-*• a 0 (980)7) and of their ratio helps us to understand the nature of these scalars.
1.2
Analysis
Since both the branching ratio and the resonance mass shape depend strongly on the meson structure, the analysis follows a scheme independent, as much as possible, from the model implemented in the Monte Carlo. The detections of (j> —> ao (980)7 a n d 4> -^ /o (980)7 n a v e been performed in the 5 photons final state through the decay chains: 1. 7r°7r°7 - > 5 7 ;
2. (j> -*• o 0 (980)7 -> ?77r07 -> 57.
The first selection procedure is the same for both channels: fully neutral events are selected with 5 prompt neutral clusters on the calorimeter in the acceptance region (21° < # 7 < 159°). A photon pairing is performed to look for the best combination in the hypotheses 7r°7r°7 and rj7r°7 and a kinematic constrained fit is applied requiring each photon to have the speed of light, the 4-momentum conservation and the intermediate masses ( M 7 7 = M^a or M 7 7 = M^) constraints. The selection of the
7r°7r°7 and cf> —> T?7T°7 samples and the suppression of the related backgrounds (the main backgrounds for <$> —> 7r°7r°7 are e+e~ —• W7T° and 4> —* ??7r07 —> 57; for <j> —> 7j7T°7 events the main sources of background are e + e~ —+ wn°, <j> —> 7r°7r°7 and <j> —> 777 —> 37 or 7j where some cluster are splitted, merged or lost) rely on variables such as the x 2 of the kinematic fits performed in different hypotheses, the angle between the primary photon and the 7r°'s flight direction in the 7r°7r° rest frame and the energy of the non associated photon. The final efficiencies for the signals are evaluated as a function of the invariant masses (M^o^o or Mvno) dividing the generated masses in 20 MeV bins: the average values are eTo„.o7 = 39.7% and enira1 — 27.2%. The bin by bin efficiencies are used in the evaluation of the branching ratios. A^7ro^o7 = 1967 and N^o^ = 666 events survive the analysis cuts with expected backgrounds, respectively, of Bckg^o^Oj = 305 ± 13(stat) and Bckgvno7 = 253 ± ll(stat) events. The invariant mass spectra are shown in fig. 1.
270
200
100
600
800
+
1000
M m (MeV/c') Figure 1: Invariant mass Mnono backgrounds subtraction.
1.3
750
800
050
900
950
1000 1050
M^CMeV)
(left) and M„no (right) after all the selection cuts and
Results
The BR{4> —> /o(980)7) and BR{(j> —> a 0 (980)7) are evaluated by normalising with respect to the 4> —» 777 —> 37 events detected by KLOE, using the PDG value22 for BR{ —> 777 —* 37). Neglecting interference 12 between signals and, respectively, $ —»/9°7r° —> 7r°7r°7 and 0 —> p°7r° —»777r°7 , the results are: BiE(0 -» / 0 (980) 7 -»7r°7r°7) = (7.9 ± 0.2 stat ) x lO" 5 RR(0 - • a 0 (980) 7 - » V M = (5-8 ± 0.5 5tat ) x 10"
5
(1) (2)
The systematic error is under study but will not exceed 10%. The eq.l includes the mass interval M^o^o > 700 MeV up to the kinematic limit. The contribution of (j> —> p°7r° —> 777T°7 to (2) has been subtracted using the average value from recent results 13 BR(p° -c 777) = (3.0 ± 0.3) x 10~ 4 . The ratio of the two branching ratios ( BR{4> -> / 0 (980)7) = 3 • BR(<j> -> / 0 (980)7 -> 7r°7r°7): BR{cj>~* / 0 (980) 7 ) BR(4> -> a0 (980)7)
4.1 ± 0.4 stat
(3)
is in good agreement with recent theoretical predictions9. 2 2.1
Detection of <> / —> 77^, 777 decays Introduction
The measurement of the BR( —> 77^) allows us to probe the \ss) and gluonium content of 77' u . In particular, the ratio of its value to that of <j> —> 777 can be re-
271
lated to the rj—77' mixing parameters 15 , 16 and determine the mixing angle in the flavor basis -> r)'j)/BR(^ -> 777) can be related 16 to the 77 — 77' mixing angle as follows:
\
m sin 2ipP)
\Pn J
In the approach of Feldmann 21 the following relation yields: (smtppsimpv
2.2
cos
/ cos ipp sin (pv
sin
(pv>
Analysis
The measurement of R has been performed 10 with the following decay chains: 1. 4> —> 7 / 7 , 77' —> T7?T + 7r - , 77 —> 7 7 ;
2. 4> ~* m-, V —> 7r+7r_7r°, TT° -* 77. The final state 7T+7T~777 is the same for both 77 and 77' decays, so most of the systematics approximately cancel out in the ratio. The 77 decay, being almost two orders of magnitude bigger than the 77' decay, is an useful control sample for the analysis, but is also the main source of background for the 77'. Further sources of background are <j> —> KSKL where KL decays near the IP and more than one photon is lost and (f> —> 7T+7r~7r°, with additional photons coming from cluster splitting and/or accidentals. The selection of 7r + 7r _ 777 common final state requires 3 prompt neutral clusters on the calorimeter in the acceptance region, the opening angle between each 77 pair > 18° and a charged vertex inside a cylindrical region r < 4 cm and \z\ < 8 cm. A cut on the charged pions energies (E^+ 4- Ew- < 430 MeV) reduces strongly the 4> —* n+Tt~ir° background. A global kinematic fit constraining the total 4momentum and that each photon has the speed of light is performed; a loose cut (P(x2) > 1%) on this fit ensures good reconstruction of the event. These cuts completely remove the KSKL and the •K+ir~TT° backgrounds. To select the (f> —• 77'7 events over the <j> —» 777 background, an elliptical cut on the energy plane of the two hardest photons is applied (fig. 2). Selected events show a clear peak at 77' mass (fig. 2). A fit with a gaussian plus a polynomial allows us to evaluate the background directly from data. The final number of events, selected in the region 942 MeV/c 2 < M w + w - 7 7 < 974 MeV/c 2 after the subtraction of the expected background, is JV,,»7 = 124 ± 12 s t a t ± 5 s v s t. The
272 Monte Carlo evaluated efficiency for this selection is e^'7 = 23 %. The <j> —* 777 events are selected from the 7r + 7r - 777 sample with a ±10CT cut on the energy of the radiative photon. The number of 777 events is Nnj = (502.1 ± 2.2) • 102 with total efficiency of 37.6%.
100
ISO
200
250
300
350
400
450
500 "
"9 0 920 930 940 950 960 970 980 990 1000 MeV/c 2
E l vs. E2 (kin Fit)
Figure 2: Elliptical cut on the energy plane of the two hardest photons for —» 7/7 Monte Carlo events (left). 7r + 7r _ 777 invariant mass events selected as —> 77*7 candidates (right).
2.3
Results
The ratio of the events selected as 7/7 and 777 is related to the ratio of the branching fractions R = BR(cj> —» r]'j)/BR(4> —> 777) as follows10:
Nn-f
X6^!
J common
\£V'l
J analysis
BR(rj -> w+7r-7r0)BR{w0 -> 77) BR(r]' -> TT+ir-r))BR(ri - • 77)
(6) where (£m/sn'-f)common is the ratio of the efficiencies for the selection of the common 7r + 7r _ 777 sample. Using the values for the efficiencies and intermediate Bi?'s we get: R = (5.3 ± 0.5 s t a t ± 0.4 syst ) • 10- 3
(7)
From the two equations (4 and 5) with the values quoted in the cited papers 16 21 for all the parameters entering the ratio excepting for the mixing angle, we get the same value
273
value in ref.22 for BR((f> —> 777) we can extract the most precise determination of BR{(t> -»• 7/7) to date: BR{4> -> 7/7) = (6.8 ± 0.6 stat ± 0.5 syst ) • 10~ 5
(8)
which, together with the value of the mixing angle, disfavours large gluonium content of r / 1 4 2 1 . References 1. F. E. Close, N. Isgur and S. Kumano, Nucl. Phys. B 389, 513 (1983). 2. The KLOE Collaboration, KLOE, A General Purpose Detector for DAQNE, LNF-92/019 (IR) (1992); The KLOE Collaboration, The KLOE Detector- Technical Proposal, LNF-93/002 (IR) (1993). 3. S. Guiducci et al., Proceedings of PAC99, New York, March 1999. 4. The KLOE Collaboration, hep-ex/0107024. 5. R. L. Jaffe, Phys. Rev. D 15, 267 (1977); M. Alford, R. L. Jaffe, Nucl. Phys. B 578, 367 (2000). 6. J. Weinstein and N. Isgur, Phys. Rev. Lett. 48, 659 (1982). 7. N. A. Tornqvist, Z. Phys. C 68, 647 (1995). 8. R. L. Jaffe and F. E. Low, Phys. Rev. D 19, 2105 (1979). 9. F. E. Close and A. Kirk, Phys. Lett. B 515, 13 (2001). 10. The KLOE Collaboration, hep-ex/0107022. 11. M. N. Achasov et al., Phys. Lett. B 479, 53 (2000); M. N. Achasov et al., Phys. Lett. B 485, 349 (2000); R. R. Akhmetshin et al., Phys. Lett. B 462, 380 (1999). 12. M. N. Achasov and V. V. Gubin, Phys. Rev. D 63, 094007 (2001). 13. M. N. Achasov et al., JETP Lett.72,282 (2000); R. R. Akhmetshin et al., Phys. Lett. B 509, 217 (2001). 14. F. E. Close, Pseudoscalars mesons at DAQNE, in The DA&NE Physics Handbook Vol. II, (ed. L. Maiani at al., Frascati 1992). 15. J. L. Rosner, Phys. Rev. D 27, 1101 (1983). 16. A. Bramon et al. Phys. Lett. B 403, 339 (1997); Eur. Phys. J. C C7, 271 (1999); Phys. Lett. B 503, 271 (2001). 17. R. Kaiser and H. Leutwyler, hep-ph/9806336. 18. R. Escribano and J. M. Frere, Phys. Lett. B 459, 288 (1999). 19. T. Feldmann, P. Kroll and B. Stech, Phys. Rev. D 58, 114006 (1998); Phys. Lett. B 449, 339 (1999). 20. F. De Fazio and M. R. Pennington, hep-ph/0104289. 21. T. Feldmann, Int. Jou. Mod. Phys. A 15, 159 (2000). 22. The Particle Data Group, Eur. Phys. J. C 15, (2000).
RESONANCES IN
TJ TT+TT" A N D Kg K * * * FINAL STATES I N 7 7 COLLISIONS AT LEP
I. VODOPIANOV Petersburg Nuclear Physics Institute, Orlova Roscha, E-mail: Representing
188350 Gatchina, Russia [email protected] the L3 Collaboration
The r] 7r+7r~ and Kg K * ^ final states in two-photon collisions are studied with the L3 detector at LEP. The fi(1285) meson is observed in both channels. The 77 (1440) and fi(1420) states are observed in the Kg K^TT^ channel. The Q2 dependences of their production are studied. The fi(1285) 77-coupling width, r 7 7 , is evaluated to be 3.5±0.6 (stat.)±0.5 (sys.) keV. The branching fraction for fi(1285) -» ao(980)7r is estimated. T 7 7 x BR(r; (1440) —• KKw) is evaluated to be 199 ± 52 eV.
1
Introduction
Resonance formation in two-photon interactions offers a clean environment to study the spectrum of mesonic states. The reactions e + e _ —> e + e~R with the decays R —> 77 7r+7r~ and R —» Kg K ± 7T : F are studied. The data are collected with the L3 detector [1] at LEP at centre-of-mass energies between 183 GeV and 209 GeV, corresponding to a total integrated luminosity of 664.6 p b _ 1 . In these channels one could expect to observe the axial vector mesons fi(1285) and ft (1420) and the pseudoscalars 77 (1440) and 77 (1295) [2]. The analysis is based on the study of resonance formation as a function of the transverse momentum squared of the final system, P%- To a good approximation Pj. = Q2, where Q2 is the maximum virtuality of the two photons. Production of a spin-one resonance is suppressed for real photons, according to the Landau-Yang theorem [3]. On the contrary, production of a spin-zero resonance is predominantly at low Q2.
2
77 7r+7r~ Final S t a t e
Events are selected by requiring two particles of opposite charge and two photons. The pions are identified by dE/dx measurement. The effective mass of the two photons must be consistent with the r\ mass within detector resolution. To improve the r)-K+ir~ mass resolution, a kinematic fit, constrained to the TJ mass, is performed.
274
Tib 2.1
fj(1285) Formation
b)0.1
L3
10'
i DatanitV -f, A = M(f,) -f, A fit •f, Ret. 7
C3 1 0 '
*^ O •o
iio
1.5
2 M(TITIV)
1
1.5
(GeV)
10
Q2 (GeV2)
1
Figure 1. r)7r+7r spectra for different Pj, bins (left). Experimental differential cross section dcr/dQ2 compared to the GaGaRes Monte Carlo and to the calculations of Ref. [7] (right).
