, D. C. Lu and R. C. Minehart, Phys. Rev. Lett. 11, 477-479 (1963). 50. Sources of Polarized Electrons. V. W. Hughes, Proceedings of the Conference on Photon Interactions in the BeV-Energy Range, ed. by B. T. Feld, (M. I. T. Cambridge, Mass., 1963) pp. VI. 13-15. 51. Electromagnetic Pair Production. V. W. Hughes, Proceedings of the Conference on Photon Interactions in the BeV-Energy Range, ed. by B. T. Feld, (M. I. T. Press, Cambridge, Mass., 1963) pp. VIII. 1-7 52. Atomic Beam Source of Polarized Electrons for High Energy Accelerators. V. W. Hughes, R. L. Long and W. Raith, Proceedings of the International Conference on High Energy Accelerators, ed. by A. A. Kolomensky, A. B. Kusnetsov, and A. N. Lebedev, Atomizdat, Moscow 1964) pp. 988-992. 53. New Value for the Fine-Structure Constant from Muonium Hyperfine Structure Interval. W. E. Cleland, J. M. Bailey, M. Eckhause, V. W. Hughes, R. M. Mobley, R. Prepost and J. B. Rothberg, Phys. Rev. Lett. 13, 202-205 (1964). 54. Muonium and Positronium Physics. J. M. Bailey and V. W. Hughes, Prcceedings of the Third International Conference on the Physics of Electronic and Atomic Collisions, ed. by M. R. C. McDowell (North-Holland Publishing Co., Amsterdam, 1964) pp. 839-846. 55. The Lyttleton-Bondi Universe and Charge Equality. V. W. Hughes, Gravitation and Relativity, ed. by H. Y. Chiu and W. F. Hoffmann, (W. A. Benjamin, Inc., N.Y., 1964) pp. 259-278. 56. Mach’s Principle and Experiments on Mass Anisotropy, V. W. Hughes, Gravitation and Relativity, ed. by H. Y. Chiu and W. F. Hoffmann, (W. A. Benjamin, Inc., N.Y., 1964) pp. 106-120. 57. Status of Knowledge of the Fine-Structure Constant, Particularly as It Relates to Proton Structure, V. W. Hughes, Proceedings of the International Conference on Nuclear Structure, ed. by R. Hofstadter and L. Schiff, (Stanford University Press, California, 1964) pp. 235-244. 58. Evidence for the Photoproduction of the Y = 0 States with Masses Greater Than 1900MeV, W. A. Blanpied, J. S. Greenberg, V. W. Hughes, P. Kitching, D. C. Lu, and R. C. Minehart, Phys. Rev. Lett. 14, 741-744 (1965). 59. Polarized Electrons from a Polarized Atomic Beam. W. Raith, R. L. Long, Jr., V. W. Hughes and M. Posner, Proceedings of the IVth International Conference on the Physics of Electronic and Atomic Collisions, (Science Bookcrafters, Inc., N.Y. 1965) pp. 256-260. 60. Polarized Electrons from a Polarized Atomic Beam. R. L. Long, Jr., W. Raith, and V. W. Hughes, Phys. Rev. Lett. 15, 1-4 (1965).
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61. Atomic Interactions of Muonium, R. M. Mobley, J. M. Bailey, W. B. Cleland, V. w. Hughes and J. E. Rothberg, Proceedings of the IVth International Conference on the Physics of Electronic and Atomic Collisions, (Science Bookcrafters, Inc., N.Y. 1965) pp. 194-197. 62. Polarization of Photoelectrons from Magnetized Nickel, R.L. Long, Jr., V. W. Hughes, J. S. Greenberg, I. Ames and R. L. Christensen, Phys. Rev. 138, A1630-A1635 (1965). 63. Production of Stopped Pions and Muons from a Multi-Be V Proton Synchrotron, V. W. Hughes and R. D. Edge, IEEE Trans. Nuclear Sci. NS-12, 943-948 (1965). 64. Removal of the RF Microstructure from a Proton Linear Accelerator Beam, R.D. Edge, V. W. Hughes and J. Sandweiss, IEEE Trans. Nuclear Sci. NS12, 949-953 (1965). 65. A Polaried Electron Source for High Energy Accelerators, V. W. Hughes, R. L. Long, Jr., M. Posner and W. Raith, Proceedings of the International Symposium on Electron and Photon Interactions at High Energies, Vol. 11, ed. by C. Hohler, G. Kramer and U. Meyer-Berkhout, (Springer Verlag, Berlin, 1966) pp. 440-444. 66. The Ratio of the Cross Sections for Photoproduction of Asymmetric Muon and Electron Pairs in Hydrogen and Carbon, V. W. Hughes, W. A. Blanpied, J. S. Greenberg, P. Kitching, D. C. Lu and R. C. Minehart, Proceedings of the International Symposium on Electron and Photon Interactions at High Energies, Vol. 11, ed. by C. Hohler, C. Kramer and U. Meyer-Berkhout, (Spring-Verlag, Berlin, 1966) pp. 361-368. 67. The Photoproduction of Charged Pions in Hydrogen and Carbon for Photon Energies u p to 6 Be V, W. A. Blanpied, J. S. Greenberg, V. W. Hughes, P. Kitching, D. C. Lu and R. C. Minehart, Proceedings of the International Symposium on Electron and Photon Interactions at High Energies, Vol. 11, ed. by G. Hohler, G. Kramer and U. Meyer-Berkhout, (Springer-Verlag, Berlin, 1966) pp. 185-192. 68. The Photoproduction of Charged K Mesons and Evidence for New High Mass Hyperons, J. S . Greenberg, W. A. Blanpied, V. W. Hughes, P. Kitching, D. C. Lu and R. C. Minehart, Proceedings of the International Symposium on Electron and Photon Interactions at High Energies, Vol. 11, ed. by G. Hohler, G. Kramer and U. Meyer-Berkhout, (Springer-Verlag, Berlin, 1966) pp. 192-200. 69. Parity Conservation in Strong Interactions, C. W. Drake, D. C. Bonar, R. D. Headrick and V. W. Hughes, Proceedings of the 2nd International Symposium on Polarization Phenomena of Nucleons, ed. by P. Huber and H. Schopper, (Birkhauser Verlag, Basel and Stuttgart, 1966) pp. 362-364. 70. Muonium Chemistry, R. M. Mobley, J. M. Bailey, W. E. Cleland, V. W. Hughes and J. E. Rothberg, J. Chem. Phys. 44, 4354-4355 (1966). 71. Recent Experiments on Muonium, V. W. Hughes, J. Amato, R. Mobley, J. Rothberg and P. Thompson, Proceedings of the Williamsburg Conference on Intermediate Energy Physics, ed. by H. 0. Funsten, (College of William and Mary, Virginia, 1966) pp. 377-409.
228 72. The Muonium Atom, V. W. Hughes, Scientific American 214, 93-100 (1966). 73. Muonium, V. W. Hughes, Ann. Rev. Nuci. Sci. 16, 445-470 (1966). 74. Physics with Polarized Particles, V. W. Hughes, V International Conference on High Energy Accelerators, ed. by M. Grilli, (Comitato Nazionale Per L’Energia Nucleare, Rome, 1966) pp. 531-545. 75. Atomic Beam Study of the $ P State of Helium, F. M. J. Pichanick, C. E. Johnson, R. D. Swift and V. W. Hughes, Abstracts of the Conference on The Physics of Free Atoms, ed. by V. W. Cohen, (University of California, Berkeley, 1966) pp. 68-80. 76. Precision Redetermination of the Hyperfine Structure Interval of Positronium, E. D. Theriot, Jr., R. H. Beers and V. W. Hughes, Phys. Rev. Lett. 18, 767-769 (1967). 77. Search for S = + 1 Baryon States in Photoproduction, J. Tyson, J. S. Greenberg, V. W. Hughes, D. C. Lu, R. C. Minehart, S. Mon and J. E. Rothberg, Phys. Rev. Lett. 19, 255-259 (1967). 78. Hyperfine Structure of the v = 0, J = 1 State in-Rbg5F, Rbs7F, K3’F, and €?IF by the Molecular-Beam Electric-Resonance Method, P. A. Bonczyk and V. W. Hughes, Phys. Rev. 161, 15-22 (1967). 79. Detection of Positrons and of Positronium, V. W. Hughes, Methods of Experimental Physics, Vol. 4A and 4B, ed. by V. W. Hughes and H. L. Schultz (Academic Press, N.Y., 1967) pp. 389, Vol. 4A. 80. Muonium Chemistry II, R. M. Mobley, J. J. Amato, V. W. Hughes, J. E. Rothberg and P. A. Thompson, J. Chem. Phys. 47, 3074-3075 (1967). 81. Muonium, V. W. Hughes, Phys. Today 20, 29-40 (1967). 82. A Pulsed Source of Highly Polarized Electrons, V. W. Hughes, M. S. Lubell, M. Posner and W. Raith, Proceedings of the Sixth International Conference on High Energy Accelerators, ed. by R. A. Mack, (Cambridge Electron Accelerator, Cambridge, 1967) pp. A-144-A-147. 83. Production of Polarized Electrons b y Pulsed Photoionization of a Polarized Atomic Beam of Lithium-6, V. W. Hughes, M. S. Lubell, M. Posner and W. Raith, Fifth International Conference on the Physics of Electronic and Atomic Collisions, ed. by I. P. Flaks (NAUKA, Leningrad, 1967) pp. 544545. 84. Ratio of h and Co Photoproduction Cross Sections; High-Mass Hyperon Resonances, J. S . Greenberg, V. W. Hughes, D. C. Lu, R. C. Minehart, S. Mori, J. E. Rothberg and J. Tyson, Phys. Rev. Lett. 20, 221-223 (1968). 85. Parity Conservation in the Reaction T ( d ,n) He4, D. C. Bonar, C. W. Drake, R. D. Headrick and V. W. Hughes, Phys. Rev. 174, 1200-1207 (1968). 86. Experiments on the $ P State of Helium I. A Measurement of the $ P i %?Pz Fine Structure, F. M. J. Pichanick, R. D. Swift, C. E. Johnson and V. W. Hughes, Phys. Rev. 169, 55-78 (1968). 87. Further Search for S = $1 Baryon States in Photoproduction, S . Mori, J. S. Greenberg, V. W. Hughes, D. C. Lu, J. B. Rothberg and P. A. Thompson, Phys. Lett. 28B, 152-154 (1968). 88. Search for Muonium-Antimuonium Conversion, J. J. Amato, P. Crane, V. W. Hughes, J. E.Rothberg and P. A. Thompson, Phys. Rev. Lett. 21, 17091712 (1968).
229 89. Muonium, V. W. Hughes, Vistas in Science, ed. by David L. Arm (Univ. of New Mexico Press, Albuquerque, 1968) pp. 237-256. 90. A Fine Structure Constant a , V. W. Hughes, A Tribute to I. I. Rabi, (Columbia University Symposium 1967). 91. Determination of Muonium Hyperfine Structure Interval Through Measurements at Low Magnetic Fields, P. A. Thompson, J. J. Amato, P. Crane, V. W. Hughes, R. M. Mobley, G. zu Putlitz and J. E. Rothberg, Phys. Rev. Lett. 22, 163-167 (1969). 92. Atoms, V. W. Hughes, Phys. Today 22, 33-37 (1969). 93. The Fine-Structure Constant, V. W. Hughes, Comments on Atomic and Molecular Physics 1, 5-11 (1969). 94. Tests of Quantum Electrodynamics from Radiofrequency Studies of Atoms, V. W. Hughes, Magnetic Resonance and Radiofrequency Spectroscopy: Prcceedings of the XVth. Colloque. A. M. P. E. R. E., ed. by P. Averbuch (North-Holland Pubi. Co., Amsterdam, 1969) pp. 1-22. 95. Quantum Electrodynamics: Experiment, V. W. Hughes, Atomic Physics, ed. by V. W. Hughes, B. Bederson, V. W. Cohen and F. M. J. Pichanick, (Plenum Press, NY, 1969) pp. 15-51. 96. Muon g-2 Experiment at LAMPF, V. W. Hughes, Some Physics Uses at LAMPF 1968 Summer Study Group at Los Alamos, LA-4080 Rev., (1969) pp. 2-4. 97. Experimental Test for Mass Anisotropy Based on Nuclear Magnetic Resonance, V. w. Hughes and w. L. Williams; Gravity Research Foundation (Essay Award First Prize, 1969). 98. Elastic Scattering of Positive Kaons by Polarized Protons at 1.54 and 1.71 Ge V/c. G. A. Rebka, Jr., J. Rothberg, A. Etkin, P. Glodis, J. Greenberg, V. W. Hughes, K. Kondo, D. C. Lu, S. Mori and P. A. Thompson, Proceedings of the Boulder Conference on High Energy Physics, ed. by K. T. Mahanthappa, W. D. Walker and W. B. Brittin, (Colorado Associated University Press, Boulder, 1969) pp. 531-532. 99. Magnetic Moment and hfs Anomaly for He3, W. L. Williams and V. W. Hughes, Phys. Rev. 185, 1251-1255 (1969). 100. Search for S = +1 Baryon States i n Photoproduction, S . Mori, J. S. Greenberg, V. W. Hughes, D. C. Lu, R. C. Minehart, J. B. Rothberg, P. A. Thompson and J. Tyson, Phys. Rev. 185, 1687-1701 (1969). 101. Muonium and Positronium, V. W. Hughes, Physics of the One-and TwoElectron Atoms, ed. by F. Bopp and H. Kleinpoppen, (North-Holland Publishing Co., Amsterdam, 1969) pp. 407-428. 102. Atom-Antiatom Collision, D. L. Morgan, Jr. and V. W. Hughes, Sixth International Conference on the Physics of Electronic and Atomic Collisions, ed. by I. Amdue, (Massachusetts Institute of Technology Press, Cambridge, 1969) pp. 830-834. 103. Recent Muonium Hyperfine Structure Measurements, P. Crane, J. J. Amato, V. W. Hughes, D. M. Lazarus, G. zu Putlitz and P. A. Thompson, HighEnergy Physics and Nuclear Structure, ed. by Samuel Devons, (Plenum Press, NY, 1970) pp. 677-679.