The data are subdivided into four P£ intervals, as shown in Fig. 1, the spectra are fitted with a resonance plus a background function. The resonance is the convolution of a Breit-Wigner of width T = 0.024 GeV [2], with a Gaussian resolution function. The background is a second order polynomial. The mass values obtained in the four intervals are compatible within statistics with the mass of fi(1285), 1.2819 ± 0.0006 GeV [2]. The detector acceptance for each interval is estimated with Monte Carlo, and the trigger efficiency is obtained directly from the data. Two different approaches have been proposed to describe the cross section for the formation of an axial vector meson in two-photon collisions. In [4] the Q 2 -dependence of the resonance formation is derived using a hard scattering approach [5] and the form factor is written as: F2{Q2)
=
M2 [l + 2M2) (1 + QVA2)4 '
W
where A is a parameter whose value is expected to be close to the resonance mass [4]. We use the GaGaRes Monte Carlo [6], based on this formalism.
276 >2D0-.
a)
L3
1150:
-Data
A
-Ft
}\ ,
-Bkgd
8
CM
¥
8
Events /
1
MY^
y/>
0:
^Vi
1 1 1.4
TT'I
| 1 >
1.2 1.6 M(Ti7iV) (GeV)
M^Tt*
Figure 2. Search for the fi(1285) —> ao(980)7r decay, a.) T)Tt+ir eflFective mass spectrum, the hatched area shows fi(1285) sidebands (SB), b) r]^ mass spectrum.
The form [7] was derived in approximation Q2
91( 1+QL) 2 2
?
(2) K M\ 2M )(1 + Q2/M2)2 ' ' where Mp is the p meson mass. Both of these models are compared to the experimental differential cross section, Fig. 1. First, the mass parameter A in the form factor of Eq. (1) is fixed to the resonance mass, M = 1.282 GeV. Normalising the Monte Carlo histogram to the experimental cross section, a confidence level (CL) of 2% is found. A fit of the GaGaRes prediction is then performed, with A and f 7 7 as free parameters. It gives: A = 1.04 ± 0.06 (stat.) ± 0.05 (sys.) GeV f77 = 3.5 ± 0.6 (stat.) ± 0.5 (sys.) keV
(3) (4)
with CL = 91%. The systematic uncertainty on f 7 7 includes the uncertainty on the branching ratio BR(fi(1285) —> rjTnr) [8]. Previous single-tag low statistics fi(1285) analyses [9,10] used the form [7], their results are f77 = 2.2 ± 0.5 (stat.) keV and f77 = 4.4 ± 1.2 (stat.) keV, respectively. Comparison of the prediction [7] with our data gives CL < 1 0 - 9 . The incompatibility of this model with the measurements is evident in Fig. 1. 2.2
fi(1285) -> ao(980)7r Branching Fraction
The decay fi(1285) -> T]-K-K is dominated by fi(1285) -> ao(980)7r, the world average for this fraction is 0.69 ±0.13 [2], but some experiments observed only the ao7r channel [8,11,12].
277 To search for this decay we select only data with P£ > 0.1 GeV2. The corresponding r)n+Tr~ mass spectrum is shown in Fig. 2a. The ao(980) signal is evident in the r]n± spectrum, Fig. 2b, where the fi(1285) mass region is selected as 1.22 GeV < M(rj-K+IT~) < 1.34 GeV. No signal is observed in the fi (1285) sideband regions. The r)^ spectrum is fitted with a resonance plus a background function, obtained from the fi(1285) sidebands shown in Fig. 2a. The fit gives M = 0.985 ± 0.007 GeV, in good agreement with the world average [2], T = 0.050 ± 0.014 GeV and 318 ± 55 events. A fit to the corresponding T}TV+/K~ mass spectrum of Fig. 2a gives 313 ± 30 events in the fi(1285) peak. Thus the number of fi(1285) events is compatible with 100% decay into ao7r. Taking into account the statistical and systematic uncertainties, the measured branching fraction r(fi(1285) —• ao7r)/r(fi(1285) —» rjinr) is found to be greater than 0.69 at the 95% confidence level. 3
Kg K ^ T T T final s t a t e (preliminary)
a)
Pf<0.02 GeV2 Data Fit Bkgd
b) 0.02
30:
I
1
2010-
0-
L3 Preliminary
A Ikii /•••'W^i
2.3 1.1
20-
L3
10'
• 10'
%
t
O
• DataKgKV - -Tl(1440) MC •••1,(1420) MC — SumMC
|10
t
-o
"£ 1
....t... 10 1.75 2.4 1.15 1.825 MfKgKV) (GeV)
10
10 Pf (GeV2)
Figure 3. K g K * ^ spectra for different P%, bins (left). Experimental differential cross section da/dQ2 compared to the GaGaRes Monte Carlo (right).
Events are selected by requiring four particles, K± and n^, coming from the interaction point, and a Kg decaying into 7r+7r~ at a secondary vertex.
278
The data are subdivided into P% intervals as shown in Fig. 3. The peak in these spectra is the overlap of the signal of r\ (1440), which dominates at low P%, and fi(1420) at higher Pjl. The fourth spectrum shows also fi(1285) formation. The experimental differential cross section is fitted with the GaGaRes prediction [6]. Only the sum of both spin-zero and spin-one waves is sufficient to reproduce the data, Fig. 3. The r) (1440) two-photon width times branching ratio is then determined with the events with Pj. < 0.02 GeV2, where the fi(1420) contribution is found to be negligible: T 7 7 x BR(TJ (1440) -> KKTT) = 199 ± 47 (stat.) ± 22 (sys.) eV,
(5)
consistent with our previous measurement 212 ± 50 (stat.) ± 23 (sys.) eV [13], Acknowlegments I would like to acknowlege all the members of the L3 two-photon analysis group, in particular M.-N. Focacci-Kienzle, J.H. Field and V.A. Chtcheguelski. References 1. L3 Collaboration., B. Adeva et al, Nucl. Instrum. Methods. A 289, 35 (1990); M. Acciarri et al, Nucl. Instrum. Methods. A 351, 300 (1994); M. Chemarin et al, Nucl. Instrum. Methods. A 349, 345 (1994); A. Adam et al, Nucl. Instrum. Methods. A 383, 342 (1996); I.C. Brock et al, Nucl. Instrum. Methods. A 381, 236 (1996). 2. D.E. Groom et al, Eur. Phys. J. C 15,1 (2000). 3. L.D. Landau, Dokl Akad. Nauk. USSR 60, 207 (1948); C.N. Yang, Phys. Rev. 77, 242 (1950). 4. G.A. Schuler, F A . Berends, R.van Gulik, Nucl. Phys. B 523, 423 (1998). 5. S.J. Brodsky and G.P. Lepage, Phys. Rev. D 22, 2157 (1980); Phys. Rev. D 24, 1808 (1981). 6. R.van Gulik, Nucl. Phys. B 82 (Proc. Suppl.), 311 (2000). 7. R.N. Cahn, Phys. Rev. D 35, 3342 (1987); Phys. Rev. D 37, 833 (1988). 8. WA102 Collaboration, D. Barberis et al, Phys. Lett. B 440, 225 (1998). 9. TPC-27 Collaboration, H. Aihara et al, Phys. Lett. B 209, 107 (1988); Phys. Rev. D 38, 1 (1988). 10. Mark II Collaboration, G. Gidal et al, Phys. Rev. Lett. 59, 2012 (1987); Phys. Rev. Lett. 59, 2016 (1987). 11. WA76 Collaboration, T A . Armstrong et al, Z. Phys. C 52, 389 (1991). 12. S. Fukui et al, Phys. Lett. B 267, 293 (1991). 13. L3 Collaboration, M. Acciarri et al, Phys. Lett. B 501, 1 (2001).
EXCLUSIVE P R O D U C T I O N OF C H A R G E D K A O N A N D P I O N PAIRS IN P H O T O N - P H O T O N COLLISIONS AT LEP2 K. GRZELAK Warsaw University, ul. Hoza 69, 00-681 Warsaw, Poland Two measurements of the cross-sections for the two-photon production of charged kaon and pion pairs at LEP2, based on data taken by ALEPH and DELPHI experiments are presented. The cross-sections have been measured for the invariant masses of the two-photon system above 2 GeV and for meson scattering polar angles, 9*, in the photon-photon centre-of-mass system in the region |cos#*| < 0.6. The results are compared to the QCD-based prediction by Brodsky and Lepage.
1
Introduction
We present preliminary results on kaon and pion pair production in the interactions of quasi-real photons using ALEPH and DELPHI detectors at LEP2. The measurements of cross-sections for K+K~ and 7r+7r~ production are based on data collected at the e + e~ centre-of-mass energy ^ = 1 8 3 - 2 0 8 GeV (ALEPH) and ^ = 1 8 9 - 2 0 8 GeV (DELPHI). Here we concentrate on the study of hardly known region of high invariant masses in which QCD-based models can be tested. The detailed QCD-inspired calculations for the studied processes were originally done by Brodsky and Lepage x . At large polar angles in the two-photon centre-of-mass system, the 77 —> MM amplitude was assumed to be factorised into a hard-scattering amplitude that describes valence parton interactions, and into the probability amplitude for finding valence partons in a meson. In this model the absolute normalisation is determined by the non-perturbative part, described by the meson form factor FM- The hard-scattering part is responsible for the shape of invariant mass and angular distributions. In this analysis we use F^W*,) « (0.4GeV 2 )/W 7 2 r 2
Data Analysis
In both experiments, events with K+K~ or n+n~ final states were selected by requiring exactly two, good quality and oppositely charged tracks, measured in the limited range of polar angles 9 in the laboratory frame, with sufficiently large momentum p and transverse momentum pr- The tracks should in addition have small distances of closest approach to the nominal interaction point in both the z-direction (Impz) and in the rcf> plane (Impr<j>)- Events
279
280
should be well balanced in transverse momentum (small -Pr i m i s s ), and the two tracks should be opposite in azimuthal angle (small \n — A0| rad) to ensure the exclusivity of the event. In DELPHI, the two tracks had also to pass an acolinearity cut, \ir — ATJ\ > 0.1 rad, where A77 is the angle between the tracks in the three dimensions. All measurements are performed for | cos#*| < 0.6. Identification of charged particles (kaons, protons, electrons and pions) in ALEPH is based on measurement of ionisation energy loss in the T P C . The DELPHI analysis, in addition to the measurement of ionisation energy loss, takes advantage of the unique possibility of the detector to identify charged particles with Ring Imaging Cherenkov counters (RICH). The summary of the cuts used in both experiments is given in Table 1. The total luminosity used in DELPHI is 483 p b _ 1 and 101 p b _ 1 , for K+K~ and TT+TT" samples respectively, whereas for ALEPH it is 676 p b _ 1 in both cases. After the above selection, the background for the process 77 -»• K+K~, estimated using Monte Carlo simulation is less than 7% in both experiments. In the case of pion pair production a huge background from the two-photon muon pair production is left. In ALEPH this background is on the level of 25%, while in DELPHI it can be as high as 75%. The trigger efficiency in DELPHI was estimated 2 from the data as a function of each variable used for the cross-section measurements. In ALEPH, the trigger efficiency was found by comparing the data and Vermaseren Monte Carlo 3 for the process 77 —> /J,+/J,~ . The efficiency was calculated as a function of the smallest value of the | cos#| of the two tracks. The process e+e" -» e+e~n+fi~ is theoretically well understood and the cross-section is calculated to high precision within QED. In DELPHI it was used to check the main steps of the analysis, our understanding of trigger and detector efficiencies and quality of the experimental data description by the
DELPHI | ALEPH Ntrack = 2 & £ <;h = 0 & Nneut = 0 Impz < 4cm/ sin 9 & Impr 1.2 GeV pT > 0.6 (fwd) or 1 (barrel) GeV pT > 1 GeV P P lmiss < 0-05 (K) or 0.02 (*) GeV 2 T,misS < ° - 0 1 ( K ) o r ° - 0 0 2 5 M G e V 2 |TT - A 0 | < 0.17 (K) or 0.044 rad (TT) \n - A\ < 0.0095 rad (ir) |TT - Arj| > 0.1 rad (;r) |COS0 | < 0 . 6 W-f-y > 2 GeV (K) or W 7 7 >2.3 GeV (TT) Wyy > 2.25 GeV (K) or W 7 7 > 2 GeV (TT)
Table 1. List of DELPHI and ALEPH selection cuts
281 detector simulation program for low-multiplicity events with low-momenta tracks. As a result, an excellent agreement with QED predictions was found. In ALEPH a modified version of the Vermasseren Monte Carlo for muon pair production (by weighting the cross-section by 1/W 77 to approximate the prediction of Brodsky and Lepage) was used to simulate processes with K+K~ or 7r+7r_ in the final state. For these processes DELPHI used a modified version of the Galuga 4 program. Meson pairs were generated from the flat distribution in cos0*. The cross-sections for interaction of two real photons were taken to be proportional to 1/W 77 , as suggested by the QCD-based models. 3
Results
The cross-sections for the processes 77 -» K+K~ and 77 -» 7r+7r~ have been extracted from the e+e~ cross-sections using the transverse luminosity function, d £ 7 7 / d W 7 7 , determined from the Galuga 4 ' 5 program. The crosssections have been measured for | cos0*| < 0.6, as a function of W 7 7 (Fig.l) and | cos 9* \ (Fig.2). In comparison to the previously available results 2 , the measurements were extended to so far unexplored kinematical region. In the case of charged kaon production, the measured cross-sections agree both in shape and in absolute normalisation with the Q CD-inspired predictions by Brodsky and Lepage 1. There is also a good agreement between both LEP experiments and with TPC/Two-Gamma results. For pions the agreement with Brodsky and Lepage model is worse. In addition there is no good agreement between DELPHI and ALEPH. However, the shapes of the distributions of invariant mass and cos 9* agree with that predicted by Brodsky and Lepage. Acknowledgements I would like to thank A. Finch for explaining me the details of the ALEPH analysis and for fruitful discussions. I also would like to thank all the members of the DELPHI two-photon analysis group for helpful discussions. References 1. S.J.Brodsky, G.P.Lepage, Phys. Rev. D 24, 1808 (1981). 2. K. Grzelak, Nucl. Phys. B 82, 316 (2000) (Proc.Suppl.) and references therein. 3. J.Vermaseren, Nucl. Phys. B 229, 347 (1983). 4. G.Schuler, Comp. Phys. Comm. 108, 279 (1998); CERN-TH-96-297. 5. V.Budnev, I.Ginzburg, G..Meledin, V.Serbo, Phys. Rep. 15, 181 (1975).
282 i—i
•2 10
i
i
|—i
i
i
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i
i
i—|—i—i—r—i-
Is 10 flcos9*| < 0.6
|cos9 | < 0.6 • o n
A) . hSn t*-< i-I-i tQl "
DELPHI preliminary ALEPH preliminary TPC/Two-Gamma 1 Brodsky & Lepage
• °
DELPHI preliminary ALEPH preliminary " Brodsky & Lepage
10
W^ [GeV]
W n [GeV]
Figure 1. Cross-section for the process 77 -* K+K~ (left) and for the process 77 -> 7r+7r~ (right) as a function of invariant mass W 7 7 for | cos 0* | < 0.6. The DELPHI data are shown as full dots, the ALEPH data are shown as open circles. The results from T P C / T w o Gamma at y/s — 29 GeV are shown as open squares. The QCD prediction from Brodsky and Lepage is shown as the solid line. 1
J2
,
1
1
1
1
|—
T
£
DELPHI preliminary (2.<Wyy<5.) ALEPH preliminary (2.25<Wyy<4.) Brodsky & Lepage
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10 -
1
|—1
1
1
1
r
DELPHI preliminary (2.3<W n <5.) ALEPH preliminary (2.<Wyy<6.) Brodsky & Lepage
+
^
g0.6
l
-§0.4
•a
* 0.8
0.2 0
0
0.2
0.4
0.6
|cos9
|cos0
Figure 2. Cross-section for the process 77 -> K+K~ (left) and for the process 7 7 - • ?r+7r~ (right) as a function of |cos0*|. On the right plot, the ALEPH data are multiplied by a factor of 4.5. The Brodsky and Lepage predictions are shown as the solid line. The normalisation of the curve is arbitrary.
EXPERIMENTAL INVESTIGATION OF THE TWO-PHOTON WIDTHS OF THE XcO AND \di HANS P. PAAR. Physics Department 0319 University of California, San Diego La Jolla, CA 92037-0319, U.S.A. e-mail: [email protected] Abstract I present the first observation of the XcO in photon-photon collisions and measurements of the two-photon widths of the Xco and Xc2- These results were obtained with the CLEO detector at the Cornell e+e~ collider CESR and are based upon an integrated luminosity of 12.7 fb _1 obtained at centre-of-mass energies near the T(4S). The Xc have been detected in their decays into 7r+7r_7r+7r_. We obtained r 77 (xco) x B(Xco-»47r) = 75 ± 13(stat) ± 8(syst)eV and r 77 (xc2) x B(XC2-+4TT) = 6.4±1.8(stat)±0.8(syst) eV. Using the world average values for B(XC-*4-K) we found r 77 (xco) = 3.76 ± 0.65(stat) ± 0.41(syst) ± 1.69(br)keV and T77(xc2) = 0.53±0.15(stat)±0.06(syst)±0.22(br)keV. The two-photon width of the Xc2 agrees with the world average within the large uncertainty. We avoid the 40% branching fraction uncertainties and cancel the systematic uncertainties in the measurements by measuring the ratio r 77 (xco)/r 77 (xc2) and find 7.4 ± 2.4(stat) ± 0.5(syst) ± 0.9(br). Nonperturbative factors in the QCD calculation cancel in the ratio so as a result the ratio has sensitivity to the value of a3. The measurements are in excellent agreement with expectations from QCD. 1
Introduction
The measurement of the two-photon widths of the Xco and Xc2 are of interest because there exist QCD based next-to-leading order (NLO) perturbative calculations 1 for them. There is no published measurement for the twophoton production of the Xco while the PDG value2 for r 7 7 (x C 2) is 0.46 ±0.17. The average has contributions from measurements based upon two-photon production and pp annihilation. There is poor agreement between the two groups of measurements and the PDG applies a scale factor S — 1.9 to obtain the uncertainty in the average. While the pp experiments benefit from the 10% accuracy of B(xc2—>pp), the two-photon production experiments use branching fractions that have 40% uncertainties. Because it is the product T 7 7 (xc) x B{Xc~>47r) that is measured, the uncertainty in the resulting value for r T 7 ( x c ) is in excess of 40%. CLEO has observed the Xc in their
283
284
decays into 7r+7r_7r+7r_. The PDG values for 2?(xc-+47r) is an average of a 25 year old Mark I value3 and a recent BES 4 value. The experiments disagree and the PDG has assigned a larger error to the mean. However, the two experiments agree on the ratio B(xC2~*4x) I B(XcQ—^47r). In addition, each experiment's systematic uncertainties almost cancel in the ratio. Furthermore, systematic uncertainties in CLEO's measurement of the ratio #(x47r)r 77 (x c2 ) a m i o s t cancel. CLEO therefore also reports a measurement of r 7 7 (xco)/r 7 7 (xc2) with a very small uncertainty leading to a more precise comparison with the QCD expectation where nonperturbative factors cancel. Thus, the ratio is sensitive to the value of a8. 2
Theoretical Estimates
The interpretation of the two-photon widths of the Xc in terms of QCD based next-to-leading-order (NLO) calculations is based upon the ratio of the twophoton widths to the two-gluon widths of the Xc where non-perturbative factors cancel 1 r 77 (Xco) = 8 / a \ 2 (1 + 0.18a 9 /7r\ ( r 99 (Xco) 9\as) \ l + 9.5a./n J ' r 7 7 (Xc 2 ) ^ 8 fa\2 r s 9 (Xc 2 ) 9\aJ
/l-5.3a.M \l-2.2aa/nj
^
)
The two-gluon widths can be obtained from the measured total widths reported by the PDG 2 by subtracting the radiative widths T(xc-*'yJ/'>l>) and the coloroctet contribution as measured by the hadronic width of the Xci5- These subtractions are significant only for the Xc2- Using the two-gluon widths thus obtained, we get r 7 7 ( x c 0 ) = 5.0 ± 0.8keV and T 77 (x C 2) = 0.47 ± 0.04keV using 1 as = 0.28. We also have r 7 7 (xco) r77(xc2)
=
f l 5 \ / l + 0.18a g /7r\ V 4 A 1 - 5.3a8/?r J
Note that the term 5.3as/ir is of order 0.5. A calculation of the next term of order (as/w)2 is badly needed. 3
Detector, Dataset, and Event Simulation
The CLEO II detector 6 is a general purpose detector that provides charged particle tracking, precision electro-magnetic calorimetry, charged particle identification, and muon detection. Charged particle detection over 95% of the solid angle is achieved by tracking devices in two different configurations, situated
285 in a magnetic field of 1.5 T. In the first configuration (CLEO II) tracking is provided by three concentric wire chambers while in the second configuration (CLEO II. V) the innermost wire chamber is replaced by a precision three-layer silicon vertex detector 7 . The momentum resolution is 0.5% at p = 1 GeV. The drift chambers are surrounded by a time-of-ftight (TOF) system. Energy loss (dE/dx) in the outer drift chamber and the TOF system provide pion-kaon separation. A Csl based electro-magnetic calorimeter giving an energy resolution of 4% for 100 MeV electro-magnetic showers provides n° detection. A super-conducting coil and muon detectors surround the calorimeter. Redundant triggers provide efficient registration of mutiparticle final states. The Cornell Electron Storage Ring CESR operates at a center-of-mass energy near the T(45). The results in this report are based upon an integrated luminosity of 12.7 fb _ 1 . The event simulation uses uses the BGMS 8 formalism for the event generation. Photon form-factors based upon vector-meson dominance with the Jft/) mass were used. The Monte Carlo simulation of the CLEO II detector is based upon GEANT. The detector is simulated down to the component level. The trigger simulation and the event reconstruction use this information to determine the detector response. Simulated events are processed in the same manner as the data. 4
Event Selection
The Xc are detected through their decays into 7r+7r_7r+7r_. The event selection requires exactly four good quality tracks whose sum of charges is zero. dE/dx measurements are used in the identification of the pions, the probability for the ir+n~w+ir~ asignment has to be greater then 10%. The transverse component of the vector sum of the tracks (the event px) has to be less than 0.4 GeV and the total energy measured in the calorimeter, not associated with one of the four tracks, has to be less then 0.6 GeV. The visible energy of the event (the sum of the four track's energies) has to be less then 6 GeV. To keep the systematics related to the trigger efficiency small, only events satisfying the two-track trigger are used. It's efficiency was measured using the simulation which in turn is checked using data taken with redundant triggers. 5
Results
We show in Fig. 1 the 7r+7r_7r+7r_ invariant mass distribution. Clear peaks are seen at the x c 0 and \ci mass. The solid line represents a fit consisting of the sum of two Breit-Wigners, each convolved with two Gaussians, and a background represented by a power law in m(47r). The parameters of the
286
Gaussians are taken from the simulation. There are 234 ± 40 events in the XcO peak and 89 ± 25 events in the Xc2 peak. The fit has a x 2 /ndof — 44.0/54. Prom the number of signal events in the peaks we find r 7 7 (x c o) xi3(Xco->47r) 75 ± 13(stat) ± 8(syst)eV and T 7 7 (x c 2 ) x #(x c2 ->47r) = 6.4 ± 1.8(stat) ± 0.8(syst)eV. Systematic errors for the XcO and the Xc2 are dominated by uncertainties from the cut on the event px (7% for both), the particle identification (4% and 6% respectively), the unmatched neutral energy cut (4% for both), the helicity (4% for Xc2), and the width (4% for Xco)- Together with a number of smaller uncertainties we obtain total systematic errors of 11% and 12% respectively. Most of these are correlated between the XcO and the Xc26
Interpretation
Using PDG values2 for B(xc-+4ir) we find T 7 7 (x c 0 ) = 3.76 ± 0.65(stat) ± 0.41(syst) ± 1.69(br)keV and r 7 7 ( x c 2 ) = 0.53 ± 0.15(stat) ± 0.06(syst) ± 0.22(br)keV. The two-photon width of the Xc2 agrees with the world average within the large uncertainty.
300
i
I
i
I
i
I
i
I
i
3080401-004
I
i
>
'
i
i
0
i
i
i
I
^200 o •>>
fWfe
1100 > LU
0 3200
,
i <J\ V i l \ \
3400 3600 M (AJC) (MeV)
Figure 1: Invariant mass of w+ir n+ir solid line represents a fit, see text.
,
1
3800
. The data are the dots with the error bars, the
287 We avoid the 40% branching fraction uncertainties and cancel the systematic uncertainties in the measurements by measuring the ratio r 7 7 (xco)/r 7 7 (xc2) and find 7.4 ± 2.4(stat) ± 0.5(syst) ± 0.9(br). Non-perturbative factors in the calculation also cancel in the ratio so as a result the ratio has sensitivity to the value of as. I show the result of the measurement and the QCD expectation in Fig. 2. We find as « 0.29to;°4. Here we have updated the branching fractions using detailed information from the original publications 3 ' 4 and took into account the correlated uncertainties between the Xco and Xc2 in each experiment. Both experiments require a value for B(i()(2S)—>fXc) and the resulting correlation is taken into account when calculating the average ratio of branching fractions. The measurements are in excellent agreement with expectations from QCD. The uncertainty in the ratio of two-photon widths is dominated by statistics so BaBar and BELLE can improve the measurement and obtain a more precise value for as. A more precise determination of the two-photon widths themselves awaits a more precise measurement of their hadronic branching fractions at BES. 3080401-003
-I
0.1
I
I
I
I
0.2
0.3
cc.
0.4
0.5
Figure 2: Comparison of the measurement of the ratio r 7 7 ( x c o ) / r 7 7 ( X c 2 ) (shaded region represents the ±lcr value) with the expectation from NLO QCD as function of a s .