230 104. Asymmetry and Differential Cross Section f o r Elastic Scattering of K+ Mesons by Polarized Protons at 1.54 and 1.71 Ge V/c, G. A. Rebka, Jr., J. Rothberg, A. Etkin, P. Glodis, J. Greenberg, V. W. Hughes, K. Kondo, D.C. Lu, S. Mon and P. A. Thompson, Phys. Rev. Lett. 24, 160-164 (1970). 105. Muonium I: Muonium Formation and Larmor Precession, V. W. Hughes, D. W. McColm, K. Ziock and R. Prepost, Phys. Rev. Al, 595-553 (1970); A2, 551-553 (1970). 106. Precision-Redetermination of the Fine-Structure Interval of the Ground State of Positronaum and a Direct Measurement of the Decay Rate of Parapositronium, B. D. Theriot, Jr., R. H. Beers, V. W. Hughes and K. 0. H. Ziock, Phys. Rev. A2, 707-721 (1970). 107. Photoproducton of Y* Resonances above 1800 MeV, D. C. Lu, J. S. Greenberg, V. W. Hughes, R. C. Minehart, s. Mori, J. E. Rothberg and J. Tyson, Phys. Rev. D2, 1846-1851 (1970). 108. Experiments on the $ P State of Helium 11, Measurements of the Zeeman Effect, S . A. Lewis, F. M. J. Pichanick and V. W. Hughes, Phys. Rev. A2, 86-101 (1970). 109. Atomic Processes Involved in Matter-Antimatter Annihilation, D. L. Morgan, Jr. and V. W. Hughes, Phys. Rev. D2, 1389-1399 (1970). 110. Search for Strangeness S = + l Baryon States, V. W. Hughes, R. D. Ehrlich, A. Etkin, P. Glodis, K. Kondo, D. C. Lu, S. Mori, R. Patton, G. A. Rebka, Jr., J. E. Rothberg, P. A. Thompson and M. E. Zeller, Hyperon Resonances70, ed. by E. C. Fowler (Moore Publishing Co., Durham, North Carolina, 1970) pp. 349-366. 111. Determination of the Fine Structure Constant a! from Helium Fine Structure, A. Kponou, V. W. Hughes, C. E. Johnson, S. A. Lewis and F. M. J. Pichanick, Proceedings of the International Conference on Precision Measurements and Fundamental Constants, ed. by D. N. Langenberg and B. N. Taylor (NBS Special Publication 343, Washington, D. C., 1971) pp. 389-391. 112. Precision Measurement of the Fine Structure Interval of the Ground State of Positronium, E. R. Carlson, V. W. Hughes and E. D. Theriot, Jr., Proceedings of the International Conference on Precision Measurements and Fundamental Constants, ed. by D. N. Langenberg and B. N. Taylor (NBS Special Publication 343, Washington, D. C. , 1971) pp. 313-316. 113. Hyperfine Structure Interval of the Ground State of Muonium, P. A. Thompson, D. Casperson, P. Crane, T. Crane, P. Egan, V. W. Hughes, G. zu Putlitz and R. Stambaugh, Proceedings of the International Conference on Precision Measurements and Fundamental Constants, ed. by D. N. Langenberg and B. N. Taylor (NBS Special Publication 343, Washington, D. C., 1971) pp. 339-343. 114. The Breit Interaction, V. W. Hughes, Facets of Physics ed. by D. A. Bromley and V. W. Hughes, (Academic Press, NY, 1970) pp. 125-140. 115. Muonium II, Observation of Muonium Hyperfine-Structure Interval, J. M. Bailey, W. E. Cleland, V. W. Hughes, R. Prepost and K. Ziock, Phys. Rev. A3, 871-884 (1971).
231 116. Asymmetry Measurements for Elastic Scattering o f @ Mesons by Polarized Protons, R. D. Ehrlich, A. Etkin, P. Glodis, V. W. Hughes, K. Kondo, D. C. Lu, S. Mori, R. Patton, G. A. Rebka, Jr.; J. E. Rothberg, P. Thompson and M. E. Zeller, Phys. Rev. Lett. 26, 925-928 (1971). 117. Precise Measurement of the $Po - $ P i Fine-Structure Interval of Helium, A. Kponou, V. Hughes, C. E. Johnson, S. A. Lewis and F. M. J. Pichanick, Phys. Rev. Lett. 26, 1613-1616 (1971). 118. Stopped Muon Channel for LAMPF, V. W. Hughes, S. Ohnuma, K. Tanabe, P. Thompson and H. F. Vogel, Los Alamos Scientific Laboratory, LA-4474MS (February, 1971), pp. 1-38. 119. Observation of a Quadratic Term in the hfs Pressure Shift for Muonium and a New Precise Value f o r Muonium Av, T. Crane, D. Casperson, P. Crane, P. Egan, V. W. Hughes, R. Stambaugh, P. A. Thompson and G. zu Putlitz, Phys. Rev. Lett. 27, 474-476 (1971). 120. Polarized Electrons and Some of Their Uses, V. W. Hughes, I1 International Conference on Polarized Targets, ed. by G. Shapiro, (University of California, Lawrence Berkeley Laboratory, 1971), pp. 191-204. 121. Muonium Chemistry in Gases, V. W. Hughes, The Meeting on Muons in Solid State Physics, (Schweizerisches Institute fr Nuckearforschung (SIN) Zurich, 1971) pp. 129-134. 122. Polarized Electrons from Photoionization of Polarized Alkali Atoms, V. W. Hughes, R. L. Long, Jr., M. S. Lubell, M. Posner and W. Raith, Phys. Rev. A5, 195-222 (1972). 123. Measurements of the Asymmetries in the Differential Cross Sections for pp --+ pp and pp + 7r-7r+ Using Polarized Protons, R. D. Ehrlich, A. Etkin, P. Glodis, V. W. Hughes, K. Kondo, D. C. Lu, S. Mori, R. Patton, G. A. Rebka, Jr., P. A. Thompson and M. E. Zeller, Phys. Rev. Lett. 28, 1147-1150 (1972). 124. Muonium III. Precision Measurement of the Muonium Hyperjine-Structure Interval at Strong Magnetic Field, W. E. Cleland, J. M. Bailey, M. Eckhause, V. W. Hughes, R. Prepost, J. E. Rothberg and R. M. Mobley, Phys. Rev. A5, 2338-2356 (1972). 125. Higher Precision Determination of the Fine-Structure Interval in the Ground State of Positronium, and the Fine-Stmcture Density Shift in Nitrogen, E. R. Carlson, V. W. Hughes, M. L. Lewis and I. Lindgren, Phys. Rev. Lett. 29, 1059-1061 (1972). 126. Status of QED Experiments, V. W. Hughes, Third International Conference on Atomic Physics, ed. by S. J. Smith and G. K. Walters, (Plenum Press, NY, 1973) pp. 1-32. 127. Observation of a Positroniurn Zeeman Transition y - A 1 2 4 , D. J. Judd, Y. K. Lee, L. Madansky, E. R. Carlson, V. W. Hughes and B. Zundell, Phys. Rev. Lett. 30, 202-204 (1973). 128. A t o m Anti-atom Interactions, D. L. Morgan, Jr. and V. W. Hughes, Phys. Rev. A7, 1811-1825 (1973). 129. The Third International Conference o n Atomic Physics, V. W. Hughes, Comments on Atomic and Molecular Physics, Vol. IV, Number 2, 35-41 (1973).
w.
232 130. Higher-Order Relativistic Contributions to the Combined Zeeman and Motional Stark Effects in Positronium, M. L. Lewis and V. w. Hughes, Phys. Rev. A8, 625-639 (1973). 131. Muonium I V Precision Measurement of the Muonium Hyperfine-Structure Interval at Weak and Very Weak Magnetic Fields, P. A. Thompson, P. Crane, T. Crane, J. J. Amato, V. W. Hughes, G. zu Putlitz and J. E. Rothberg, Phys. Rev. A8, 86-112 (1973). 132. Higher-Order Relativistic Contributions to the Zeeman Effect in Helium, M. L. Lewis and V. W. Hughes, Phys. Rev. A8, 2845-2856 (1973). 133. Positronium and Muonium, V. W. Hughes, Physik 1973, German Physical Society Conf., (Physik Verlag Hmblt, Germany, 1973), pp. 123-155. 134. New Experimental Limit on T Invariance in Polarized-Neutron Decay, R. I. Steinberg, P. Liaud, B. Vignon and V. W. Hughes, Phys. Rev. Lett. 33, 41-44 (1974). 135. Remarks Relevant to Fine Stmcture Measurements of Muonic Hydrogen and Muonic Helium, K. N. Kuang, V. W. Hughes, M. L. Lewis, R. 0. Mueller, H. Rosenthal, C. S. Wu and M. Camani, High-Energy Physics and Nuclear Structure, ed. by B. Tibell, (North-Holland Publishing Co., 1974) pp. 312314. 136. Atomic Regime in which the Magnetic Interaction Dominates the Coulomb Interaction for Highly Excited States of Hydrogen, R. 0. Mueller and V. W. Hughes, Proceedings of the National Academy of Science 71, 3287-3289 (1974). 137. Muonium Formation in Noble Gases and Noble-Gas Mixtures, R. D. Stambaugh, D. B. Casperson, T. W. Crane; V. W. Hughes, H. F. Kaspar, P. A. Souder, P. A. Thompson, H. Orth, G. zu Putlitz and A. B. Denison, Phys. Rev. Lett. 33, 568-571 (1974). 138. Behavior of Positive Muons in Liquid Helium, T. W. Crane, D. E. Casperson, H. Chang, V. W. Hughes, H. F. Kaspar, B. Lovett, A. Schiz, P. A. Souder, R. D. Stambaugh, G. zu Putlitz and J. P. Kane, Phys. Rev. Lett. 33, 572-574 (1974). 139. Evidence for Formation of the First Excited State of Positronium, S . L. Varghese, E. S. Ensberg, V. W. Hughes and I. Lindgren, Phys. Lett. 49A, 415-417 (1974). 140. Polarized Electron Source for the Stanford Linear Accelerator, M. J. Alguard, R. D. Ehrlich, V. W. Hughes, J. Ladish, M. S. Lubell, W. Lysenko, K. P. Schler, G. Baum and W. Raith, Proceedings of the IXth International Conference on High Energy Accelerators, (Stanford Linear Accelerator Center, CONF-740522, 1974) pp. 309-313. 141. Higher-Order Relativistic Contributions to the Zeeman Eflect in Helium and Helium-Like Ions, M . L. Lewis and V. W. Hughes, Phys. Rev. All, 383-384 (1975). 142. Collision Quenching of the Metastable 2s State of Muonic Hydrogen and the Muonic Helium Ion, R. 0. Mueller, V. W. Hughes, H. Rosenthal and C. S. Wu, Phys. Rev. All, 1175-1186 (1975).