288
7
S u m m a r y and F u t u r e
I report the first observation of the two-photon production of the Xco and a measurement of the two-photon widths of the Xco and \c2 using an integrated luminosity of 12.7 fb _ 1 . The two-photon width for the Xc2 agrees with the world average within the large uncertainty, mainly due to the \c2 branching fraction. We avoid the 40% branching fraction uncertainties and cancel the systematic uncertainties in the measurements and the non-perturbative factors in the QCD expectation by measuring the ratio r 7 7 ( x c o ) / r T 7 ( x c 2 ) and find 7.4±2.4(stat) ±0.5(syst) ±0.9(br). This ratio has sensitivity to the value of as. Within the large uncertainties, the measurements are in excellent agreement with expectations from QCD. In the future, BaBar and BELLE can improve the measurements of the two-photon widths of the Xco and the Xc2 and obtain a more precise value for as from their ratio. A more precise determination of the two-photon widths themselves awaits a more precise measurement of their hadronic branching fractions at BES. Finally, a NNLO theoretical calculation of two-photon and two-gluon widths of the Xc up to (a s /7r) 2 is needed to better interpret measurements. Acknowledgments I would like to thank my colleagues in CLEO and CESR, especially R. Galik and R. Mahapatra for an enjoyable and fruitful collaboration. I also thank the organisers of PhotonOl for their hospitality in beautiful Ascona, Switserland. 1. W. Kwong, P.B. Mackenzie, Rogerio Rosenfeld, and J.L. Rosner, Phys. Rev. D 37, 3210 (1988). 2. D.E. Groom et al. (Particle Data Group), Eur. Phys. Jour. C 15, 1 (2000). 3. W.M. Tanenbaum et al. (Mark I Collaboration), Phys. Rev. D 17, 1731 (1978). 4. J.Z. Bad et al. (BES Collaboration), Phys. Rev. D 60, 072001 (1999). 5. M.L Mangano and Andrea Petrelli, Phys. Lett. B 352, 445 (1995). Inclusion of the the color-octet contribution was the original idea of E. Braaten. 6. Y. Kubota et al. (CLEO Collaboration), Nucl. Instrum. Methods A 320, 66 (1992). 7. T. Hill et al., Nucl. Instrum. Methods A 418, 32 (1998). 8. V.M. Budnev, I.F. Ginzburg, G.V. Meledi, and V.G. Serbo, Phys. Rep. C 15, 181 (1975).
SEARCH FOR r]b IN T W O - P H O T O N E V E N T S ARMIN BOHRER Fachbereich Physik, Universitat Siegen, 57068 Siegen, E-mail: [email protected]
Germany
A search for the pseudoscalar meson rft, was performed at LEP II energies with an integrated luminosity of 700 p b - 1 . The search, done for the decay modes into 4 and 6 charged particles yielded 0 and 1 candidates, respectively. Upper limits on T 7 7 (jjb) x BR for both modes of 57 eV and 128 eV were obtained with corresponding limits of 17% and 38% on branching ratios BR(»jb -> 4 charged particles) and BR(% -¥ 6 charged particles) at a confidence level of 95%. The candidate has a mass of 9.30 ±0.04 GeV.
1
Introduction and Motivation
The bb ground state, the »jb meson has not been observed yet. Because of their initial state two-photon collisions are well suited for the study of pseudoscalar mesons Jpc = 0 + _ , in which they can be produced exclusively. The high 77 cross section, the high LEP luminosity and energy as well as the low background from other processes make LEP II events a good sample to search for this meson. The ALEPH experiment has started a search for the still undiscovered T]^ pseudoscalar meson 1 . The meson has been searched for in two-photon events in its exclusive decays to 4 and 6 charged particles. The analysis is motivated by various predictions for the mass of the r?b, e.g., from potential models, pQCD, NRQCD, and lattice calculations, which are tested or constrained by a measurement of the r/b mass. See the contributions by G. Bali 2 and by S. Collins3 at this conference and the contributed paper 1 . The allowed mass m{rjb) of these estimates ranges from 9.32GeV/c 2 to9.45GeV/c 2 . 2
Potential for the Measurement
The production cross sections has been estimated as follows. In two-photon collisions the cross section for •% is calculated with the equivalent photon approximation 5,6 using the estimated r?b mass in the form factor (a mass of 9.4 GeV is used). The partial width r 7 7 is calculated from the ratio r 77 (?7b)/r 77 (77 c ) using the Coulomb potential approach 7 . Using the measured partial width r 77 (77 c ) = 7.4 ± 1.4 keV a value of r77(77b) = 416 eV is obtained. (See, however, the contribution 4 by N. Fabi-
289
290
ano at this conference indicating a larger r 77 (?jb)-) This translates into a production cross section of 0.222 pb at yfs = 197 GeV (luminosity weighted for the 7 0 0 p b - 1 at LEP II above W + W ~ threshold). This would correspond to 156 r?b mesons produced in ALEPH during LEP II data taking. The branching ratios of the r/b decay can only be estimated. Here, a new (different to the ALEPH conference note 1 ) approach is used, where for the production probability of n p a j r pion (or kaon) pairs a Poisson distribution is assumed. The number n p a i r can be obtained, because the energy evolution of the mean charged multiplicity (n) is predicted in modified leading log approximation (MLLA) with the assumption of local parton-hadron duality (LPHD) 8 and is fitted to e + e~ data 9 . With the choice n p a i r = (n)/2 for charged and "pair = (n}/4 for neutral pairs, the branching ratios can be estimated. Evaluation for the 77c a branching ratio to (0 neutral and) 4 charged particles of P0P2 = 9.9% is estimated, while the measured decays add up to 9.3 ± 1.8%5. For the rft, decay to 4 and 6 charged particles P0P2 — 2.7% and P0P3 = 3.3% are obtained, respectively. The selection and reconstruction efficiences are studied using events generated with PHOT02 10 . For the decays it is assumed that the momentum distributions are given by phase space. The efficiencies are found to be 15.7% and 10.1%, respectively. mean cms energy total luminosity
cross section
= = = = =
196.6 GeV 700pb" 1 0.22, 0.36 220MeV,306MeV 0.222 pb (lumi.weighted)
# produced 77b
=
156
efficiency (4 charged) efficiency (6 charged)
= =
15.7% 10.1%
# r/b (BR(4 charged) == 2.7%) # •% (BR(6 charged) == 3.3%)
= =
0.65 events 0.52 events
a»(n*(W2)), <* S MW 2 )) A5,4
2.1
Data Analysis
In order to keep the efficiency high, loose selection cuts are chosen for event and track selection. So, no attempt is made to reconstruct the Ks at this stage. The mass resolution of the accepted events is around 0.14 GeV, mainly due to 7T—K misidentification and mass assignment, with an average reconstructed
291
Figure 1. Invariant mass distributions in the search for the %, meson. Data (solid line) are compared to the expected signal for an assumed branching ratio of 100% for the decay to 4 and 6 charged particles
r view of the % -> 2 . An K s K-7r+7r-7r+ candidate event with the reconstructed mass of 9.30 ± 0.02 ± 2 selected in the signal region 0 0 2 Qev/c ,
Figure
mass of 9.4 GeV. A signal region 9.0 GeV to 9.8 GeV is chosen. The background, which is dominated by 77 continuum production, is therefore estimated from the number of data events: a) the number of events in the signal region before the final cuts, which is 78 (139) events for 4 (6) charged particles, and b) by a fit to the ratio of the mass spectra after all cuts are applied and before the final cuts on X)Pt,»i thrust, ^(thrust axis), and hemisphere mass are applied. The background is estimated to be 0.3 ± 0.3 (0.8 ± 0.4) events. 3
Results
The invariant mass spectra of the selected events from 700pb _ 1 at LEP II with 4 (and 6) charged particles are shown in Figure 1. In the signal region 0 (and 1) events are found. From the knowledge of the background, the efficiency and its uncertainty (±25%) the observed number of events are converted 11 into upper limits. For a confidence limit of a = 95% upper limits for r 7 7 (t/b)xBR of 57eV (and 128 eV) are obtained. Including the evaluated two photon width of 416 eV and its uncertainty (±25%) the upper limits on the branching ratio
292 of the 77b meson at 95% C.L. are BR(77b -> 4 charged particles) < 17% and BR(r7b -> 6 charged particles) < 38%. The selected event, shown in Figure 2, has a V° particle compatible with a Ks- One daughter of the V° has the kaon mass assigned. Compatible in dE/dx with a pion (xi = 0-86 rather than xic — 0.18) we recalculate the mass of the event. A mass estimate of 9.30 ± 0.04 GeV is obtained, where the error is a conservative estimate of the total error. 4
Conclusion
In an integrated luminosity of 700 p b _ 1 at LEP II energies the pseudoscalar meson 77b has been searched for by the ALEPH collaboration in its decays to 4 and 6 charged particles. One candidate is retained in the decay mode into 6 charged particles, while the expected signal is 0.65 and 0.52 events for the two decay modes and a background of 0.3 ± 0.3 (0.8 ± 0.4) events is expected. The candidate has a mass of 9.30 ± 0.04 GeV. The event is compatible with background. Upper limits on r 7 7 (r/b)xBR of 57eV and 128eV corresponding to limits of the branching ratios, BR(?7b —¥ 4 charged particles) and BR(r7b —¥ 6 charged particles), of 17% and 38% are obtained with a confidence level of 95%. A discovery would need the effort of all 4 LEP experiments. References 1. 2. 3. 4. 5. 6. 7.
8. 9. 10. 11.
ALEPH Collaboration, ALEPH 2001-037, CONF 2001-025 (2001). G. Bali, these proceedings. S. Collins, these proceedings. N. Fabiano, these proceedings. Review of Particle Physics, Eur. Phys. J. C 15, 1 (2000). V.M. Budnev, I.F. Ginzburg, G.V. Meledin, and V.G. Serbo, Phys. Rep. 15 C, 181 (1975). P. Aurenche, G.A. Schuler (Conv.), Eds.: G. Altarelli, T. Sjostrand and F. Zwirner, CERN-YELLOW report 96-01, 291 (1996); and references therein. Z. Kunszt et al., in Proceedings of the Workshop on Z Physics at LEP 1, eds. G. Altarelli et al., CERN report 89-08, 373 (1989). ALEPH Collaboration, ALEPH 2001-007 (2001). ALEPH Collaboration, Phys. Lett. B 313, 509 (1993). G. Zech, Nucl. Instr. Meth. A 277, 608 (1989) and private communicar tions.
TWO P H O T O N W I D T H OF r)C NICOLA FABIANO Perugia
University
and INFN,
via Pascoli 1-06100,
Perugia,
Italy
GIULIA PANCHERI INFN
National
Laboratories,
P.O.Box
IS, IOOO44 Frascati,
Italy
We discuss the measured partial width of the pseudoscalar charmonium state, r)c , into two photons. Predictions from potential models are examined and compared with experimental values. Including radiative corrections, it is found that present measurements are compatible both with a QCD type potential and with a static Coulomb potential, with as evaluated at two loops. Results are also compared with those from J/tp d a t a through the NRQCD model.
1
Introduction
In this note, we examine the theoretical predictions for the electromagnetic decay of the simplest and lowest lying of all the charmonium states, i.e. the pseudoscalar r\c . We shall compare the two photon decay width with the leptonic width of the J/ip, which has been measured with higher precision 1 and found to be 15% higher than in previous measurements 2 . The most recently reported Particle Data Group average 3 is given by Texp(vc -» 77) = 7.4 ± 1.4 keV 2
(1)
R e l a t i o n to J/ip —* e+e~ w i d t h
The two photon decay width of a pseudoscalar quark-antiquark bound state can be written as 4 ' 5 T(7?c -> 77) = 12e*a^ S£) 47r>(Q)I 2
as fir2 - 20
2*
M
y-V
/TT^
1+— 7T V
rg(l-a.) (2)
3
where i/;(0) is the wavefunction of the interquark potential evaluated at the origin. It is useful to compare eq. (2) with the expressions for the vector state J/if 6 , i.e. T(J/i, - ee) = ^
4
,
*
(l - H 2 i ) „
F£
(1 - 1.7a.).
(3)
The expressions in eq. (2) and (3) can be used to estimate the radiative width of 77c from the measured values of the leptonic decay width of J/ip, if
293
294 one assumes that the tp(0) values for both the pseudoscalar and the vector state should be the same. This is true up to errors of 0(aa/m%). Prom Texp(J/ip -* e+e~) = 5.26 ± 0.37 keV
(4)
expanding in as one has: Tfac -+77) ^ 4 (1 - 3.38a,/7r) ., 4 r - e+e") ~ 3 (1 - 5.34as/7r) ~ 3 L1 +
r(J/V,
L96
a. n
+
g , 2 ,1 °(aJJ
(&) (5)
From the value as(Mz) = 0.118 ± 0.003 the renormalization group evolution gives as(Q = 2mc = 3.0 GeV) = 0.25 ± 0.01. Combining the formulae (4) and (5) we obtain a, error r(r7 c -> 77) ± Ar(?7c -*• 77) = 8.18 ±0.57
±0.04
keV
(6)
J/^ error This estimate agrees within la with the value given in formula (1). 3
Potential models predictions
We shall extract now the wave function at the origin from potential models. For the calculation of the wavefunction we have used four different potential models, like the Cornell type potential 7 V(r) = — £ + -^ with parameters a = 2.43, k = 0.52, the Richardson potential 8 V#(r) = with N 3 A 398 MeV and the CD
- t 3 3 ^ IjgfrtujZ,*/^)
f = - =
>
Q
inspired potential Vj of Igi-Ono 9 ' 10 Vj(r) = VAR(T) + dre~gr + ar, VAR(T) = ~ l " r W ^ t n t w o different parameter sets, corresponding to h.jjg = 0.5 GeV and A.j£g = 0.3 GeV respectively 9 . We also show the results from a Coulombic type potential with the QCD coupling as frozen to a value of r corresponding to the Bohr radius of the quarkonium system, r& = 3/(2mcas) (see for instance n ) . The error sources in calculation are given by the choice of scale in radiative correction, the choice of various potential parameters and the fluctuations in results from different models. The T(r}c —> 77) potential models prediction gives a range of values: r(r/ c -> 77) = 7.6 ± 1.5 keV 4
(7)
Octet Component model
We will present now another model which admits other components to the meson decay beyond the one from the colour singlet picture (Bodwin, Braaten
295 and Lepage) 12 . NRQCD has been used to separate the short distance scale of annihilation from the nonperturbative contributions of long distance scale. This model has been successfully used to explain the larger than expected J/rp production at the Tevatron. According to 12 , in the octet model for quarkonium the decay widths of charmonium states involve four unknown long distance coefficients which can be reduced to two by means of the vacuum saturation approximation: G\ = (J/T/>|OI( 3 SI)|J/tp) = (r?c|Oi(1So)|r7c) and Fi = (J/V'|-Pi( 3 5'i)|J/V') = (»7c|i3i(1S'o)|7yc>, correct up to 0(v2), the velocity of the quarks inside the meson. We use the J/\p experimental decay widths as input in order to determine the long distance coefficients G\ and F\ . This result in turn is used to compute the rjc decay widths. The BBL model gives the following decay width of the r]c meson: a, error
T(r)c -> 77) = 9.02 ±0.65
±0.14 keV
(8)
J/i> error This value agrees with experimental data within la. 5
Summary
We present in fig. (1) a set of predictions coming from different methods: r(TK-»Yy) •i"11
:
Jty-> LH JA((-» eV
•
f
*
RICHARD. BBL
1—
-•—
-H -
CORNELL
|_
VJ.AM^.3
" COULOMB
1
# •
_
3.0
-
—
,
,
4.0
5.0
6.0 7.0 Width (keV)
.!.,..
Figure 1. Potential Models results; BBL model with input from J/ip decay data; Lattice evaluation of Gi and Fi factors; Singlet picture with G\ obtained from J/tp —* e+e~ and J/ip —• LH processes respectively. The vertical lines represent the PDG average value and its indetermination.
results from potential models; BBL model with G\ and F\ extracted from the
296
J/V" decay data; lattice calculation of the long distance terms for the BBL model 13 ; singlet picture: Gi extracted from J/tp —• e+e~ decay width, and singlet picture: G\ extracted from J/ip —> LH decay width. 6
Conclusions
The T(r]c —> 77) decay width prediction of the potential models considered gives the value 7.6 ± 1.5 keV which is consistent with the PDG average. The Coulombic model is in agreement with other models prediction. Predictions of the BBL model for the r/c —> 77 decay width is consistent with the experimental measures, for both the long distance terms G\ and F\ extracted from the J/ip experimental decay widths and the one evaluated from lattice calculations. References 1. J.Z. Bai et al, Phys. Lett. 355 (1995) 374; S.Y. Hsueh and S. Palestini; Phys. Rev. D45 (1992) 2181. 2. A. M. Boyarski et al, Phys. Rev. Lett. 34 (1975) 1357; R. Baldini-Celio et al., Phys. Lett. 58 (1975) 471; B. Esposito et al., Nuovo Cimento Lett. 14 (1975) 73; R. Brandelik et al, Z. Phys. C I (1979) 233. 3. Review of Particle Properties, D.E. Groom et al., EuroPhys. Journ. C15 (2000) 1; http://pdg.lbl.gov/. 4. R.Van Royen and V.Weisskopf, Nuovo Cimento 50A (1967) 617. 5. R. Barbieri, G. Curci, E. d'Emilio and R. Remiddi Nuclear Physics B154 (1979) 535. 6. P. Mackenzie and G. Lepage, Phys. Rev. Lett. 47 (1981) 1244. 7. E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane and T. M. Yan, Phys. Rev. 21D (1980) 203. 8. J.L. Richardson, Phys. Lett. 82B (1979) 272. 9. J. H. Kiihn and S. Ono, Zeit Phys. C21 (1984) 385; K. Igi and S. Ono, Phys. Rev. D33 (1986) 3349. 10. W. Buchmuller and S. H. H. Tye, Phys. Rev. D24 (1981) 132. 11. N. Fabiano, A. Grau and G. Pancheri, Phys. Rev. D 5 0 (1994) 3173; Nuovo Cimento A, Vol 107 {1994). 12. G.T. Bodwin, E. Braaten and G.P. Lepage, Phys. Rev. D51 (1995) 1125. 13. G.T. Bodwin, D.K. Sinclair and S. Kim, Int. J. Mod. Phys. A12 (1997) 4019.
S E A R C H F O R T H E D E C A Y T(lS)-»777;
DAVID G. C A S S E L Newman
Laboratory,
Cornell E-mail:
University, Ithaca, [email protected]
NY 14853,
USA
The CLEO Collaboration searched for the radiative decay T(1S)—>yr)' in 1.45 x l O 6 T(IS') decays. We found no candidate events and set an upper limit of 1.6 x 10 — 5 at 90%CL. This limit, which is significantly smaller than the previous upper limit, is compared to other radiative T and J/4> decays and to theoretical predictions.
1
Motivation
Many J/ip —> 7 M decays appear in the Particle Data Group (PDG) summary 1 . The modes J/tp —+ 777, J/tp —> 777', and J/ip —> 7/2(1270) are among those with the largest branching fractions (6). However, only one T(15) —>7M decay has been measured so far - CLEO 2 observed T—^7/2, followed by ji —>7r+7r~. Assuming that all T —>77r+7T~ events found in the 7r+7r~ mass peak at 1270 MeV are Y—>7/2, and using B(f2 —>7T+7r~) = § x 84.7%, the T - ^ 7 / 2 branching fraction is B(T^jf2) = (8.2 ±3.6) x 10~ 5 . Two simple simple scaling relations can provide estimates of the branching fraction for T - ^ 7 7 ' . The ratio R(V) = B(V-+jri')/B(V-^7/2) is R(J/ip) ~ 3 for J/ip decays 1 . Naively applying the same ratio to T decays gives S(Y—>7r/) ~ 2 5 x l 0 - 5 . Alternately, the simplest scaling of decay widths from cc to 66 gives, B(t^Xi)IB(JH>^Xi) = ( r ^ / T r ) (qb/mbf (mc/qc)2 « 0.045 « 1/22, where qq and mq are the charge and mass of quark q, respectively. This ratio and the PDG value for B(J/I/J —> 77') give B(T —> 777') ~ 19 x 10- 5 . CLEO has N(T) = (1.45 ± 0.03) x 106 T(15) decays, so observation of B ^ 1 0 - 5 is possible. The previous upper limit B(Y—> 777') < 1 . 3 x l 0 - 3 (90% CL) from the Crystal Ball 3 is much larger than these estimates and CLEO sensitivity. Observation of T—>7?7' could be much more interesting than just another branching fraction measurement. For example, the branching fractions 4 for 77' are much larger than expected and are still not well understood. Gluonic components of the 77' could play a role in making these branching fractions large. A simple picture of T —• 777' decay suggests that the environment is "glue-rich" so this decay could probe the gluonic component of the 77' (see Figure 1). Finally, theoretical predictions 5'6>7'8 for B(Y->jr]') exist and will be compared to the results of this search.
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Figure 1. Diagram for V—>fP decay illustrating production of P by two gluons.
2
T—>7?7' Reconstruction
The strategy for reconstructing T —»777' decays is quite straightforward and highly efficient. Eq. (1) illustrates the decay chains utilized, the particles detected, the 77' and 77 branching fractions for the observed modes, and the overall efficiency (e) for detecting each mode. T
B £
->7T/
L-> 7r+7r—77 U 77 7tW> TT+TT-TT0 43.8% 39.2% 32.2% 23.1% 31.8% 15.0% 21.1%
(1)
To search for T—>7?7' decays, we: • reconstructed 77 meson candidates in the modes given in Eq. (1), • required M(?7) (candidate mass) within 3a of the PDG value of Mn, • constrained M(r7) to Mv with a kinematic fit, • added two (±) tracks and required 939 < M(rj') -Mv> < 981 MeV ( > 3a), • added a 7 with £(7) > 4 GeV, and • required ^(777') - Mr\ < 300 MeV. These three successive mass cuts highly suppress backgrounds and are very efficient for an T —> 777' signal. Nevertheless, no T —> 777' candidates were found in either the T(15') data or in data taken in the nearby continuum. Because no T —> 777' candidates were observed, we made several careful checks of the reconstruction. In particular, the detector data had been reprocessed with improved reconstruction software after the T —> 7/2 result was obtained, so we compared the 77r+7r~ mass distribution in the current analysis with the one obtained earlier. We found that the distributions are consistent. We also searched for inclusive 77 and 77' signals in a larger data sample and found clear peaks with resolutions consistent with the estimates from Monte Carlo calculations.
299 3
Results
We calculated an upper limit for the T —> 777' branching fraction using: N(-yr]') = N(T)B(T—>7r]')B(r]'-^'n+-K~ri)Y,£iBi(v)> where i runs over the 77 decay modes: 77, 7r°7r°7r0, and 7T+7r~7r°. When no signal events are observed, the frequentist upper limit 1 for the number of signal events is AT (777') < 2.3 (90% CL). The overall efficiency is £(77'^TT+TT-T?) £ < ^ f a ) = (9.7 ±0.5)%. The systematic contributions to the upper limit were estimated in a Monte Carlo calculation. The final result is: £ ( T ^ 7 r / ) < 1 . 6 x 10~5 (90% CL)
(2)
We can compare T and J/tp branching fractions directly without any theory using R(V) defined in Section 1. We calculate these ratios ignoring possible correlations and find R{J/ip) = 3.1 ± 0.4 while R(T) < 0.26 (90% CL). Clearly R(T) is very different from R(J/ijj)\ 4
Comparison with Theory
As mentioned earlier, there are a number of theoretical predictions with which to compare our upper limit: • Korner, Kiihn, Krammer, and Schneider 5 and Kiihn 6 found that highly virtual gluons minimize suppression of radiative pseudoscalar production. KKKS used a nonrelativistic quark model for the bound states, while Kiihn extended the analysis using a light cone expansion. The predictions are proportional to a*. We use recent values 1 of as and obtain B(T —>7T/) = (5 — 10) x 1 0 - 5 , significantly above our upper limit. A double ratio of rates is a more robust prediction because it is independent of as: _ BjT^rj') g(J/V>-^7/ 2 ) 0.11 nthry= () B(T-,7f2) Whh^T)~^iHowever, Tlexpt < 0.09 (90% CL), and the probability that CLEO and KKKS are consistent is 0.6% • Intemann 7 used an extended vector meson dominance model. His result, which depends on phase of the interference of the virtual vector mesons, is fi(T—>777') = (0.05 — 0.25) x 1 0 - 5 - significantly below our upper limit. • Chao 8 extended familiar 77 — 77' mixing to also include 77c and 776 in a 4 x 4 mixing matrix, which allowed him to relate B(Y—>-fr]') to S(T—->777b). He then used a theoretical estimate of the allowed Ml T—^7776 transition to obtain, £?(Y—>7?7') = 6 x 1 0 - 5 , significantly above our upper limit. Figure 2 compares the experimental V —> 7 P branching fractions and upper limits to the theoretical predictions of KKKS and Chao and to scaling.
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5
Conclusions and Future Prospects
CLEO's upper limit B(T~^-yr]') < 1.6 x 10" 5 (90% CL) is about a factor of 80 below the previous upper limit 3 . The ratio of 77/ to 7/2 is very much less in T decay than it is in J/V decay. The theoretical predictions of KKKS 5 ' 6 and Chao 8 are well above this value, but the range of Intemann's 7 predictions is safely below this limit. In the next year CLEO intends to accumulate a factor of 15-20 more data at the T(15) and could reach sensitivities in the range of Intemann's predictions. Acknowledgments I am delighted to express my appreciation of my CESR and CLEO colleagues whose effort provided the results described here. Our research was supported by the NSF and DOE. I appreciate the hospitality of the DESY Hamburg laboratory where I prepared the conference and proceedings reports. Finally, I want to thank Maria Kienzle-Focacci, Maneesh Wadhwa, and the entire staff of Photon 2001 for the delightful conference that they organized. References 1. Particle Data Group, D.E. Groom et al, E. Phys J. C 15, 1 (2000). 2. CLEO Collaboration, A. Anastassov et al, Phys. Rev. Lett. 82, 286 (1999). 3. Crystal Ball Collaboration, P. Schmitt et al, Z. Phys. C 40, 199 (1988). 4. CLEO Collaboration, T. Browder et al, Phys. Rev. Lett. 8 1 , 1786 (1998). 5. J.G. Korner, J.H. Kvihn, M. Krammer, and H. Schneider, Nucl. Phys. B 229, 115 (1983). 6. J.H. Kiihn, Phys. Lett. B 127, 257 (1983). 7. G.W. Intemann, Phys. Rev. D 27, 2755 (1983). 8. K.-T. Chao, Nucl. Phys. B 335, 110 (1990) and 317, 597 (1989).