143. Formation of the Muonic Helium Atom, a p - e - , and Observation of Its Larmor Precession, P. A. Souder, D. E. Casperson, T. W. Crane, V. W. Hughes, D. C. Lu, H. Orth, H. W. Reist, M. H. Yam and G. zu Putlitz, Phys. Rev. Lett. 34, 1417-1420 (1975). 144. Polarized Electron- Electron Scattering at GeV Energies, P. S . Cooper, M. J. Alguard, R. D. Ehrlich, V. W. Hughes, H. Kobayakawa, J. S. Ladish, M. S. Lubell, N. Sasao, K. P. Schiiler, P. A. Souder, G. Baum, W. Raith, K. Kondo, D. H. Coward, R. H. Miller, C. Y. Prescott, D. J. Sherden and C. K. Sinclair, Phys. Rev. Lett. 34, 1589-1592 (1975). 145. Beam Calculations for LAMPF Muon Channel. W. P. Lysenko, V. W. Hughes, S. Ohnuma, P. A. Thompson and H. F. Vogel, IEEE Transactions on Nuclear Science, Vol. NS-22, 1593-1597 (1975). 146. Muons: Muonic Atoms and Muonium, V. W. Hughes, High-Energy Physics and Nuclear Structure 1975, ed. by D. E. Nagle, R. L. Burman, B. G. Storms, A. S. Goldhaber and C. K. Hargrove, (Alp Conf. Proceedings No. 26, Santa Fe and Los Alamos, 1975), pp. 515-539. 147. Positronium: Precision Determination of the Ground State Fine-Structure Interval Av and Measurement of Density Shifts in the Noble Gases, P. 0. Egan, W. E. Frieze, V. W. Hughes and M. H. Yam, Phys. Lett. 54A, 412-414 (1975). 148. A New High Precision Measurement of the Muonium Hyperfine Structure Interval Av, D. E. Casperson, T. W. Crane, V. W. Hughes, P. A. Souder, R. D. Stambaugh, P. A. Thompson, H. Orth, G. zu Putlitz, H. F. Kaspar, H. W. Reist and A. B. Denison, Phys. Lett. 59B, 397-400 (1975). 149. Muon Physics Vol. I1 and 111, ed. by V. W. Hughes and C. S. Wu, (Academic Press, NY., 1975). 150. K - Mass from Kaonic Atoms, S . C. Cheng, Y. Asano, M. Y . Chen, G. Dugan, E. Hu, L. Lidofsky, W. Patton, C. S. Wu, V. W. Hughes and D. C. Lu, Nucl. Phys. A254, 381-395 (1975). 151. Mass and Magnetic Moment of K - by the Exotic Atom Method, C. Dugan, Y . Asano M. Y. Chen, S. C. Cheng, B. Hu, L. Lidofsky, W. Patton, C. S. Wu, V. W. Hughes and D. C. Lu, Nucl. Phys. A254, 396-402 (1975). 152. Mass and Magnetic Moment of the Antiproton by the Exotic Atom Method, G. Dugan, Y. Asano, M. Y. Chen, S. C. Cheng, E. Hu, L. Lidofsky, W. Patton, C. W. Wu, V. W. Hughes and D. C. Lu, Nucl. Phys. A254, 403-412 (1975). 153. E2 Dynamic Mixing in and K - Atoms of 238U, M. Y. Chen, Y. Asano, S. C. Cheng, G. Dugan, E. Hu, L. Lidofsky, W. Patton, C. S. Wu, V. W. Hughes and D. C. Lu, Nucl. Phys. A254, 413-421 (1975). 154. Search for a Nonzero Triple-Correlation Coeficient and New Experimental Limit on T Invariance in Polarized-Neutron Beta Decay, R. I. Steinberg, P. Liaud, B. Vignon and V. W. Hughes, Phys. Rev. D13, 2469-2477 (1976). 155. The Fine Structure Constant from Helium Fine Structure, M. L. Lewis, P. H. Serafino and V. W. Hughes, Phys. Lett. A58, 125-126 (1976). 156. Elastic Scattering of Polarized Electrons b y Polarized Protons, M. J. Alguard, W. Ash, G. Baum, J. E. Clendenin, P. S. Cooper, D. H. Coward,
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R: D. Ehrlich, A. Etkin, V. W. Hughes, H. Kobayakawa, K. Kondo, M. S. Lubell, R. H. Miller, D. A. Palmer, W. Raith, N. Sasm, K. P. Schler, D. J. Sherden, C. K. Sinclair and P. A. Souder, Phys. Rev. Lett. 37, 1258-1261 (1976). Deep Inelastic Scattering of Polarized Electrons by Polarized Protons, M. J. Alguard, W. W. Ash, G. Baum, J. E. Clendenin, P. S. Cooper, D. H. Coward, R. D. Ehrlich, A. Etkin, V. W. Hughes, H. Kobayakawa, K. Kondo, M. S. Lubell, R. H. Miller, D. A. Palmer, W. Raith, N. Sasm, K. P. Schiiler, D. J. Sherden, C. K. Sinclair and P. A. Souder, Phys. Rev. Lett. 37, 12611265 (1976). Precise Measurement of Electronic g J Value of Helium, g J p He, 9s'). B. E. Zundell and V. W. Hughes, Phys. Lett. 59A, 381-382 (1976). Precision Determination of the Fine-Structure Interval i n the Ground State of Positronium 111, E. R. Carlson, V. W. Hughes and I. Lindgren, Phys. Rev. A15, 241-250 (1977). Precision Determination of the Fine-Structure Interval in the Ground State of Positronium IV. Measurement of Positronium Fine-Structure Density Shifts in Noble Gases. P. 0. Egan, V. W. Hughes and M. H. Yam, Phys. Rev. A15, 251-260 (1977). New Precise Value for the Muon Magnetic Moment and Sensitive Test of the Theory of the hfs Interval i n Muonium, D. E. Casperson, T. W. Crane, A. B. Denison, P. 0. Egan, V. W. Hughes, F. G. Mariam, H. Orth, H. W. Reist, P. A. Souder, R. D. Stambaugh, P. A. Thompson and G. zu Putlitz, Phys. Rev. Lett. 38, 956-959 (1977); 38, 1504 (1977). Parity Nonconservation in Hydrogen Involving Magnetic/Electric Resonance, E. A. Hinds and V. w. Hughes, Phys. Lett. 67B, 487-488 (1977). Operating Experience with the Polarized Electron Gun at SLAC, M. J. Alguard, G. Baum, J. E. Clendenin, V. W. Hughes, M. S. Lubell, R. H. Miller, W. Raith, K. P. Schuler and J. Sodja, IEEE Transactions on Nuclear Sciences, NS-24, 1603-1604 (1977). Depolarization Effects in Pulsed Photoionization of State-Selected Lithium, M. J. Alguard, J. E. Clendenin, P. S. Cooper, R. D. Ehrlich, V. W. Hughes and M. S. Lubell, Phys. Rev. A16, 209-212 (1977). Measurement of Spin-Exchange Effects in Electron-Hydrogen Collisions: Impact Ionization, M. J. Alguard, V. W. Hughes, M. S. Lubell and P. F. Wainwright, Phys. Rev. Lett. 39, 334-338 (1977). The Fine Structure Constant a. V. W. Hughes, A Festschrift for 1.1. Rabi, ed. by Lloyd Motz, (The New York Academy of Sciences Series 11, Volume 38, 1977) pp. 62-76. Introduction and History, C . S . Wu and V. W. Hughes, Muon Physics Vol. I, ed. by V. W. Hughes and C. S. Wu, (Academic Press, NY, 1977) pp. 2-8; Electromagnetic Properties and Interactions of Muons, V. W. Hughes and T. Kinoshita, Muon Physics Vol. I, ed. by V. W. Hughes and C. S. Wu, (Academic Press, NY, 1977) pp. 11-199. Deep Inelastic e-p Asymmetry Measurements and Comparison with the Bjorken Sum Rule and Models of Proton Spin Structure, M. J. Alguard,
235 W. W. Ash, G. Baum, M. R. Bergstrom, J. E. Clendenin, P. S. Cooper, D. H. Coward, R. D. Ehrlich, V. W. Hughes, K. Kondo, M. S. Lubell, R. H. Miller, S. Miyashita, D. A. Palmer, W. Raith, N. Sasm, K. P. Schiiler, D. J. Sherden, P. A. Souder and M. E. Zeller, Phys. Rev. Lett. 41, 70-73 (1978). 169. Parity Non-Conservation in Inelastic Electron Scattering. C. Y. Prescott, W. B. Atwood, R. L. A. Cottell, H. DeStaebler, E. L. Garwin, A. Gonidec, R. H. Miller, L. S. Rochestere, T. Sato, D. J. Sherden, C. K. Sinclair, S. Stein, R. E. Taylor, J. E. Clendenin, V. W. Hughes, N. Sasm, K. P. Schuler, M. G. Borghini, K. Lubelsmeyer and W. Jentschke, Phys. Lett. 77B, 347-352 (1978). 170. Development of a Low-Momentum “Surface” Muon Beam for LAMPF, H. W. Reist, D. E. Casperson, A. B. Denison, P. 0. Egan, V. W. Hughes, F. G. Mariam, G. zu Putlitz, P. A. Souder, P. A. Thompson and J. Vetter, Nucl. Inst. and Meth. 153, 61-64 (1978). 171. Positronium Fine-Structure Interval in Oxide Powers, M. H. Yam, P. 0. Egan, W. E. Frieze and V. W. Hughes, Phys. Rev. A18, 350-353 (1978). 172. Search for Parity Violation in Deep-Inelastic Scattering of Polarized Electrons b y Unpolarized Deuterons, W. B. Atwood, R. L. A. Cottell, H. DeStaebler, R. Miller, H. Pessard, C. Y . Prescott, L. S. Rochester, R. E. Taylor, M. J. Alguard, J. Clendenin, P. S. Cooper, R. D. Ehrlich, V. W. Hughes, M. S. Lubell, G. Baum, K. P. Schiiler and K. Lubelsmeyer, Phys. Rev. D18, 2223-2226 (1978). 173. A Source of Highly Polarized Electrons at the Stanford Linear Accelerator Center, M. J. Alguard, J. E. Clendenin, R. D. Ehrlich, V. W. Hughes, J. S. Ladish, M. S. Lubell, K. P. Schiiler, G. Baum, W. Raith, R. H. Miller and W. Lysenko, Nucl. Inst. and Meth. 163, 29-59 (1979). 174. Further Measurements of Parity Non-Consewtion in Inelastic Electron Scattering, C. Y. Prescott, W. B. Atwood, R. L. A. Cottell, H. DeStaebler, E. L. Garwin, A. Gonidec, R. H. Miller, L. S. Rochester, T. Sato, J. Sherden, C. K. Sinclair, S. Stein, R. E. Taylor, C. Young, J. E. Clendenin, V. W. Hughes, N. Sasao, K. P. Schuler, M. C. Borghini, K. Lubelsmeyer and W. Jentschke, Phys. Lett. 84B, 524-528 (1979). 175. Experimental Test of Special Relativity from a High-y Electron 9-2 Measurement, S . Cooper, M. J. Alguard, R. D. Ehrlich, V. W. Hughes, H. Kobayakawa, J. S. Ladish, M. S. Lubell, N. Sum, K. P. Schuler, P. A. Souder, D. H. Coward, R. H. Miller, C. Y . Prescott, D. J. Sherden, C. K. Sinclair, G. Baum, W. Raith and K. Kondo, Phys. Rev. Lett. 42, 1386-1389 (1979). 176. Polarized Lepton-Hadron Scattering, V. W. Hughes High Energy Physics with Polarized Beams and Polarized Targets, ed. by G. H. Thomas, (AIP Conf. Proc. No. 51, Argonne, 1978) pp. 71-202. 177. The Stopped Muon Channel at LAMPF, P. A. Thompson, V. W. Hughes, W. P. Lysenko and H. F. Vogel, Nucl. Inst. and Meth. 161, 391-411 (1979). 178. Polarized Electroproduction, V. W. Hughes, Proceedings of the 19th International Conference on High Energy Physics, ed. by S. Homma, M. Kawaguchi and H. Miyazawa, (Physical Society of Japan, 1979) pp. 286-290.