CLEO-c A N D CESR-c: A N E W F R O N T I E R OF W E A K A N D STRONG INTERACTIONS DAVID G. CASSEL Newman Laboratory, Cornell University, Ithaca, NY 14853, USA E-mail: [email protected] The CLEO collaboration and CESR accelerator physicists are proposing to convert CESR to operate in the charm threshold region. The achievable CESR luminosities and the excellent capabilities of the CLEO III detector would open a new frontier of exploration of weak and strong interaction physics. The principal goals of this program include: searches for glue-rich exotic states, searches for new physics, and challenging lattice QCD calculations with precise experimental data.
1
Introduction
CLEO-c is a focused program of measurements and searches in e+e~ collisions in the the yfs = 3—5 GeV energy region 1 . Topics to be studied include: • Charm measurements: absolute charm branching fractions, the decay constants fr)+ and fus, semileptonic decay form factors, and the CKM matrix elements \Vcci\ and \VCS\ • Searches for new physics in the charm sector: CP violation in D decay, DD mixing without DCSD, and rare D decays • r studies: precision measurements and searches for new physics • QCD studies: cc spectroscopy, searches for glue-rich exotic states (glueballs and hybrids), and measurements of R (direct between 3 and 5 GeV, and indirect using initial state radiation between 1 and 3 GeV) The existing state-of-the-art CLEO III detector is a crucial element of this program. It includes a central drift chamber for measuring the momenta of charged particles and identifying them via their energy losses (dE/dx), a Csl electromagnetic calorimeter for photon detection and electron identification, and a ring imaging Cherenkov detector (RICH) for charged particle identification at higher momenta. The capabilities and performance of this detector represent a substantial advance above those of other detectors that have operated in the charm threshold region. Testing Lattice QCD (LQCD) calculations with precision measurements is a major emphasis of the CLEO-c program. Theoretical analysis of strongly-coupled, nonperturbative quantum field theories remains one of the foremost challenges in modern physics. Experimental progress in flavor physics (e.g., the CKM matrix elements |Vcfc|, \Vub\, and \Vtci\) is
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frequently limited by knowledge of nonperturbative QCD effects (e.g., semileptonic form factors and decay constants). In the last decade several technical problems in LQCD have been identified and overcome and substantially improved algorithms have been developed. LQCD theorists are now poised to move from 0(15%) precision to 0(1%) precision in calculating many important parameters that can be measured experimentally or are needed to interpret experimental measurements, including: • masses, leptonic widths, EM transition form factors, and mixing amplitudes for bound states in the J/ip and T families; • masses and semileptonic form factors of low-lying baryons containing b and c quarks; and • masses, decay constants, and semileptonic decay form factors of D and B mesons. CLEO-c will provide data in the charm sector to motivate and validate many of these calculations. This will help to establish a comprehensive mastery of nonperturbative QCD, and enhance confidence in LQCD calculations in the beauty sector. The CLEO-c program is based on a four-year run plan, where the first year is spent on the T resonances while constructing hardware for CESR improvements. The data samples anticipated are: 2002 k, 1 f b - 1 at each of the T(15), T(2S), T(3S) resonances (10-20 times the existing world's data) 2003 3 fb" 1 at the V(3770): 30 M DD events and 6 M tagged D decays (310 times the MARK III data) 2004 3 fb" 1 at V i ~ 4.1 GeV: 1.5 M DSDS events and 0.3 M tagged Ds decays (480 times the MARK III data and 130 times the BES II data) 2005 1 fb" 1 at the J/ip: 1 G Jftp decays (170 times the MARK III data and 20 times the BES II data) In the T region, synchrotron radiation damping reduces the size of beams in CESR and is a crucial factor for achieving high luminosity. This damping will be much less at lower energies in the charm threshold region, and that would substantially reduce luminosity. Much of this luminosity loss can be recovered by installing wiggler magnets (magnets with alternating magnetic field directions) to increase synchrotron radiation. We plan to use superferric magnets (Fe poles and superconducting coils) and we have already constructed a three-pole prototype. The anticipated luminosity will still be below that achieved in the T region, and will increase with energy, ranging from 0.2 to 0.4 c m - 2 s _ 1 in the energy region between 3.1 and 4.1 GeV and rising to > 1 c m - 2 s _ 1 in the T region. These wiggler magnets are the only substantial
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CESR hardware upgrade required for the CLEO-c program, and - not entirely incidentally - they are also excellent prototypes for the wiggler magnets that would be needed in Linear Collider damping rings. Using a fast parameterized Monte Carlo program, we have studied the ability of the CLEO-c program to address many of the most important physics questions whose answers may lie in the charm threshold region. The parameters of the program were carefully tuned to match the performance of the CLEO III detector that has already been achieved. In the following sections, I summarize a few of the conclusions of these studies. These studies, the performance of the CLEO-c detector, and the CESR upgrade plans are described in much more detail (and with comprehensive references) in the CLEO-c/CESRc project description 1 . 2
Measuring Absolute D Branching Fractions
The branching fractions, B(D° -» K~ir+), B(D+ -> jf-7r+7r+), and B(D+ -> 4>TT+) are the reference branching fractions for all D meson decays. Ultimately they also set the scales of nearly all b and t quark branching fractions. CLEO-c can measure absolute D branching fractions by comparing double tag (DD) rates to single tag (D and D) rates - the method pioneered by MARK III 2 . Very precise measurements are possible with large data samples in the CLEO III detector because: single tag and double tag events are very clean with little background, most systematic errors cancel in the ratio of double tags to single tags, and no knowledge of luminosities or production cross sections is required. We expect tracking uncertainties to dominate systematic errors. We will measure tracking efficiencies in data using a missing mass technique and we expect to be able to achieve a precision of ±0.2% per track. Figure 1 demonstrates that particle identification and total energy cuts - applied to the very simple low-multiplicity cc states produced near charm threshold - provide large single tag D samples with very little background. Monte Carlo studies using only the cleanest double tag modes indicate that statistical and systematic errors would be comparable, and that we should be able to achieve total errors of 0.6%, 0.7%, and 1.9% for B(D° -+ K--K+), B(D+ —> K~n+n+), and B(D+ —• 7r+), respectively. The precisions of the 3 corresponding PDG averages are 2.3%, 7.7%, and 25%, so the improvements in precision expected from CLEO-c is almost a factor of 4 for B(D° —> K~n+) and a factor of 10 for the others. These improvements will ripple through measurements of nearly all other D and B meson branching fractions, particularly those involving b —> c transitions where the uncertainties in the underlying D branching fractions often contribute significantly to the systematic errors.
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1.86 M (D) (GeV/c2)
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Figure 1. The distributions in reconstructed D mass M(D) expected in 1 f b - 1 of CLEO-c data. The different histograms illustrate the reduction of background achieved with particle identification and the requirement that the energy measured for D candidates match the beam energy (AE cut).
The large samples of very clean single tag D decays are also the key to the rest of the CLEO-c D physics program. Most other measurements will rely on one of these clean single tags to identify and reconstruct the other D or D in the decay. 3
M e a s u r i n g D M e s o n Decay C o n s t a n t s
The decay constants fp for pseudoscalar mesons P are nonperturbative QCD parameters that appear in theoretical calculations of purely leptonic decays {P~ —> t~v£) and of P°p° mixing. These constants are not well known, so they contribute large uncertainties to some crucial measurements. For example, the uncertainty in fB is the dominant error in the determination of the CKM matrix element |V td | from measurements of B°B° mixing. In the next few years LQCD calculations of these constants could reach precisions of 0(1%). However, confidence in these calculations can only come from comparison of theoretical results with experimental measurements. These measurements in B~ —• t~v decays are extremely difficult due to: the high multiplicities in BB events and very low rates (B~ —> yrv (e~p) decays) or low rates and the difficulties in reconstructing final states with two undetected neutrinos (B~ —> T~V decays). Rates and event reconstruction are much
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more favorable in D+ —> n+v, Df —> ^+v, and Df —> r + ^ decays, so it is natural to use measurements of /£>+ and fos to establish the validity of LQCD calculations of these constants. Monte Carlo simulations indicate that reconstruction of D+ —> £+is decays in the CLEO III detector is very clean if hadronic Dq decays are used to tag DqDq events, to constrain the kinematic reconstruction of the ^(s), and to identify the fi+ in D+ —»fi+v decays. The decay amplitude for D+ —+ l^v contains the product fo^cq, s o measurements of B(D+ —» l+vt) and B(Df —» l+ut) determine the products \fTD+fD+\Vcd\ and y/TDsfDa\Vcs\, respectively. Conventionally we expect to use measurements of / # |VCq| and unitarity constraints on \Vcq\ to obtain foq from measurements of the leptonic branching fractions. (As described in the next section, we will also measure \Vcd\ and \VCS\ accurately with semileptonic D decays.) Monte Carlo simulations indicate that uncertainties in the leptonic branching fraction measurements will be comparable to uncertainties in the product y/TDjIKql- Overall we expect decay constant uncertainties (SIDJID,) of 2.3%, 1.9%, and 1.6% from D+ -» p+v, D+ -* v+v, and Df —> T+U decays, respectively. This will challenge LQCD theorists to reach precisions of 0(1%) in decay constants. 4
Measuring \VCS\ and \Vcd\ in Semileptonic D Decays
The decay width for the semileptonic decay Dq —» XqdZ+vi (where Xqd is a hadronic state containing q and d quarks) can be written as T(Dq —> Xqd(.+ve) = TDqi{Xqd)\Vcd\2, where ^y(Xqd) is again a nonperturbative QCD parameter that must be obtained from theory. (There is a similar expression - with s replacing d -for decay to a state containing q and s quarks.) Again we expect LQCD calculations to be able to estimate i(Xqd) with precision of (9(1%). More detailed measurements of these semileptonic decays can be used to establish the validity of the LQCD calculations. Differential decay rates T(Dq —> Xqd £+ve)/dq2, where q2 is the square of the invariant mass of the tv system, depend on one form factor f(q2) when Xqd is a pseudoscalar and on three form factors if it is a vector. The factor j(Xqd) comes from the integral of T(Dq —> Xqd£+yt)/dq2, so measurements of the q2 dependence of the form factors can be compared with LQCD calculations in order to validate the calculations of ^(Xqd). In CLEO-c we can detect semileptonic decays in events with a single hadronic tag and an e^ accompanied by one or more hadrons (Xqd or daughters of its decay). The branching fractions and q2 dependencies can be measured quite accurately because: rates are high due to high single tag rates and large Dq —• Xqd£+ve branching fractions, and background rejection from
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kinematics and particle identification is excellent. For example, Monte Carlo studies show that there will be a clean D° —> n~e+i/e signal, well separated from D° -> K~e+Pe, even though B(D° -> K-e+ve) ~ 10B(D° -» n~e+Pe). We expect to be able to measure semileptonic branching fractions with errors 6B/B « 1% and the exponential slopes (a) of form with errors 5a/a ~ 4%. These measurements will challenge LQCD theorists to calculate form factors and "f(X) with precisions of 0(1%). If the challenges are met, CLEO-c measurements of semileptonic D branching fractions will provide values of \Vcd\ and \VCS\ with errors ^ 2%. 5
Searching for Gluonic Matter
Gluons carry color charge, so they self-interact and should bind to produce glueballs, states composed primarily of gluons. Theoretical predictions indicate that there should be a rich spectrum of glueballs in the few-GeV mass region. However, glueballs may mix with nearby conventional qq mesons, making it difficult to establish that a given observed state is indeed a glueball. At the parton level, radiative J/ip decays (J/V1 —* 7^0 decays should proceed via a jgg intermediate state, providing a glue-rich environment for glueball production. Hence J/IJJ —» 7X decays are an ideal hunting ground for glueballs or glue-rich exotic states. The hermetic CLEO III detector with its excellent 7, TV^, and K^ detection and resolution is nearly ideal for glueball searches because it will be possible to observe decays of glueballs in many different modes (one of the signatures of glueball decay) and to establish Jp values for the parent through accurate partial-wave analysis. Searching for the /j(2220) gluon candidate in 109 J/ip decays is an excellent example of the reach of the CLEO-c experiment in glueball searches. The /j(2220) meson has been rather elusive: it was observed by MARK III, it was not seen by the Crystal Ball, the most robust signal comes from BES, and essentially all other claimed sightings have disappeared. The product branching fractions - B(J/ip -> -yfj)B{fj -> YY) - measured by BES 4 lead to enormous CLEO-c rates. For example, peaks with 23,000, 13,000, and 15,600 events would be observed in the /j(2220) decay channels 7r+7r~, 7r°7r°, and K+K~, respectively. Figure 2 shows that these /j(2220) —» 7T7T signals would stand out well above reasonable estimates of backgrounds. The inclusive J/ip —> "fX spectrum is also a rich hunting ground for new states. For example, Monte Carlo studies with only 60 M Jjt\i decays show a clear fj{2220) signal if B(J/ip -»-yfj) = 8 x H T 4 (BES estimates > 3 x l 0 " 3 ) . We expect that B(J/ip —» jX) > 10~ 4 should be observable with the full 1 G J/tp CLEO-c data sample.