236 179. Spin Effects in Electromagnetic Interactions, P. A. Souder and V. W. Hughes, High-Energy Physics in the Einstein Centennial Year (1979), ed. by B. Kursunoglu et al., (Plenum Publishing Corp., NY, 1979) pp. 395-439. 180. Theoretical Hyperfine Structure of Muonic Helium, K. N. Huang and V. W. Hughes, Phys. Rev. A20, 706-711 (1979); A21, 1071 (1980). 181. Muonium, V. W. Hughes, Exotic Atoms '79 Fundamental Interactions and Structure of Matter, ed. by K. Crowe, J. Duclos, G. Fiorentini and G. Torelli (Plenum Publishing Corp., NY, 1980) pp. 3-18. 182. Positronium, V. W. Hughes, Exotic Atoms '79 Fundamental Interactions and Structure of Matter, ed. by K. Crowe, J. Duclos, G. Fiorentini and G. Torelli (Plenum Publishing Corp., NY, 1980) pp. 19-22. 183. Neutrino Experiment to Test the Nature of Muon-Number Conservation, E. Willis, V. W. Hughes, P. Nemethy, R. L. Burman, D. R. F. Cochran, J. S. Frank, R. P. Redwine, J. Duclos, H. Kaspar, C. K. Hargrove and U. Moser, Phys. Rev. Lett. 44,' 522-524 (1980); 44, 903 (1980). 184. Formation of the Muonic Helium Atom, P. A. Souder, T. W. Crane, V. W. Hughes, D. C. Lu, H. Orth, H. W. Reist, M. H. Yam and G. zu Putlitz, Phys. Rev. A22, 33-50 (1980). 185. Parity Nonconservation and Neutral Current Interactions Involving Muons, V. W. Hughes, International Workshop on Neutral Current Interactions in Atoms, ed. by W. L. William (Crgese, 1979) pp. 327-356. 186. Precise Measurement of the $Po - $P2 Fine Structure Interval in Helium, W. E. Frieze, E. A. Hinds, V. W. Hughes and F. M. J. Pichanick, Phys. Lett. A78, 322-324 (1980). 187. Measurement of Asymmetry in Spin-Dependent e-p Resonance-Region Scattering, G. Baum, M. R. Bergstrom, J. E. Clendenin, R. D. Ehrlich, V. W. Hughes, K. Kondo, M. S. Lubell, S. Miyashita, R. H. Miller, D. A. Palmer, W. Raith, N. Sasao, K. P. Schiiler and P. A. Souder, Phys. Rev. Lett. 45, 2000-2003 (1980). 188. First Observation of the Ground-State Hyperfine-Structure Resonance of the Muonic Helium Atom, H. Orth, K. P. Arnold, P. 0. Egan, M. Cladish, W. Jacobs, J. Vetter, W. Wahl, M. Wigand, V. W. Hughes and G. zu Putlitz, Phys. Rev. Lett. 45, 1483-1486 (1980). 189. Measurements of Parity Violation in the Scattering of Polarized Electrons from Protons, P. A. Souder, V. W. Hughes, M. S. Lubell and S. Kowalski, Future Directions in Electromagnetic Nuclear Physics, 385-395 (1980). 190. Limits on Neutrino Oscillations from Muon-Decay Neutrinos, P. Nkmethy, S . B. Willis, V. W. Hughes, R. L. Burman, D. R. F. Cochran, J. Frank, R. P. Redwine, J. Duclos, H. Kaspar, C. K. Hargrove and U. Moser, Phys. Rev. D23, 262-264 (1981). 191. Search f o r Long-Lived 2s Muonic Hydrogen in H2 Gas, P. 0. Egan, S. K. Dhawan, V. W. Hughes, D. C. Lu, F. C. Mariam, P. A. Souder, J. Vetter, G. zu Putlitz, P. A. Thompson and A. B. Denison, Phys. Rev. A23, 1152-1163 (1981). 192. Internal Spin Structure of the Proton from High Energy Polarized e-p Scattering, V. W. Hughes, G. Baum, M. R. Bergstrom, P. R. Bolton, J. E.
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Clendenin, N. R. DeBotton, S. K. Dhawan, R. A. Fong-Tom, Y . N. Guo, V. R. Harsh, K. Kondo, M. S. Lubell, C. L. Mao, R. H. Miller, S. Miyashita, K. Morimoto, U. F. Moser, I. Nakano, R. F. Oppenheim, D. A. Palmer, L. Panda,W. Raith, N. Sasao, K. P. Schiiler, M. L. Seely, J. Sodja, P. A. Souder, S. J. St. Lorant, K. Takikawa and W. Werlen, High-Energy Physics with Polarized Beams and Polarized Targets, ed. by C. Joseph and J. Soffer (Birkhuser, Verlag, 1981) pp. 331-343. Measurements of the Polarization Parameter i n K+ p Elastic Scattering at Low Energies, B. R. Lovett, V. W. Hughes, M. Mishina, M. Zeller, D. M. Lazarus and I. Nakano, Phys. Rev. D23, 1924-1932 (1981). Experiments on the 9 P State of Helium. 111. Measurement of the $Po 23P1 Fine Structure Interval. A. Kponou, V. W. Hughes, C. E. Johnson, S. A. Lewis and F. M. J. Pichanick, Phys. Rev. A24, 264-278 (1981). Experiments on the 9 P State of Helium. IV. Measurement of the 23Po ~ P Fine z Structure Interval, W. Frieze, E. A. Hinds, V. W. Hughes and F. M. J. Pichanick, Phys. Rev. A24, 279-287 (1981). A Planned Experiment on Parity Violation for Atomic Hydrogen, V. W. Hughes, Weak Interactions as Probes of Unification, ed. by G. B. Collins L. N. Chang and J. R. Ficenec, (AIP, 1981) pp, 78-83. New Results on Polarized Electron-Proton Scattering at SLAC, G. Baum, M. R. Bergstrom, P. R. Bolton, J. E. Clendenin, N. R. DeBotton, S. Dhawan, R. Fong-Tom, Y . Guo, V. Harsh, V. W. Hughes, K. Kondo, M. S. Lubell, R. Miller, S. Miyashita, K. Morimoto, U. Moser, I. Nakano, R. Oppenheim, D. Palmer, L. Panda, W. Raith, N. Sasao, K. P. Schiiler, M. Seely, J. Sodja, P. A. Souder, S. St. Lorant, K. Takikawa and M. Werlen, High Energy Physics 1980, ed. by L. Durand and L. G. Pondrom, (AIP, XX International Conference, Madison, Wisconsin, 1981) pp. 781-783. Dynamic Nuclear Polarization of Irradiated Targets, M. L. Seely, M. R. Bergstrom, S. K. Dhawan, R. A. Fong-Tom, V. W. Hughes, R. F. Oppenheim, K. P. Schiiler, P. A. Souder, K. Kondo, S. Miyashita, I. Nakano, S. J. St. Lorant, Y . N. Guo and A. Winnacker, Polarized Phenomena in Nuclear Physics 1980, ed. by G. G. Ohlsen, R. E. Brown, N. Jarmie, W. W. McNaughton and G. M. Hale, (AIP, 1981) pp. 933-935. Dynamic Nuclear Polarization of Irradiated Targets, M. L. Seely, M. R. Bergstrom, S. K. Dhawan, V. W. Hughes, R. F. Oppenheim, K. P. Schuler, P. A. Souder, K. Kondo, S. Miyashita, S. J. St. Lorant and Y . N. Guo, High Energy Physics with Polarized Beams and Polarized Targets, ed. by C. Joseph and J. Soffer (Birkhuser, Verlag, 1981) pp. 453. Additive Versus Multiplicative Muon Conservation, P. NBmethy and V. W. Hughes, Comments on Nuclear and Particle Physics 10, 147-153 (1981). Observation of Muonium in Vacuum, P. R. Bolton, A. Badertscher, P. 0. Egan, C. J. Gardner, M. Gladisch, V. W. Hughes, D. C. Lu, M. Ritter, P. A. Souder, J. Vetter, G. zu Putlitz, M. Eckhause and J. Kane, Phys. Rev. Lett. 47, 1441-1444 (1981). Polarization Effects, V. W. Hughes et al., ISABELLE, Proceedings of the 1981 Summer Workshop, (Brookhaven National Laboratory, 1981) pp. 601617.
238 203. Plans for Measurement of Parity Nonconservation in Elastic Scattering of Polarized Electrons by Nuclei at the Bates Linear Accelerator Center, P. A. Souder, G. Cates, T. J. Gay, V. W. Hughes, D. C. Lu, C. W. Tu, S. Kowalski, W. Bertozzi, C. P. Sargent, W. Turchinetz, M. S. Lubell and R. Wilson, High Energy Physics with Polarized Beams and Polarized Targets, ed. by C. Joseph and J. Soffer, (Birkhauser, Verlag, 1981) pp. 454-457. 204. New Experimental Limit on the Muon-Neutrino Lifetime, J. S . Frank, R. L. Burman, D. R. F. Cochran, P. NBmethy, S. E. Willis, V. W. Hughes, R. P. Redwine, J. Duclos, H. Kaspar, C. K. Hargrove and U. Moser, Phys. Rev. D24, 2001-2003 (1981). 205. Precise Measurement of the Hyperfne-Structure Interval and Zeeman Effect in the Muonic Helium Atom, C. J. Gardner, A. Badertscher, W. Beer, P. R. Bolton, P. 0. Egan, M. Gladisch, M. Greene, V. W. Hughes, D. C. Lu, F. G. Mariam, P. A. Souder, H. Orth, J. Vetter and G. zu Putlitz, Phys. Rev. Lett. 48, 1168-1171 (1982). 206. Measurement of Spin-Exchange Effects in Electron-Hydrogen Collisions: 90" Elastic Scattering from 4 to 30 eV, G. D. Fletcher, M. J. Alguard, T. J. Gay, V. W. Hughes, C. W. Tu, P. F. Wainwright, M. S. Lubell, W. Raith and F. C. Tang, Phys. Rev. Lett. 48, 1671-1674 (1982). 207. Dynamic Nuclear Polarization of Irradiated Targets, M. L. Seely, A. Amittay, M. R. Bergstrom, S. K. Dhawan, V. W. Hughes, R. F. Oppenheim, K. P. Schuler, P. A. Souder, K. Kondo, S. Miyashita, K. Morimoto, S. J. St. Lorant, Y . N. Guo and A. Winnacker, Nucl. Inst. Meth. 201, 303-308 (1982). 208. Higher Precision Measurement of the hfs Interval of Muonium and of the Muon Magnetic Moment, F. G. Mariam, W. Beer, P. R. Bolton, P. 0. Egan, C. J. Gardner, V. W. Hughes, D. C. Lu, P. A. Souder, H. Orth, J. Vetter, U. Moser and G. zu Putlitz, Phys. Rev. Lett. 49, 993-996 (1982). 209. Theoretical Hyperfine Structure of the Muonic 3He and 4He Atoms, K. N. Huang and V. W. Hughes, Phys. Rev. A26, 2330-2333 (1982). 210. Summary Talk. V. W. Hughes, Polarized Proton Ion Sources, ed. by A. D. Krisch and A. T. M. Lin, (AIP, 1982) pp. 8-20. 211. Measurement of Spin-Exchange Effects in Electron-Hydrogen Collisions: Further Studies of Impact Ionization, T. J. Gay, G. D. Fletcher, M. J. Alguard, V. W. Hughes, P. F. Wainwright and M. S. Lubell, Phys. Rev. A26, 3664-3667 (1982). 212. Workshop Report o n Polarized Proton Ion Sources, V. W. Hughes, High Energy Spin Physics 1982, ed. by G. Bunce, (AIP, 1983) pp. 534-545. 213. Polarized Electron Source for Parity Experiment at Bates, P. Souder, A. Barber, W. Bertozzi, G. Cates, G. Dodson, T. J. Gay, M. Goodman, V. W. Hughes, S. Kowalski, M. S. Lubell, A. Magnon, C. P. Sargent, R. Schaefer, W. Turchinetz and R. Wilson, High Energy Spin Physics 1982, ed. by G. Bunce, (AIP, 1983) pp. 574579. 214. Measurement of the Internal Spin Structure of the Proton, R. Oppenheim, G. Baum, M. R. Bergstrom, P. R. Bolton, J. E. Clendenin, N. R. DeBotton, S. K. Dhawan, R. A. Fong-Tom, Y. N. Guo, V. R. Harsh, V. W. Hughes, K.