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If strong glueball candidates are found in radiative J/ip decays, searching for them in CLEO data from the T region will be very useful. Two photon collisions are "glue-poor", so demonstrating that a gluon candidate's 77 coupling is small would help to establish that the candidate is glue-rich. The CLEO Collaboration already has nearly 23 fb _ 1 of data in the region near the T(AS) than can be used for searching for glueball candidates in two-photon collisions. Failure to observe a glueball candidate in these two-photon data would be very significant, since these data were accumulated with the CLEO III detector and the quite similar CLEO II and II.V detectors. 6
Studies of T Bound States
So far the only T bound states that have been observed are: T(1S), T(2S), T(3S), l3Pj, and 23Pj. Many predicted ^ 0 {rjb, ...), 1P1 {hb, ...), and D states are missing. In the next year CLEO will run on the T resonances to search for the missing states and to measure accurately Tee, transition rates, and hyperfine splittings. Most of the quantities that will be measured in this program can then be used to validate precise LQCD calculations. We also wish to explore the region above the T(45') with substantially greater luminosity than was available in previous searches. One important motivation for this program is the suggestion that a hybrid (bgb) state may exist in this region. 7
Conclusions
High event rates, very clean signals with small and well-controlled backgrounds, and very small and well-understood systematic errors are unique features of the CLEO-c program.
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The program will provide data samples that are one or two orders of magnitude larger than previous data samples in this energy range. The simplicity of the cc state in the charm threshold region, coupled with the acceptance, resolution, and particle identification of the CLEO III detector are an outstanding match to the requirements of a program of precise - 0(1%) measurements, including: absolute reference hadronic branching fractions for D decay, \Vcd\ and \VCS\ from semileptonic D° and D+ decays, and \VC(i\fD+ and \Vcs\fo, from leptonic D+ and D+ decays, respectively. These results will challenge the ability of LQCD theorists to calculate decay constants and form factors for D decay with 0(1%) precision. Validation of LQCD in the c quark sector is necessary in order to gain confidence for its application in the b quark sector. High-statistics, high-resolution, and low-background searches for gluonic states in the 1-2 GeV mass region in J/ip —> 7 X decays should definitely establish or rule out the fj (2220) and would be a rich arena for finding other glueball candidates. The hermetic CLEO III detector will facilitate the partial wave angular analysis that will be required to determine the Jp of any particles that are observed. The CLEO-c program will create a new frontier in the interaction between experiment and nonperturbative QCD theory that will lay the foundation for future searches for physics beyond the Standard Model. Acknowledgments I am delighted to express my appreciation of my CESR and CLEO colleagues whose effort provided the results described here. Our research was supported by the NSF and DOE. I appreciate the hospitality of the DESY Hamburg laboratory where I prepared the conference and proceedings reports. Finally, I want to thank Maria Kienzle-Focacci, Maneesh Wadhwa, and the entire staff of Photon 2001 for the delightful conference that they organized. References 1. CLEO-c Taskforce, CESR-c Taskforce, and CLEO-c Collaboration, Cornell Report No. CLNS 01/1742, Revised 10/2001 (2001). Links to electronic copies are available at h t t p : / / w w w . l n s . c o r n e l l . e d u . 2. MARK III Collaboration, J. Baltrusaitis et al, Phys. Rev. Lett. 56, 2140 (1986) and J. Adler et al, Phys. Rev. Lett. 60, 89 (1988). 3. Particle Data Group, D.E. Groom et al, E. Phys J. C 15, 1 (2000). 4. BES Collaboration, Z.J. Bai et al, Phys. Rev. Lett. 76, 3502 (1996).
PRODUCTION OF EXCITED P-WAVE CHARM MESONS AT HERA URI KARSHON Weizmann
Institute
of Science,
ISRAEL
ON BEHALF OF THE ZEUS COLLABORATION The production of excited charm mesons has been observed with the ZEUS detector at HERA. Neutral orbitally excited P-wave charm mesons have been reconstructed in the D'^n^ final state and the charm-strange meson nf1(2536) was found in the Dr±K® final state. The fraction of D*± mesons originating from the decays of these mesons has been calculated and converted to the rate of c quarks hadronising as the excited charm mesons. A search for radially excited charm mesons in the •D* ± 7r + 7r - final state has also been performed. The results are compared with those obtained in e+e~ annihilations.
1
Introduction
P-wave charm states (orbital angular momentum L = l of the cq system) are expected in addition to the L=0 D and D* mesons. These P-wave mesons appear as singlet or triplet states and can decay to L=0 states plus a w or a. K 1. Heavy Quark Effective Theory 2 predicts that the four states appear in two doublets with total angular momentum j = L + s = 3 / 2 (narrow states) or 1/2 (broad states), where s is the spin of the light quark. Narrow excited charm mesons, D\ (2420) and D\ (2460), were observed in the D*ir decay mode and identified as members of the j = 3 / 2 doublet with spin-parity Jp = 1 + and 2 + , respectively 1. A charm-strange excited meson, .0^(2536), was found in the D^K® final s t a t e 1 . Radially excited charm mesons with mass about 2.6 GeV are predicted 3 to decay into Drnr or D*inr. A narrow resonance in the D*±Tr+ir~ final state at 2.637 GeV, interpreted as the radially excited D* ± , was reported by DELPHI 4 . No evidence for this state has been found by OPAL and CLEO 5 . We report on orbitally excited charm-meson production and a search for radially excited charm states in e-p collisions. The analysis was performed with ZEUS 1995-2000 data, when HERA collided 27.5 GeV positrons or electrons with 820 GeV (1995-1997) or 920 GeV (1998-2000) protons. Events from photoproduction and deep inelastic scattering were selected with a three-level trigger and used for these analyses.
309
310 ZEUS
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M(Kim,) - M(KTC) (GeV)
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M ( K m y i 4 J i 6 ) - M(Krtn s ) + M(D') (GeV)
Figure 1. (a) M(Knivs) - M(KTV) distribution in the £1° mass region (full dots). The histogram is the distribution for wrong charge combinations, (b) M(Kmvsff4n5) — M(Knns) + M(D") for D* ± candidates. The rectangle is the D* ± signal window. Dashed histogram in inset is Monte Carlo D* ± signal normalised to the obtained upper limit and added to the fit interpolation (dotted curve) in the signal window.
2
Z>?(2420) and D*°(2460) production
D° and D^0 mesons were reconstructed 6 via their decays to D*^Tr^ followed by the Dt:t decays, £>*+ -» D°nj ->• {K-TT+)TT^(+C.C), where 7Ts is the soft pion from the D*± decay. Fig. l a shows the mass difference distribution, A M = M(KirKs) ~ M(Kir), in the D° mass region 1.83 < M(Kn) < 1.90 GeV with transverse momentap±(K,jr) > 0.5 GeV and D P X ( T S ) > 0.125 GeV in the kinematic range p^* > 2 GeV and —1.5 < rj * < 1.5, where rj — — lntan(0/2) is the pseudorapidity and the polar angle 6 is defined with respect to the proton beam direction. A clear D*± signal is seen (dots) on top of a small combinatorial background, estimated by wrong charge combinations (histogram) where both D° tracks have the same charge and ITS has the opposite charge. Dt:t candidates with 0.144 < A M < 0.147 GeV were kept for the excited charm meson reconstruction. A signal of 31350 ±240 D*^
311 ZEUS ZEUS (prel.) 1995-2000 (127 pb"1) Fit: Gauss + A (AMe*)B N(Djf -» D ' X ) = 62 ± 9
2.35
2.4
2.45
2.5
2.3
2.35
2.4
2.45
2.5
M(Kmyi„) - M(Kitn,) + M(D') (GeV)
MfD'X) = AMe"
Figure 2. (a-c) Extended mass difference distribution for D*± candidates (full dots). Dashed histogram is for wrong charge cominations. The curves are the results of unbinned likelihood fits. In (a) and (b) the solid curves are fits to background parametrisation and two Breit-Wigner distributions convoluted with a Gaussian function. In (c) an additional Gaussian-shaped resonance near 2.4GeV is assumed in the fit. Dotted curves are fitted shapes of the combinatorial background, (d) Effective M(D*±Kg) distribution (full dots). Solid line is a fit to a Gaussian resonance plus a background of the form A(AMext)B.
mesons was found in this range after background subtraction. A neutral excited charm-meson candidate was formed by combining a D * ± candidate with another pion (7r4) with charge opposite to that of the D * ± and px(7r4) > 0.3 GeV. Figure 2a shows the "extended" mass difference distribution, M(Kir-Ks^i) -M(Kinrs) + M(D*), where M(D*) is the nominal D*± mass 1 (full dots). A clear excess is seen around 2.4 - 2.5 GeV, where contributions from D° (2420) and D^0 (2460) mesons are expected. No excess is seen for wrong charge combinations (dashed histogram), where D*^ and 7T4 have the same charges. The solid curves in Figs. 2a and 2b result from a unbinned likelihood fit to two Breit-Wigner shapes with masses and widths fixed to the nominal D^ and £>20 values 1, convoluted with a Gaussian function and multiplied by helicity spectrum functions for Jp = l+ and 2 + states, respectively. The background shape was parametrised by the form xa • exp{—{3 • x + 7 • x2), where x — M(K-Kirs^i) — M(KTnrs) — M(TT). The fitted curve describes the distribution
312
reasonably well in the whole range, except for a narrow enhancement near 2.4 GeV. In Fig. 2c a similar fit is performed with an additional Gaussianshaped resonance with free mass and width. The fit yielded 211 ±49 entries for the narrow enhancement with mass value 2398.1 ±2.1 ( s t a t . ) ^ ( s y st -) M e V The width was consistent with the expected resolution. The enhancement may indicate a new excited charm meson, a result of an interference effect or a statistical fluctuation. The number of reconstructed D° and Z)£° mesons in the 3-resonance fit are 526 ± 65 and 203 ± 60, respectively. The acceptance-corrected fractions of D*^ mesons originating from Di and D^ in the measured kinematic range were found to be #D»->£>*±7TT/D*± = 3.40 ± 0.42 (stat.)^°g3 (syst.)% and RDf^D'±^/D*± = 1.37 ± 0.40 ( s t a t . ) ^ ' ^ (syst.)%. Extrapolating to the full kinematic phase space by a Monte Carlo (MC) simulation and using the measured partial width ratio, T(D? ->• D+n~)/T(Df ->• Z>*+TT-) = 2.3 ± 0.6, the rate of c quarks hadronising as D*+ mesons, f(c -> £>*+) = 0.235 ± 0.007 ± 0.007, and isospin conservation, the above fractions can be converted to the rates of c quarks hadronising as £>° and D^0 mesons. We obtain: / ( c —> £>?) = 1.46 ± 0.18 (stat.)+°27 (syst.) ± 0.06 (ext.)% and / ( c -> Df) = 2.00 ± 0.58 (stat.)_ 0 ' 4g (syst.) ± 0.41 (ext.)%, where the third errors are uncertainties in f(c —> D*+) and the D^ —> D*+n~ branching ratio. These rates are consistent with e+e~ rates for these resonances as measured, for example, by the CLEO Collaboration 7 : f(c -> D%) = 1.8 ± 0.3% and f(c^D?) = 1.9 ±0.3%.