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Kondo, M. S. Lubell, C. L. Mao, R. H. Miller, S. Miyashita, K. Morimoto, U. F. Moser, I. Nakano, D. A. Palmer, L. Panda, W. Raith, N. Sasao,K. P. Schuler, M. L. Seely, J. Sodja, P. A. Souder, S. J. St. Lorant, K. Takikawa and M. Werlen, High Energy Spin Physics 1982, ed. by G. Bunce, (AIP, 1983) pp. 255-258. Status of the A G S Polarized H - Source, A. Kponou, K. P. Schuler and V. W. Hughes, High Energy Spin Physics 1982, ed. by G. Bunce, (AIP, 1983) pp. 607-610. Dynamic Nuclear Polarization of Irradiated Targets, M. L. Seely, A. Amittay, M. R. Bergstrom, S. K. Dhawan, V. W. Hughes, R. F. Oppenheim, K. P. Schuler, P. A. Souder, K. Kondo, S. Miyashita, K. Morimoto, J. S. St. Lorant, Y. N. Guo and A. Winnacker, High Energy Physics 1982, ed. by G. Bunce, (AIP, 1983) pp. 526-533. Internal Spin Structure of the Nucleon, V. W. Hughes and J. Kuti, Ann. Rev. Nucl. Part. Sci. 33, 611-644 (1983). New Measurement of Deep-Inelastic e-p Asymmetries, G. Baum, M. R. Bergstrom, P. R. Bolton, J. E. Clendenin, N. R. DeBotton, S. K. Dhawan, Y. N. Guo, V. R. Harsh, V. W. Hughes, K. Kondo, M. S. Lubell, Z. L. Mao, R. H. Miller, S. Miyashita, K. Morimoto, U. F. Moser, I. Nakano, R. F. Oppenheim, D. A. Palmer, L. Panda, W. Raith, N. Sasao, K. P. Schuler, M. L. Seely, P. S. Souder, S. J. St. Lorant, K. Takikawa and M. Werlen, Phys. Rev. Lett. 51, 1135-1138 (1983). Reply to “Direct Comparison Between the Ray Fluxes from Proton Beam Dumps at LAMPF and SIN,” J. S . Frank, R. L. Burman, D. R. F. Cochran, P. NBmethy, S. E. Willis, V. W. Hughes, R. P. Redwine, J. Duclos, H. Kaspar, C. K. Hargrove; U. Moser, Phys. Rev. D28, 1790-1792 (1983). Precision Exotic Atom Spectroscopy. V. W. Hughes, Precision Measurement and Fundamental Constants 11, ed. by B. N. Taylor and W. D. Phillips, (Natl. Bur. Stand, (U.S.), Spec. Publ. 617, 1984) pp. 237-248. Formation of Muonium in the ZS State and Observation of the Lamb Shift Transition, A. Badertscher, S . Dhawan, P. 0. Egan, V. W. Hughes, D. C. Lu, M. W. Ritter, K. A. Woodle, M. Gladisch, H. Orth, G. zu Putlitz, M. Eckhause, J. Kane, F. G. Mariam and J. Reidy, Phys. Rev. Lett. 52, 914-917 (1984). Muonium Has Not Yet Decayed!, V. W. Hughes and G. zu Putlitz, Comments Nucl. Part. Phys. 12, 259-272 (1984). Precision Determination of the Hyperfine-Structure Interval in the Ground State of Positronium, V. M. W. Ritter, P. 0. Egan, V. W. Hughes and K. A. Woodle, Phys. Rev. 30, 1331-1338 (1984). A Possible Higher Precision Measurement of the Muon g-2 Value, V. W. Hughes and G. T. Danby, Intersections Between Particle and Nuclear Physics, ed. by R. E. Mischke, (AIP 123, 1984) pp. 534537. The Lamb Shift in Muonium. A. Badertscher, V. W. Hughes, D. C. Lu, M. W. Ritter, K. A. Woodle, M. Gladisch, H. Orth, G. zu Putlitz, M. Eckhause, J. Kane and F. G. Mariam, Atomic Physics 9, ed. by R. S. van Dyck, Jr. and E. N. Fortson, (World Scientific, 1985) pp. 83-98.
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226. Development of ‘Subsurface” Positive Muon Beam at LAMPF, A. Badertscher, P. 0. Egan, M. Gladisch, M. Greene, V. W. Hughes, F. G. Mariam, D. C. Lu, G. zu Putlitz, M. W. Ritter, G. Sandars, P. A. Souder and R. Werbeck, Nucl. Instr. and Meth. A238, 200-205 (1985). 227. The Anomalous Magnetic Moment of the Muon, V. W. Hughes, and T. Kinoshita, Comments on Nucl. Particle Physics 14, 341-360 (1985). 228. The Muon and the Electron, V. W. Hughes, Ann. Phys. Fr. 10, 955-983 (1985). 229. Experimental Study of Spin-Exchange Eoects in Elastic and Ionizing Collisions of Polarized Electrons with Polarized Hydrogen Atoms, G. D. Fletcher, M. J. Alguard, T. J. Gay, V. W. Hughes, P. F. Wainwright, M. S. Lubell and W. Raith, Phys. Rev. A31, 28542884 (1985). 230. High-Energy Polarized Electrons and Muons as a Probe for Studying the Quark Structure of Hadrons, V. W. Hughes, Proc. Sixth Int. Symp. Polar. Phenom. in Nucl. Phys., Osaka, 1985, J. Phys. SOC.Jpn. 55, 327-343 (1986). 231. The Muon Anomalous g-Value. V. W. Hughes, Proc. of the Workshop on Fundamental Muon Physics: Atoms, Nuclei, and Particles, LA-l0714C, Los Alamos National Laboratory, (Los Alamos, New Mexico, May, 1986) pp. 87-98. 232. Muonium, H. Orth and V. W. Hughes, Proc. of the Workshop on Fundamental Muon Physics: Atoms, Nuclei, and Particles, LA-l0714C, Los Alamos National Laboratory, (Los Alamos, New Mexico, May, 1986) pp. 62-74. 233. Storage Ring Magnet for a Proposed New Precision Measurement of the Muon Anomalous Magnetic Moment, V. W. Hughes, G. Danby, J. Jackson, E. Kelly, A. Prodell, R. Shutt, W. Stokes, S. K. Dhawan, A. Disco, F. J. M. Farley, Y. Kuang, H. Orth, G. Vogel, W. Williams, F. Krienen, M. Lubell, P. Marston and J. Tarrh, Intersections Between Particle and Nuclear Physics, ed. by D. F. Geesaman, (AIP, New York, 1986) pp. 382-390. 234. Workshop Summary, V. W. Hughes, Proceedings of the Parity Violation Workshop, CEBAF (December, 1986) pp. 317-330. 235. Atomic Physics and Fundamental Principle, V. W. Hughes, Atomic Physics 10, ed. by H. Narumi and I. Shimamura (Elsevier Science Publishers, 1987) pp. 1-34. 236. Atomic Physics and Fundamental Principles, V. W. Hughes, Nucl. Phys. A463, 3 ~ - 3 6(1987). ~ 237. The Muon Anomalous g-Value, V. W. Hughes, Fundamental Symmetries, ed. by P. Bloch, P. Pavlopoulos and R. Klapisch, (Plenum Publishing Corp., 1987) pp. 271-285. 238. Muonium, V. W. Hughes, Fundamental Symmetries, ed. by P. Bloch, P. Pavlopoulos and R, Klapisch, (Plenum Publishing Corp., 1987) pp. 287300. 239. First Observation of the Negative Muonium Ion Produced by Electron Capture in a Beam-Foil Experiment, Y. Kuang, K. P. Arnold, F. Chmely, M. Eckhause, V. W. Hughes, J. R. Kane, S. Kettell, D. H. Kim, K. Kumar, D. C. Lu, B. Ni, B. Matthias, H. Orth, G. zu Putlitz, H. R. Schaefer, P. A. Souder.and K. Woodle, Phys. Rev. A35, 3172-3175 (1987).
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240. Search for Spontaneous Conversion of Muonium to Antimuonium, B. Ni, K. P. Arnold, F. Chmely, V. W. Hughes, S. H. Kettell, Y. Kuang, J. Markey, B. E. Matthias, H. Orth, H. R. Schaefer, K. Woodle, M. D. Cooper, C. M. Hoffman, G. E. Hogan, R. E. Mischke, L. E. Piilonen, R. A. Williams, M. Eckhause, P. Guss, J. Kane, J. Reidy and G. zu Putlitz, Phys. Rev. Lett. 59, 2716-2719 (1987). 241. Exclusive po and 4 Production in Deep Inelastic Muon Scattering, EMC Collaboration, J. Ashman, et al., Z. Phys. C 39, 169-175 (1988). 242. Search for Spontaneous Conversion of Muonium to Antimuonium, B. Ni, K. P. Arnold, F. Chmely, V. W. Hughes, S. H. Kettell, Y. Kuang, J. Markey, B. E. Matthias, H. Orth, H. R. Schaefer, K. Woodle, M. D.Cooper, C. M. Hoffmann, G. E. Hogan, R. E. Mischke, L. E. Piilonen, R. A. Williams, M. Eckhause, P. Guss, J. Kane, J. Reidy, and G. zu Putlitz, Nucl. Phys. A478, 7 5 7 ~ - 7 6 7(1988). ~ 243. Ultraprecise Superferric Storage Ring Magnet for the Muon G-2 Experiment, D. Brown, T . dewinter, F. Krienen, D. Loomba, D. Stassinopoulos, G. Cottingham, J. Cullen, G. Danby, J. Jackson, E. Kelly, S. Kuznetsov, M. May, I. Polk, A. Prodell, R. Shutt, W. Stokes, K. Endo, H. Hirabayashi, S. Kurokawa, Y . Yamamoto, P. G. Marston, J. M. Tarrh, K. Nagamine, J. M. Bailey, A. Disco, S. K. Dhawan, F. J. M. Farley, V. W. Hughes, Y . Kuang, and G. Vogel, IEEE Trans. Magn. 24, 1381-1383 (1988). 244. The Muon Anomalous Magnetic Moment, V. W. Hughes, Physica Scripta T22, 111-118 (1988). 245. A Measurement of the Spin Asymmetry and Determination of the Structure Function g1 in Deep Inelastic Muon-Proton Scattering, EMC Collaboration, J. Ashman, et al., Phys. Lett. B206, 364-370 (1988). 246. Measurement of the Polarization of Thermal Muonium in Vacuum, K. A. Woodle, K. P. Arnold, M. Cladisch, J. Hofmann, M. Janousch, K. P. Jungmann, H. J. Mundinger, G. zu Putlitz, J. Rosenkranz, W. Schafer, G. Schiff, W. Schwarz, V. W. Hughes and S. H. Kettell, Z. Phys. D9, 59-64 (1988). 247. The Integral of the Spin-Dependent Structure Function g y and the Ellis Jaffe S u m Rule, V. W. Hughes, V. Papavassiliou, R. Piegaia, K. P. Schuler and G. Baum, Phys. Lett. 212B, 511-514 (1988). 248. Measurement of the Ratios of Deep Inelastic Muon-Nucleus Cross Sections on Various Nuclei Compared to Deuterium, EMC Collaboration, J. Ashman, et al., Phys. Lett. B202, 603-610 (1988). 249. Progress Report on the Bates Parity Experiment, P. A. Souder, D. H. Kim, K. S. Kumar, M. E. Schulze, M. S. Lubell, J. S. Patch, R. Wilson, G. W. Dodson, K. A. Dow, M. Farkhondeh, J. Flanz, K. Isakovich, S. Kowalski, C. P. Sargent, W. Turchinetz, G. D. Cates, V. W. Hughes, R. Michaels and H. R. Schaefer, Intersections Between Particle and Nuclear Physics, ed. by G. Bunce (Alp Cnf. Proc. 176, 1988) pp. 543-548. 250. The Electrical Neutrality of Atoms, V. W. Hughes, L. J. Fraser and E. R. Carlson, Z. Phys. D10, 145-151 (1988). 251. Measurements of Nucleon Spin-Dependent Structure Functions - Past and Future, V. W. Hughes, Proceedings of the Symposium on Future Polarization Physics at Fermilab, (1988) pp. 19-36.
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252. Atoms, Molecules and I. I. Rabi (Post- World War 11Period), V. W. Hughes, Atomic Physics 11, ed. by S. Haroche, J. C. Gay and G. Grynberg, (World Scientific, 1989) pp. 15-35. 253. Some Recent Advances in Muonium, V. W. Hughes, The Hydrogen Atom, ed. by G. F. Bassani, M. Inguscio and T. W. Hnsch, (Springer-Verlag, Berlin, Heidelberg, 1989) pp. 171-181. 254. Muon Anomalous Magnetic Moment, V. W. Hughes, Particles and Fields Series 37, ed. by K. J. Heller (Alp Conf. Proc. 187, 1989) pp. 326-347. 255. First Observation of the Free Pionium Atom in Vacuum, H. J. Mundinger, K.-P. Arnold, M. Gladisch, J. Hofmann, W. Jacobs, H. Orth, G. zu Putlitz, J: Rosenkranz, W. Schafer, K. A. Woodle and V. W. Hughes, Europhys. Lett. 8, 339-344 (1989). 256. The Bates Polarized Electron Source, G. D. Cates, V. W. Hughes, R. Michaels, H. R. Schaefer, T. J. Gay, M. S. Lubell, R. Wilson, G. W. Dodson, K. A. Dow, S. B. Kowaiski, K. IsakovichK. S. Kumar, M. E. Schulze, P. A. Souder and D. H. Kim, Nucl. Inst. and Meth. A278, 293-317 (1989). 257. Formation of the Negative Muonium Ion and Charge-Exchange Processes for Positive Muons Passing through Thin Metal Foils, Y . Kuang, K. P. Arnold, F. Chmely, M. Eckhause, V. W. Hughes, J. R. Kane, S. Kettell, D. H. Kim, K. Kumar, D. C. Lu, B. Matthias, B. Ni, H. Orth, G. zu Putlitz, H. R. Schaefer, P. A. Souder and K. Woodle, Phys. Rev. A39, 6109-6123 (1989). 258. Parity Violation in Electron Scattering from Carbon: A Progress Report, G. W. Dodson, K. A. Dow, M. Farkhondeh, J. Flanz, K. Isakovich, S. Kowalski, C. P. Sargent, W. Turchinetz, D. H. Kim, K. S. Kumar, P. A. Souder, M. S. Lubell, J.' S. Patch, R. Wilson, G. D. Cates, V. W. Hughes, R. Michaels and H. R. Schaefer, Particles and Fields Series 37, ed. by K. J. Heller, (Alp Conf. Proc. 187, 1989) pp. 486-492. 259. Search f o r Spontaneous Conversion of Muonium to Antimuonium, V. W. Hughes, B. E. Matthias, H. Ahn, A. Badertscher, F. Chmely, M. Eckhause, K. P. Jungmann, J. R. Kane, S. H. Kettell, Y . Kuang, H. J. Mundinger, B. Ni, H. Orth, G. zu Putlitz, H. R. Schaefer, M. T. Witkowski and K. A. Woodle, Nuclear Weak Process and Nuclear Structure, ed. by M. Morita, H. Ejiri, H. Ohtsubo and T. Sato, (World Scientific Pub.C0.,1989) pp. 157-163. 260. Acceleration of Polarized Protons to 22 GeV/c and the Measurement of Spin-Spin Eflects in p +p t- p p. F. Z. Khiari, P. R. Cameron, G. R. Court, D. G Crabb, M. Fujisaki, I. Gialas, P. H. Hansen, M. E. Hejazifar, A. D. Krisch, A. M. T. Lin, S. L. Linn, D. C. Peaslee, R. S. Raymond, R. R. Raylman, T. Roser, T. Shima, K. M. Terwilliger, L. A. Ahrens, J. G. Alessi, H. N. Brown, K. A. Brown, E. D. Courant, G. T. Danby, S. Giordano, H. J. Halama, A. Kponou, R. Lambiase, S. Y . Lee, Y . Y . Lee, R. E. Lockey, Y . I. Makdisi, P. A. Montemurro, R. J. Nawrocky, L. G. Ratner, J. F. Skelly, T. J. Sluyters, A. Soukas, S. Tepikian, R. L. Witkover, J. B. Roberts, G. C. Phillips, V. W. Hughes, P. Schuler, J. A. Bywater, R. L. Martin, J. R. O'Fallon, T. S. Bhatia, L. C. Northcliffe and M. Simonius, Phys. Rev. D39, 45-85 (1989).
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261. An Investigation of the Spin Structure of the Proton in Deep Inelastic Scattering of Polarized Muons on Polarized Protons, EMC Collaboration, J. Ashman, et al., Nucl. Phys. B328, 1-35 (1989). 262. Measurement of the Lamb Shift in the n = 2 State of Muonium, K. A. Woodle, A. Badertscher, V. W. Hughes, D. C. Lu, M. Ritter, M. Gladisch, H. Orth, G. zu Putlitz, M. Eckhause, J. Kane and F. G. Mariam, Phys. Rev. 41, 94105 (1990). 263. High Energy Physics with Polarized Electrons and Muons, V. W. Hughes, Nucl. Phys. A518, 371-388 (1990). 264. Muonium, V. W. Hughes and G. zu Putlitz, Quantum Electrodynamics, ed. by T. Kinoshita (World Scientific, 1990) pp. 822-904. 265. Fine Structure in the .@PState of Helium. F. M. J. Pichanick and V. W. Hughes, Quantum Electrodynamics, ed. by T. Kinoshita (World Scientific, 1990) pp. 905-936. 266. Measurement of Parity Violation in the Elastic Scattering of Polarized Electrons from 12C, P. A. Souder, R. Holmes, D. H. Kim, K. S. Kumar, M. E. Schulze, K. Isakovich, G. W. Dodson, K. A. Dow, M. Farkhondeh, S. Kowalski, M. S. Lubell, J. Bellanca, M. Goodman, S. Patch, R. Wilson, G. D. Cates, S. K. Dhawan, T. J. Gay, V. W. Hughes, A. Magnon, R. Michaels and R. Schaefer, Phys. Rev. Lett. 65, 694697 (1990). 267. A Spectrometer for Muon Scattering at the Tevatron, E665 Collaboration, M. R. Adams, et al., Nucl. Inst. Meth. A291, 533-551 (1990). 268. Results from the Bates 12CParity Experiment, P. A. Souder, J. Bellanca, G. D. Gates, G. W. Dodson, K. A. Dow, M. Farkhondeh, R. Holmes, V. W. Hughes, T. J. Gay, K. Isakovich, D. H. Kim, S. Kowalski, K. S. Kumar, M. S. Lubell, R. Michaels, J. S. Patch, H. R. Schaefer, M. E. Schulze and R. Wilson, PANIC XI1 Particles and Nuclei ed. by J. L. Matthews, T. W. Donnelly, E. H. Farhi, and L. S. Osborne (North Holland, Amsterdam, 1991) 695~-700~. 269. The Anomalous Magnetic Moment of the Muon, AGS 821 Collaboration, V. W. Hughes, et al.,High Energy Spin Physics, ed. by K. H. Althoff and W. Meyer, (Springer-Verlag, Germany, 1991) pp. 367-382. 270. The Anomalous Magnetic Moment of the Muon, V. W. Hughes, Cooler Rings and Their Applications, ed. by T. Katayama and A. Noda, (World Scientific, Singapore, 1991) pp. 156-165. 271. The Spin Dependent Structure Functions of the Nucleon, V. W. Hughes, Polarized Collider Workshop, ed. by J. Collins, S. F. Heppelman, R. W.; Robinett, (Alp Conf. Proc. 223, NY, 1991) pp. 51-64. 272. Distributions of Charged Hadrons Observed in Deep-Inelastic MuonDeuterium Scattering at 490 GeV, E665 Collaboration, M.R. Adams et al., Phys. Lett. B 272, 163-168 (1991). 273. New Search for the Spontaneous Conversion of Muonium to Antimuonium, B. E. Matthias, H. E. Ahn, A. Badertscher, F. Chmely, M. Eckhause, V. W. Hughes, K. P. Jungmann, J. R. Kane, S. H. Kettell, Y . Kuang, H. J. Mundinger, B. Ni, H. Orth, G. zu Putlitz, H. R. Schaefer, M. T. Witkowski and K. A. Woodle, Phys. Rev. Lett. 66, 2716-2719 (1991).
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274. The Meson Factories, by D. Torlief, E. 0. Ericson, V. W. Hughes, and D. E. Nagle (University of California Press, 1991). 275. Bates Parity Experiment on Elastic Electron Carbon Scattering, J. Bellanca, G. D. Cates, S. K. Dhawan, G. W. Dodson, K. A. Dow, M. Farkondeh, R. Holmes, V. W. Hughes, T. G. Gay, K. Isakovich, D. H. Kim, S. Kowalski, K. S. Kumar, M. S. Lubell, A. Magnon, R. Michaels, J. S. Patch, H. R.Schaefer, M. E. Schulze, P. A. Souder and R. Wilson, High Energy Spin Physics, ed. by K. H. Althoff and W. Meyer (Springer-Verlag, Germany, 1991) pp. 577584. 276. Experiments on Nucleon Spin-Dependent Structure Function, G. Igo and V. W. Hughes, Vancouver Meeting Particles & Fields 91, ed. by D. Axen, D. Bryman, M. Comyn (World Scientific, 1992) pp. 593-602. 277. Anomalous Magnetic Moment of the Muon, V. W. Hughes, Particles, Strings & Cosomology, ed. by P. Nath and S. Reucroft (World Scientific, 1992), pp. 868-897. 278. Summary, V. W. Hughes, The Future of Muon Physics, ed. by K. Jungmann, V. W. Hughes and G. zu Putiitz, (Springer-Verlag, Berlin Heidelberg, 1992), pp. 301-305. 279. Muonium, V. W. Hughes, The Future of Muon Physics, ed. by K. Jungmann, V. W. Hughes and G. zu Putlitz, (Springer-Verlag, Berlin Heidelberg, 1992), pp. 35-43. 280. Thermal Muonium in Vacuo from Silica Aerogels, W. Schwarz, V. Ebert, H. Geerds, K. Jungmann, S. Kirches, S. Koppe, F. Maas, H. J. Mundinger, G. zu Putlitz, J. Rosenkranz, W. Schafer, G. Schiff, Z. Zhang, M. G. Boshier and V. W. Hughes. J. of Non-Crystalline Solids 145, 244249 (1992). 281. Shadowing in the Muon-Xenon Inelastic Scattering Cross Section at 490 GeV, E665 Collaboration, M. R. Adams et al., Phys. Lett. B 287, 375-380 (1992). 282. Muon production of J/@ and the Gluon Distribution of the Nucleon, EMC Collaboration, J. Ashman et al., Z. Phys. C 56, 21-28 (1992). 283. Search for Spontaneous Conversion of Muonium to Antimuonium, B. Ni, K. P. Arnold, F. Chmely, M. D. Cooper, M. Eckhause, P. P. Cuss, C. M. Hoffman, G. E. Hogan, V. W. Hughes, J. R. Kane, S. H. Kettell, Y . Kuang, J. Markey, B. E. Matthias, R. E. Mischke, H. Orth, L. B. Piilonen, G. zu Putlitz, J. Reidy, H. R. Schaefer, R. A. Williams and K. A. Woodle, Phys. Rev. D48, 1976-1989 (1993). 284. Measurement of the Spin-Dependent Structure Function g 1 ( x ) of the Deuteron, SMC Collaboration, B. Adeva, et al. Phys. Lett. B302, 533-539 (1993). 285. Measurement of Cross Section Ratios in Inelastic Muon-Nucleon Scattering at Very Low x and Q2, E665 Collaboration, M.R. Adams et al., Phys. Lett. B309 477 (1993). 286. A Measurement of the Ratio of the Nucleon Structure Function in Copper and Deuterium, EMC Collaboration, J. Ashman et al., Z. Phys. C 57 211218 (1993).
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287. Saturation of Shadowing at Very Low X B J . , E665 Collaboration, M. R. Adams et al., Phys. Rev. Lett. 68 3266-3269 (1992). 288. First Measurements of Jet Production Rates in Deep-Inelastic LeptonProton Scattering, E665 Collaboration, M. R. Adams et al., Phys. Rev. Lett. 69 1026-1029 (1992). 289. The Anomalous Magnetic Moment of the Muon, V. W. Hughes, et al. Frontiers of High Energy Spin Physics ed. by T. Hasegawa, N. Horikawa, A. Masaike, S. Sawada, (Universal Academy Press, Inc., Tokyo, Japan 1993) pp. 717-722. 290. A Chopped High Intensity Muon Beam at the Stopped Muon Channel at LAMPF, D. Ciskowski, H. Ahn, R. Dixson, X. Fei, V. W. Hughes B. E. Matthias, C. Pillai, K. Woodle, Nucl. Instr. and Meth. A333 260-264 (1993). 291. Perturbative QCD Effects Observed in 490 GeV Deep-Inelastic Muon Scattering, E665 Collaboration, M. R. Adams et al., Phys. Rev. D 48, 5057-5066 (1993). 292. A n Investigation of Bose-Einstein Correlations in Muon-Nucleon Interactions at 490 GeV, E665 Collaboration, M. R. Adams et al., Phys. Lett. B 308, 418-424 (1993). 293. Two-Photon Laser Spectroscopy of the Muonium 1s-2s Transition, K. Jungmann, P. E. G. Baird, J. R. M. Barr, D. Berkeland, M. G. Boshier, B. Braun, G. H. Eaton, A. I. Ferguson, H. Geerds, V. W. Hughes, F. Maas, B. Matthias, P. Matousek, M. Persaud, G. zu Putlitz, I. Reinhard, B. Riis, P. G. H. Sandars, W. Schwarz, W. T. Toner, M. Towrie, L. Willmann, K. A. Woodle, G. Woodman and L. Zhang, Proceedings of the International Workshop on Low Energy Muon Science LEMS '93 LA-12698-C ed. by M. Leon (Los Alamos National Laboratory, 1994). 294. The New Muonium Hyperfine Structure Experiment, M. G. Boshier, D. E. Ciskowski, S. K. Dhawan, X. Fei, V. W. Hughes, M. Janousch, K. Jungmann, W. Liu, C. Pillai, R. Prigl, G. zu Putlitz, W. Schwarz, P. A. Souder, 0. van Dyck, X. Wang, K. A. Woodle, and Q. Xu Proceedings of the International Workshop on Low Energy Muon Science LEMS '93 LA-12698-C ed. by M. Leon (Los Alamos National Laboratory, 1994). 295. Development of a Chopped High Intensity Muon Beam at LAMPF, X. Fei, D. Ciskowski, H. Ahn, R. Dixson, V. W. Hughes, B. E. Matthias, C. Pillai, and K. Woodle, Proceedings of the International Workshop on Low Energy Muon Science LEMS '93 LA-12698-C ed. by M. Leon (Los Alamos National Laboratory, 1994). 296. Experiments on Nucleon Spin-Dependent Structure Functions, V. W. Hughes, Quest for Links to New Physics, ed by Z. Ajduk, S. Pokorski, A. K. Wroblewski, (World Scientific, 1993) pp. 359-366. 297. A Measurement of the 1s-2s Transition Frequency in Muonium, F. E. Mass, B. Braun, H. Geerds, K. Jungmann, B. E. Matthias, G. zu Putlitz, I. Reinhard, W. Schwarz, L. Willmann, L. Zhang, P. E. G. Baird, P. G. H. Sandars, G. S. Woodman, G. H. Eaton, P. Matousek, W. T. Toner, M. Towrie, J. R. M. Barr, A. I. Ferguson, M. A. Persaud, E. Riis, I. D. Berkeland, M. G. Boshier, V. W. Hughes and K. A. Woodle, Phys. Lett. A 187, 247-254 (1994).
246 298. Combined Analysis of World Data o n Nucleon Spin Structure Functions, SMC Collaboration B. Adeva et al., Phys. Lett. B 320 400-406 (1994). 299. Measurement of the Spin-Dependent Structure Function g 1 (x)of the Proton, SMC Collaboration, B. Adeva et a1 Phys. Lett. B329, 399-406 (1994). 300. Measurement of the Polarization of a High Energy Muon Beam. SMC Collaboration, B. Adeva et al., Nucl. Instr. and Meth. A343, 363-373 (1994). 301. Measurement of the Deuteron Polarization in a Large Target, SMC Collaboration, B. Adeva et al., Nuc.1nst. and Methods. A349. 334-344 (1994). 302. Spin Asymmetry in Muon-Proton Deep Inelastic scattering on a P a n s uersely Polarized Target, SMC Collaboration, B. Adeva et a1 ., Phys. Lett. B336 125-130 (1994). 303. Q2 Dependence of the Average Squared ' h n s v e r s e Energy of Jets in Deep Inelastic Muon-Nucleon Scattering with Comparison to Perturbatiue QCD Predictions, E665 Collaboration, M.R. Adams et al., Phys. Rev. Lett. 72, 466-469 (1994). 304. Scaled Energy ( z ) Distributions of Charged Hadrons Observed in DeepInelastic Muon Scattering at 490 GeV from Xenon and Deuterium Targets, E665 Collaboration M.R. Adams et al., Phys. Rev. D 50 1836-1873 (1994) 305. Density and Correlation Integrals in Deep-Inelastic Muon-Nucleon Scatteri n g at 490 Ge V , E665 Collaboration M.R. Adams et al., Phys. Letts. B 335, 535-541 (1994). 306. Production of Charged Hadrons b y Positive Muons o n Deuterium and Xenon at 490 GeV, E665 Collaboration M.R. Adams et al., Z. Phys. C 61, f79-19.8 (1994). 307. Measurement of the Muonium Hyperfine Structure in Vacuo - A Test of Fundamental Electromagnetic Interactions, K. Jungmann, V. Ebert, V.W. Hughes, M. Janousch, S. Kirches, S. Koppe, F. Mass, G. zu Putlitz, J. Rosenkranz, W. Schaefer, G. Schiff and W. Schwarz, Appl. Phys. B 60 S159-S164 (1995). 308. Internal Spin Structure of the Nucleon from Experiments of the Spin Muon Collaboration, V. W. Hughes, Deep Inelastic Scattering and Related Subjects, ed. A. Levy (World Scientific, Singapore, 1995) pp. 237-262. 309. The Anomalous Magnetic Moment of the Muon, V. W. Hughes, Gift of Prophecy, Essays in Celebration in the Life of Robert Eugene Marshak, ed by E. C. G. Sudarshan World Scientific, Pub. Co., (1995) pp. 222-251. 310. Internal Spin Structure of the Nucleon, V.W. Hughes, Strings and Symmetries ed. by G. Aktas, C. Saclioglu and M. Serdaroglu (Springer-Verlag, 1995) pp. 356-359. 311. Observation of Resonance Line Narrowing for Old Muonium,. M. G. Boshier, S. K. Dhawan, X. Fei, V. W. Hughes, M. Janousch, K. Jungmann, W. Liu, C. R. Prigi, G. zu Putlitz, I. Reinhard, W. Schwarz, P. A. Souder, 0. van Dyck, X. Wang, K. A Woodle, and Q. Xu, Phys. Rev. A 52 1948-1953(1995). 312. Internal Spin Structure of the Nucleon, ed. by V. W. Hughes and C. Cavata (World Scientific, Singapore, 1995).
247 313. Previous Experiments on Polarized Structure Functions, V. W. Hughes, Internal Spin Structure of the Nucleon ed. by V. W. Hughes and C. Cavata (World Scientific, Singapore, 1995) pp 1-33. 314. Spectroscopy of the 1s-2s Energy Splitting in Muonium, W. Schwarz, P. E. G. Baird, J. R. M. Barr, D. Berkeland, M. G. Boshier, B. Braun, G. H. Eaton, A. I. Ferguson, H. Geerds, V. W. Hughes, K . Jungmann, F. Mass, B. E. Matthias, P. Matousek, M. A. Persaud, G. zu Putlitz, I. Reinhard, ERiis, P. G. H. Sandars, W. T. Toner, M. Towrie, L. Willmann, K. A. Woodle, G. S. Woodman and L. Zhang, IEEE Trans. lnstrum. Meas. 44 505-509 (1995). 315. A New Measurement of the Spin-Dependent Structure Function g 1 (x) of the Deuteron, SMC Collaboration B. Adeva et al., Phys. Lett. B 357 248-254 (1995). 316. Nuclear Shadowing, Diffmctive Scattering and Low Momentum Protons in Muon-Xe Interactions at 490 GeV, E665 Collaboration, M. R. Adams et al., Z. Phys. C 65, 225-244 (1995). 317. Extraction of the Ratio F T I F l from Muon-Deuteron and Muon-Proton Scattering at Small x and Q 2 ,E665 Collaboration, M. R. Adams et al., Phys. Rev. Lett. 75, 1466-1480 (1995). 318. Nuclear Decay Following Deep Inelastic Scattering of470 GeV Muons, E665 Collaboration, M. R. Adams et al., Phys. Rev Lett. 74, 5198-5201 (1995). 319. Measurement of Nuclear Transparencies from Exclusive po Meson Production in Muon-Nucleus Scattering at 470 GeV, E665 Collaboration, M . R. Adams et al., Phys. Rev. Lett 74, 1525-1529 (1995). 320. Shadowing in Inelastic Scattering of Muons Off Carbon, Calcium and Lead at Low X B J , E665 Collaboration, M. R. Adams et al., Z. Phys. C 67, 403-410 (1995). 321. Future HERA Experiment with 800 GeV Polarized Protons, V. W. Hughes, Workshop on Deep Inelastic Scattering and QCD ed. by J. F. Laporte and Y. Siros, (Edition du Bicentenaire, Ecole Polytechnique, France, 1995) pp. 515-517. 322. Muons and Nuclei, V. W. Hughes and J. D. Walecka, Symmetries and Fundamental Interactions in Nuclei ed. by W. C. Haxton and E. M. Henley, (World Scientific, Singapore, 1995) pp. 389-435. 323. Nucleon Spin Structure from Polarized Deep Inelastic Muon-Nucleon Scattering at CERN, V. W. Hughes on behalf of SMC Collaboration, XVII International Symposium on Lepton-Photon Interactions LP95 ed. by Z. Zhi-Peng and C. He-Sheng, (World Scientific, Singapore, 1996) pp. 147-169. 324. Spin Physics A Personal Recollection, V. W. Hughes, Workshop on the Prospects of Spin Physcis at HERA ed. by J. Blumlein and W. D. Nowak (DESY 952000) (1995) pp. 358-369. 325. Spin Structure Function Measurements with Polarized Protons and Electrons at HERA, R. D. Ball, A. Deshpande, S. Forte, V. W. Hughes, J. Lichtenstadt, and G. Ridolfi, Workshop on the Prospects of Spin Physics a HERA ed.by J. Blumlein and W. D. Nowak (DESY 95-2000) pp. 350-357.
248 326. Polarization of Valence and Non-Strange Sea Quarks in the Nuclean from Semi-Inclusive Spin Asymmetries, SMC Collaboration, B. Adeva et al., Lett. B~369, 93-100 (1996) 327. Perspectives of High Precision Atomic Spectroscopy of Muonic Atoms, M. G. Boshier, V. W. Hughes, K. Jungmann, and G. zu Putlitz, Comments At. And Mol. Phys. 33, 17-28 (1996). 328. High Precision Atomic Spectroscopy of Muonium and Simple Muonic Atoms, V. W. Hughes, Symposium on Atomic Physics Methods in Modern Research, Heidelberg, Germany (Feb., 1996). 329. Prospective Measurements of the Spin Structure Functions gy(x, Q 2 ) by ep Collisions at HERA, J. Lichtenstadt, A. Deshpande, and V. W. Hughes, SPIN'96 Proceedings, ed. C. W. de Jagr, T. J. Ketel, P. J. Mulders, J . E. J. Oberski and M. Oskam-Tamoezer (World Scientific, Singapore, 1997) pp. 422-425. 330. The Status of the Muon 9-2 Experiment, Muon 9-2 Collaboration, J. Berante et al., (World Scientific Singapore, 1997) pp. 250-251. 331. Improved Upper Limit on Muonium to Antimuonium Conversion, R. Abela, J. Bagaturia, W. Bertl, R. Engfer, B. Fischer von Weikersthal, A. Grobmann, V. W. Hughes, K. Jungmann, D. Kampmann, V. Karpuchin, I. Kisel, A. Klaas, S. Korenchenko, N. Kuchinsky, A. Leuschner, B. E. Matthias, R. Menz, V. Meyer, D. Mzavia, G. Otter, T. Prodscha, H. S. Pruys, G. zu Putlit, W. Reichart, 1. Reinhard, D. Renker, T. Sakhelashvilli, P. V. Schimdt, R Seeliger, H. K.walter, L. Willmann and L. Zhang, Phys. Rev Lett, 77 1950-1953 (1996). 332. Large Enchancement of Deuteron Polarization with Frequency Modulated, SMC Collaboration, B. Adeva et al., Nucl. Inst. Meth. A 372, 339-343 (1996). 333. Determination of the Gluon Distribution Function of the Nucleon Using Energy-Energy Angular Pattern I Deep-Inelastic Muon-Deuteron Scattering, E665 Collaboration, M.R. Adams et al., Z Phys. C 71, 391-403 (1996). 334. Spin Structure of the Proton from Polarized Inclusive Deep-Inelastic MuonProton Scattering, SMC Collaboration B. Adeva et al., Phys. Rev. D, 5330 (1997). 335. The Spin-Dependent Structure Function g1 (x) of the Deuteron from Polarized Deep-Inelastic Muon Scattering, SMC Collaboration, B. Adeva et a]., Phys. Lett. B396 338-348 (1997). 336. The Spin-Dependent Structure Function g1(x) of the Proton from Polarized Deep-Inelastic Muon Scattering, SMC Collaboration, B. Adeva et al., Phys. Lett. B412 414 (1997). 337. Round Table on Future Measurements of the Polarized Gluon Distribution in the Nucleon, V. W. Hughes, S. Forte, J. Collins, A. De Roeck, A. Deshpande, G. Mallot, R. Arnold, G. Bunce, W.-D. Nowak and E. W. Hughes in SPIN '96 Proceedings, eds. C. W. de Jager, T. J. Ketel, P. J. Mulders, E. J. Oberski and M. Oskam-Tamboezer (World Scientific, Singapore) pp. 643648 (1997).
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338. A Line-Shape Analysis f o r Spin-1- N M R Signals, C. Dulya, D. Adams et a1 (SMC Collaboration) Nucl. Inst. Meth., A398 109-125 (1997). 339. LAMPF Users Group, Inc. (LUGI) Symposium: Proceedings of 20 Years of Meson Factory Physics: Accomplishments and Prospects, ed. B. F. Gibson, C. M. Hoffman, P. D. Barnes, and V. W. Hughes (World Scientific, Singapore) 1997. 340. Precision Measurement of the Magnetic Field in Terms of the Free-Proton N M R Frequency, X. Fei, V. W. Hughes, and R. Prigl. Nuc. Inst. Meth. A 394 349-356 (1997). 341. Measurement of the Polarized Structure Function g y ( x , Q 2 ) and the Polarized Gluon Distribution A g ( x 1 Q 2 ) at H E R A , in Deep Inelastic Scattering off Polarized Targets; Theory Meets Experiment, Proceedings of the Workshop, Zeuthen, Sept. 1-5, 1997, ed. J. Blumlein, et a1 (DESY, 1997). 342. Polarised Quark Distribution i n the Nucleon f r o m Semi-Inclusive Spin Asymmetries, SMC Collaboration, B. Adeva et al., Phys. Lett. B420, 180190 (1998). 343. Measurement of the t Distribution an Diffractive Photoproduction at H E R A , ZEUS Collaboration, J. Breitweg, et al., Eur. Phys. J. C2, 237-246 (1998). 344. Elastic and Proton-dissociative p o Photoproduction at H E R A , ZEUS Collaboration, J. Breitweg et al., Eur. Phys. J C2, 247-267 (1998). 345. Event Shape Analysis of Deep Inelastic Scattering Events with a Large Rapidity Gap at H E R A , ZEUS Collaboratoin, J. Breitweg, et al. Phys. Lett. B421 368-384 (1998). 346. High Precision Spectroscopy of Positronium and Muonium, in Advances in Quantum Chemistry, Volume 30, (Academic Press, 1998) pp 99-123. 347. Prospects of High Energy Polarized ep Colliders, V. W. Hughes, SPIN 2000 Proceedings, Osaka, Japan. 348. The Q 2 dependence of dijet cross-sections i n ep interactions at H E R A , ZEUS Collaboration, J. Breitweg, et al., Phys. Lett. B 479 37-52 (2000). 349. Measurement of azimuthal asymmetries in deep inelastic scattering, ZEUS Collaboration, J. Breitweg, et al., Phys. Lett. B 481 199-212 (2000). 350. Measurement of inclusive (D9 *) photoproduction at H E R A , ZEUS Collaboration, J. Breitweg, et al. Phys. Lett. B 481 213-227 (2000). 351. Measurement of the proton structure function F2 at very low Q 2 at H E R A , ZEUS Collaboration, J. Breitweg, et al., Phys. Lett. B 487 53-73 (2000). 352. Measurement of D** production and charm contribution to F2 in deep inelastic scattering at HERA, ZEUS Collaboration, Eur. Phys. J. C 16, 181183 (2000). 353. Measurement of difSactive photoproduction of vector mesons at large momentum transfer at HERA, ZEUS Collaboration, Eur. Phys. J. C 14, 213238 (2000). 354. The Muon Anomalous Magnetic Moment, V. W. Hughes, Atomic Physics 17 (2001). 355. Improved measurement of the positive muon anomalous magnetic moment, H. N. Brown, et al., Phys. Rev. D Vol. 62 091101-1 (2000). 356. Various Researches in Physics', V. W. Hughes, Annu. Rev. Nucl. Part. Sci. 5O:i-xxxvii (2000).
250 357. A quad 500 MHz waveform digitizer with differential trigger for use in the m u o n g-2 experiment, S . Dhawan, V. W. Hughes, D. Kawall, W. Liu, J. Pretz, R. Sumner, Nucl. Inst. and Methods in Phys. Res. A. 450 391-398 (2000). 358. Measurement of the E 2 , p t / Q 2 dependence of forward-jet production at H E R A , ZEUS Collaboration, J. Breitweg et al., Phys. Lett. B 474 223-233 (2000). 359. Measurement of the spin-density matrix elements i n exclusive electroproduction of rho mesons at H E R A , ZEUS Collaboration, J. Breitweg. et al., Eur. Phys. J. C 12, 393-410 (2000). 360. The Muon Anomalous Magnetic Moment, V. W. Hughes, International Conference on Atomic Physics 2000, Florence, Italy June, (2000). 361. Measurement of Proton structure function F2 at very low Q 2 at H E R A , ZEUS Collaboration, Phys. Lett. B-487 (2000) 53-73. 362. The Q2 Dependence of Dijet Cross section in y p interactions at H E R A , ZEUS Collaboration, Phys. Lett. B 479 (2000) 37-52. 363. Measurement of the IS-2s energy Interval in Muonium spectroscopy, Phys. Rev. Lett. 87 No.11 Sept. 2001. 364. Precise Measurement of the Positive Muon Anomalous Magnetic Moment, Muon g-2 Collaboration, H. N.Brown et al., Phys. Rev. Lett. 86, 2227-2231 (2001). 365. Measurement of the neutral current cross section and F2 structure at H E R A , ZEUS Collaboration DESY 01-064, Aug (2001). 366. Three Jet Production in Diffractive Deep Inelastic Scattering at H E R A , ZEUS Collaboration, J. Breitweg et al., Phys. Lett. B516, 273-292 (2001). 367. The Q2 dependence of dijet cross-sections in ep interactions at H E R A , ZEUS Collaboration, J. Breitweg, et al., Phys. Lett. B479, 37-52. (2000). 368. Measurement of azimuthal asymmetries in deep inelastic scattering, ZEUS Collaboration, J. Breitweg, et al., Phys. Lett. B481, 199-212 (2000). 369. Measurement of inclusive ( D s * ) photoproduction at H E R A , ZEUS Collaboration, J. Breitweg et al., Phys. Lett. B 481, 213-227 (2000). 370. Measurement of D** production and charm contribution to F2 in deep inelastic scattering at H E R A , ZEUS Collaboration, Eur. Phys. J. C16, 181-183 (2000). 371. Measurement of diffractive photoproduction of vector mesons at large momentum transfer at H E R A , ZEUS Collaboration, Eur. Phys. J. C 14, 213238 (2000). 372. Measurement of the S M C Muon Beam Polarization Using the Asymmetry in the Elastic Scattering of Polarized Electrons, D. Adams, et al., Nucl. Instr. and Methods, A443, 1-19 (2000). 373. Measurement of the spin-density matrix elements in exclusive electroproduction o f p o mesons at H E R A , Eur. Phys. J. C12, 393-410 (2000). 374. Measurement of the 1s-2s Energy Interval in Muonium, V. Meyer et al., Phys. Rev. Lett. 84, 1136-1139 (2000). 375. The 2nd eRHIC Workshop, “What Next? Open Questions”, V. W. Hughes, Yale April, 2000, p. 382.
251 376. Precise Measurement of the Positive Muon Anomalous Magnetic Moment, Muon g-2 collaboration, H. N. Brown, V. W. Hughes et al., Phys. Rev. Lett. 86, 2227-2231 (2001). 377. The Anomalous Magnetic Moment of the Muon, V. W. Hughes, published in the International School of Subnuclear Physics, Erice-Sicily, Italy, August 29 - September 7, (2001). 378. Test of C P T and Lorentz Invariance from Muonium Spectroscopy, V. W. Hughes, et al., Phys. Rev. Lett. 87 1118041 (2001). 379. Measurement of the Analyzing Power for Proton-Carbon Elastic Scattering an the CNI Region with a 22 GeV/c Polarized Proton Beam, J. Tojo, et al, SPIN 2000 14th International Spin Physics Symposium AIP Conference Proceedings, 790-794. 380. Measurement of the Analyzing Power for Proton-Carbon Elastic Scattering in the CNI Region with a 22 GeV/c Polarized Proton Beam, J. Tojo, et al., Phys. Rev. Lett., 89, 052302 (2002). 381. RHICpc CNI Polarimeter: Status and Performance from the First Collider Run, I. G. Alekseev et al., abstract for SPIN 2002 conference, Brookhaven. 382. RHIC pc CNI Polarimeter: Experimental Setup and Physics Results, I. G. Alekseev et al., abstract for SPIN 2002 conference, Brookhaven. 383. The Electron Ion Collider White Paper, V. W. Hughes, February, 2002. 384. Proceedings of the Electron Ion Collider Workshops, QCD and the Other Fundamental Interactions, V. W. Hughes, BNL February 26-March 2, 2002. 52663 V. 2, p. 365. 385. Muon 9-2 Experiment at Brookhaven National Laboratory, V.W. Hughes, et al., Nuc. Phys. B (Proc Suppl.), editors A. DeRoeck, A. Deshpande, S. Bass 105 (2002) 156. 386. Measurement of the Positive Muon Anomalous Magnetic Moment to 0.7 ppm, Phys. Rev. Lett., August 13, (2002). 387. Deep inelastic scattering at the large energy and momentum transfers: Recent results from the HERA collider, ZEUS collaboration, DESY 01-058, May (2001) 87 No.11 10 Sept. (2001). 388. News from the Muon 9-2 experiment at BNL, Muon 9-2 Collaboration, M. Diele et al, Nucl. Physics Proc. Suppl. 116, 215 (2003). 389. Search f o r Lepton Flavor Violation in e+ p Collisions at HERA, ZEUS Collaboration , S. Chekanov et al., Eur. Phys. J. C24 345-360 (2002). 390. Exclusive Photoproduction of J / Q Mesons at HERA, ZEUS Collaboration, S. Chekanov et al., Eur. Phys. J. C25, 169 (2002). 391. Measurement of the Q 2 and Energy Dependence of Difiactive Interactions at HERA, ZEUS Collaboration, S . Chekanov et al., Eur. Phys. J C25 169187, 2002. 392. Leading Neutron Production in e p Collisions at HERA, ZEUS Collaboration, S. Chekanov et al., Nucl. Phys. B637, 3-56, (2002). 393. Measurement of the positive Muon Anomalous Magnetic moment to 0.7 p p m , g-2 Collaboration, G.W. Bennett et al., Physics Rev. Lett. 89, 1018041 (2002). 394. Inclusive Jet Cross-Sections in the Breit Frame in Neutral Current Deep In-
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elastic Scattering at HERA and Determination of as,ZEUS Collaboration, S. Chekanov et al., Phys. Lett. B547, 164-180 (2002). A ZEUS Next-to-Leading-Order QCD Analysis of Data on Deep Inelastic Scattering, ZEUS Collaboration, S . Chekanov et al., Phys. Rev. D67, 012007 (2003). Study of the Azimuthal Asymmetry of Jets in Neutral Current Deep Inelastic Scattering at HERA, ZEUS Collaboration, S . Chekanov et al., Phys. Lett. B551 226-240 (2003). Study of the Process e e + w x o + xoxoy in the CM Energy Range 920-1380 MeV at CMD-2, R.R. Akhmetshin, et al., (Novosibirsk, IYF & Novosobirsk State U. & Yale U. & Boston U. & Pittsburgh U.) Phys. Lett. B562, 173 (2003). Observation of the Strange Sea in the Proton via Inclusive Phi Meson Production in Neutral Current Deep Inelastic Scattering at HERA, ZEUS Collaboration, S. Chekanov et al., Phys. Lett. B553 141-158, 2003. Tests of C P T f o r Muons, V. W. Hughes (Yale U., Dept. of Astronomy) 2003. Published in J. Phys. G29: 181-188, 2003 Search f o r Single Top Production in ep Collisions at HERA, ZEUS Collaboration, S. Chekanov et al., Phys. Lett. B559, 153 (2003). Dijet Angular Distributions in Photoproduction of Charm at HERA, ZEUS Collaboration, S . Chekanov et al., Phys. Lett. B565, 87 (2003). A Search for Resonance Decays to Lepton plus Jet at HERA and Limits on Leptoquarks, ZEUS Collaboration, S . Chekanov et al., Phys. Rev. D68, 052004 (2003). Reanalysis of Hadronic Cross-section Measurements at CMD-2, R. R. Akhmetshin et al., Phys. Lett. B578, 285 (2004). Measurement of the Negative Muon Anomalous Magnetic Moment to 0.7 p p m , Muon g-2 Collaboration, G.W. Bennett et al., Phys. Rev. Lett. 92, 161802 (2004). Spin Asymmetries for Events with High Pt Hadrons in Deep Inelastic Scattering and an Evaluation of the Gluon Polarization, SMC Collaboration, B. Adeva et al., Phys. Rev. D70, 012002 (2004). Spin Dependence in Polarized Proton Carbon Scattering at Low Momentum nansfer and Polarimetry at RHIC, A. Bravar, I. Alekseev, L. Ahrens, M. Bai, G. Bunce, S. Dhawan, H. Huang, V. Hughes, G. Igo, 0. Jinnouchi, K. Kurita, Z. Li, W. W. MacKay, S. Rescia, T. Roser, N. Saito, H. Spinka, D. Svirida, D. Underwood, C. Whitten, J. Wood, AIP Conf. Proc. 698, 643 (2004).
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