3
Search for radially excited D*
±
D* ± candidates were reconstructed 6 from their decays to D*±TC+TV~ by combining the Dt:k candidates in the decay mode of Section 2 with two tracks, assumed to be pions (ir^ and 7^) with opposite charges and px > 0.125 GeV. Fig. lb shows the distribution of the extended mass difference M(KTnrsTT4Tr5) - M(KTnrs) + M(D*). No narrow resonance is seen. An upper limit on the fraction of Df± mesons originating from D* ± decays is given within a signal window 2.59 < M(D* *) < 2.67 GeV, which covers theoretical predictions 3 and the DELPHI measurement 4 . The background distribution was fitted outside the signal region to xa • exp(-/3 • x), where x — M{K7r7rsTT4Trs) — M(KTnrs) — 2M(n). The number of reconstructed D* mesons, 91 ± 75, was obtained by subtracting the background function, integrated over the signal mass window, from the observed number of candidates in the window. After dividing by the number of Z?*± and correcting for accep-
±
313
tance, an upper limit of RD.'+_>D,+n+v,D,+ < 2.3% (95% C.L.) is obtained in the measured kinematic region. Extrapolating by a MC simulation to the full kinematic phase space and using the known f(c —> D*) value, we obtain a D*'* production limit of / ( c -> £>*'+) • BD.l+_D.+n+n< 0.7% (95% C.L.) compared to 0.9% as reported by OPAL 8 4
Production of the charm-strange meson D^(2536)
Dfx mesons were reconstructed 9 via their decays to D*^Kg with Ks —> •K+ir~. K°s candidates were identified by using all pairs of oppositely charged tracks with p±_ > 0.2 GeV. Secondary vertices were found by calculating intersection points in the plane perpendicular to the beams. Assuming the two Kg tracks to be pions (7r3 and 7^), the invariant mass, M^TT^), was calculated for each selected Ks candidate. A clean Ks signal was extracted after applying standard cuts of a VO-finding package 9 . Only Ks candidates with 0.480 < M(^3^4) < 0.515 GeV were kept for the D ^ reconstruction. For each Dfx candidate, the extended mass difference, AMext — M{K-K-Ks'Kz'Kt)M(Kirirs) -M(7r 3 7r 4 ), was calculated. Fig. 2d shows the effective M{D*±KS) ext distribution in terms of AM + M{D*+)PDG + M{K°)PDG (solid dots), where M ( D * + ) P D G and M(K°)PDG are the nominal D*± and if0 masses 1. A clear signal is seen at the value oiM(Df1). The solid curve is a unbinned likelihood fit to a Gaussian resonance plus a background of the form A(AMext)B. The fit yielded 62.3 ± 9.3 D ^ mesons. The mass value was found to be M ( D ± ) = 2534.2 ± 0.6 ± 0.5 MeV, in rough agreement with the PDG value *. The last error is due to the uncertainty in M(D*+)PDGThe angular distribution of the £>si signal was studied via the helicity angle, a, defined as the angle between the Ks and ITS momenta in the D**1 rest frame. The distribution dN/d cos a was fitted to (1 + Rcos2a). The unbinned likelihood fit yielded R = -0.53±0.32 (stat.)_ 0 14 (syst.), consistent with the CLEO value 10 R = — 0.23lo'.32- Both measurements are consistent with R = 0, i.e. Jp = 1 + for the D s i meson. However, our result is not inconsistent with R = — 1, i.e. Jp = 1~ or 2 + n . The fraction of D*± mesons originating from Dfx mesons in the measured kinematic region is: RD± _+D.±Ko/D,± = 1.77 ± 0.26 ( s t a t . ) ^ ' ^ (syst.)%. Converting to the rate of c quarks hadronising as D^ mesons and extrapolating by a MC simulation to the full kinematic phase space, we obtain: / ( c -> D+J = 1.24 ± 0.18(stat.)+°°6 (syst.) ± 0.14 (br.)%. The third error is due to uncertainties in f(c -t D*+) and the D~^ -> D*+K° branching ratio. The rate agrees with the OPAL value 12 of 1.6 ±0.4 ±0.3%. This rate is about
314
twice that expected, assuming f(c -» Dj) « 2% 6 and 7S « 0.3 is the strangeness suppression factor in charm production. 5
13
, where 7S
Summary
Significant production of the excited P-wave charm mesons D°(2420), £>2°(2460) and 1)^(2536) has been observed in e-p collisions at HERA. The fractions of Dt:il mesons in a restricted kinematic region originating from these states were measured and converted to rates of c quarks hadronising as these mesons. The rates agree with previous e + e~ measurements. The rate for D ^ is about twice that expected from the D° rate and a strangeness suppression factor of « 0.3. A narrow mass enhancement at around 2.4 GeV was seen in the D*±TTZf: final state, which may indicate a new excited meson, an interference effect or a statistical fulctuation. No significant production of the radially excited meson D* ± seen by DELPHI was observed and the upper limit on its production is consistent with the OPAL e + e~ measurement. References 1. Particle Data Group, D. E. Groom et al., Eur. Phys. J C 1 5 , 1 (2000). 2. N. Isgur and M.B. Wise, Phys. Lett. B 232, 113 (1989); M. Neubert, Phys. Rep. ,4245, 259 (1994). 3. S. Godfrey and N. Isgur, Phys. Rev. D 32, 189 (1985); D. Ebert et al., Phys. Rev. D 57, 5663 (1998). 4. DELPHI Collaboration, P. Abreu et a l , Phys. Lett. B 426, 231 (1998). 5. OPAL Collaboration, XXIX Int. Conf. on High Energy Physics, ICHEP 98, Vancouver, Canada, July 1998; CLEO Collaboration, hep-ex/9901008. 6. ZEUS Collaboration, XXX Int. Conf. on High Energy Physics, ICHEP2000, Osaka, Japan, July-August 2000, contributed paper 448. 7. CLEO Collaboration, P. Avery et al., Phys. Lett. B 331, 236 (1994). 8. OPAL Collaboration, hep-ex/0101045, submitted to Eur. Phys. J C (April 2001). 9. ZEUS Collaboration, XXX Int. Europhys. Conf. on High Energy Physics, EPS HEP2001, Budapest, Hungary, July 2001, contributed paper 497. 10. CLEO Collaboration, J.P. Alexander et al., Phys. Lett. B 303, 377 (1993). 11. S. Godfrey and R. Kokoski, Phys. Rev. D 43, 1130 (1991). 12. OPAL Collaboration, K. Ackerstaffet al., Z. Phys. C 76, 425 (1997). 13. ZEUS Collaboration, J. Breitweg et al., Phys. Lett. B 481, 213 (2000).
R E S O N A N C E S A N D EXCLUSIVE C H A N N E L S : A N EXPERIMENTER'S SUMMARY S. BRACCINI INFN, Laboratori Nazionali di Frascati, Via E. Fermi, 40 - 1-00044 Frascati (Rome), Italy E-mail: [email protected] A very remarkable number of new results in the study of resonances and exclusive channels has been presented at this conference giving fundamental information in the understanding of strong interactions at low energies. The first results from the new high luminosity colliders are impressive and a lot of activity in this field is foreseen for the future. The most relevant issues are summarized and discussed in this paper.
1
Introduction
The study of resonances and exclusive channels mostly aims to understand the behaviour of the strong interactions in the energy range up to a few GeV. Here perturbative QCD cannot in general be applied and phenomenological models are needed to interpret the data which are often used as input to the models themselves. In this energy range the quarks and the antiquarks form a large number of bound states which are commonly interpreted as mesons and baryons. In this scheme a fundamental question is still open: do glueballs exist? According to QCD, bound states of one or more gluons can be formed but a solid experimental observation is still missing. The search for this form of matter made only by boson force carriers is one of the most actual themes of research in this field. Because of the large mass of the charm quark, the study of the formation of charmonium states allows to test non-relativistic perturbative QCD calculations and to measure a3 at the charm scale. Two-photon collisions at electron positron storage rings represent a very good and clean environment for this kind of studies l. Since gluons do not couple directly to photons, the two-photon process is a powerfull glueball anti-filter. In the last few years a very remarkable progress has been achieved due to the results of many experiments. Considering two-photon physics, LEP at CERN and CESR at Cornell have produced a large number of important results. At this conference the first results from the new e + e _ high luminosity machines DA$NE at LNF and BELLE at KEK have been presented. These
315
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results are impressive and sometimes already comparable with the achievements of the machines of the previous generation. A bright future for this field of research is therefore foreseen. 2
Lepton, meson and baryion pair production in two-photon collisions
The study of lepton pair production is a test for QED and an important tool to understand experimental apparates. The production of muon 2 and r pairs 3 is studied by L3 and bounds for anomalous couplings of the r lepton are set for the first time in this kind of studies. Charged kaon and pion pair production in two-photon collisions is studied by ALEPH and DELPHI 4 . Good agreement is found between the experimental results and the Brodsky-Lepage model for the kaons. For the pions there is not good agreement either between the two experimental measurements or between experiment and theory. More work is therefore required to understand the data. The study of baryon-antibaryon pairs allows to test the predictions of pure quark and quark-diquark models. From the study of the reaction 77 —»pp presented by OPAL 5 it is difficult to have an indication on which model reproduces better the data. The preliminary results of the same channel presented by BELLE 6 show that this channel will be studied with a much larger data sample in the near future. The production of A and E° baryon pairs is studied by L3 7 and good agreement is found with the quark-diquark model predictions. The pure quark model is disfavoured by this analysis. 3
Pseudoscalar and vector mesons
The precise measurements of BR($ ->• 7/7) and of the ratio BR($ -¥ rj'-y) /BR(3> -4 777) by KLOE 8 disfavor models with a large gluonium content in the 77'. This is in agreement with the previous results obtained by L3 9 in two-photon collisions. The K^K*** and 777r+7r final states in two-photon collisions are studied by L3 10 . The formation of the 77(1440) and of the fi(1420) as a function of Q2 is investigated for the first time, showing that also vector mesons can be studied using the two-photon process if a large data sample is available. The two-photon width of the ?7(1440) is obtained using data at low Q2, as reported in Table 2. This first observation of the 77(1440) in untagged twophoton collisions disfavors its interpretation as the 0 _ + glueball in agreement with the lattice QCD calculations. The »7(1440) can therefore be interpreted
317
as a radial excitation u . The first sign of the production of an % meson may have been shown for the first time at this conference by ALEPH 12 . 4
Scalars, tensors and glueball searches
The tensor meson nonet is well established and is nowadays used as a test for other measurements. On the other hand, the interpretation of the scalar meson nonet is still an open and important problem to be solved. According to lattice QCD predictions 13 , the ground state glueball is a scalar with a mass between 1400 and 1800 MeV and the tensor glueball is heavier with a mass between 1900 and 2300 MeV. Since several 0 + + states have been observed in the 1400-1800 MeV mass region, the scalar ground state glueball can mix with nearby quarkonia, making the search for the scalar glueball and the interpretation of the scalar meson nonet a single problem 14 . The interpretation of the 1400-1800 MeV mass region is made even more difficult by the fact that radially excited tensor meson states are also predicted in this mass region. The 7r+7r_7r° final state in two-photon collisions, studied by L3 15 and BELLE 16 , is dominated by the formation of the a2(1320). These studies clearly confirm the observation of the radially excited tensor meson a 2 (1750), already reported by L3 in a previous study 17 . The values obtained for the two-photon width (Table 2) by the two experiments are consistent and agree with the theoretical predictions 18 . The spin-parity analysis performed by L3 shows some indications for other states which will be possibly put in evidence in future as soon as larger data samples will be available. The KK final state in two-photon collisions is largely dominated by resonance formation and is therefore one of the golden channels in the study of scalar and tensor states. A final study of the K^K° final state is reported by L3 19 and a preliminary study of the K° K°s and the K + K ~ final states is presented by BELLE 2 0 . The two K5K5 mass spectra show nearly identical features. Around 1300 MeV a small signal is due to the f2(1270)-a2(1320) destructive interference. The spectrum is dominated by the formation f2(1525)
Table 1. Spin and helicity studies of the KK final state by L3 and BELLE.
f2(1525) 1750 MeV
KUSK°S (L3) (J=2, A=2) only (3=2, A=2) dominant
K£K£ (BELLE) (J=2, A=2) only (J=0) dominant
K + K " (BELLE) (3=2, A=2) only (J=2, A=0) dominant
318
tensor meson for which the two-photon width is measured with high precision by L3, as reported in Table 2. A very clear signal is present around 1750 MeV, exactly where the ss member of scalar meson nonet and the radially excited tensor mesons are expected. To investigate the spin J and the helicity A, the decay angular distributions are studied, as reported in Table 1. Good agreement is found only in the ^(1525) mass region while the interpretation of the 1750 MeV mass region is still unclear. L3 reports a measurement of the two-photon width of the £2 (1750) (Table 2), in agreement with the theoretical predictions for the radially excited tensor mesons 18 . More than one wave is very probably present in this mass region. The presence of a J = 0 state reported by L3 with a fraction of 24±16% and by BELLE, if confirmed, is very important to support the interpretation of the f0(1300), the fo(1500) and fo(1750) as the two isoscalar members of the scalar nonet mixed with the ground state glueball 14 . If this is the case, the fo(980) and the ao(980) cannot be considered as qq states, as suggested by the recent results by KLOE 8 in the study of the decays $ -> ao (980)7 and $ -> f0 (980)7No evidence for the observation of the narrow £(2230) tensor glueball candidate 2 1 is reported by L3 19 and BELLE 2 0 . Upper limits for the twophoton width of the £(2230) are derived, in agreement with the results by CLEO 22 (Table 2). This is in favour of the interpretation of the £(2230) as the tensor glueball in case of a confirmation in gluon rich environments or is just an indication that this state simply does not exist. 5
Charmonia
New preliminary results on the formation of the 7jc(2980) have been submitted by DELPHI 2 3 . The two-photon width is measured using the K g R * ^ , K + K ~ K + K ~ and K + K~7r + 7r _ decay modes leading to the combined result reported in Table 2. This measurement is in good agreement with the previous measurements 21 and with the theoretical predictions 2 4 . No signal of the f]c is observed in the 7r+7r~7r+7r~ final state and the upper limit T71(T}C) < 3.8 keV is derived. This contradictory problem is still under investigation. Two new measurements of the two-photon width of the Xc2 have been presented in this conference by BELLE 20 and CLEO 25 , as presented in Table 2. It is interesting to remark that the measurement by BELLE is based on the "usual" J / ^ 7 decay mode while CLEO performs the first measurement using the 7r+7r-7r+7r~ decay mode. The measurements of the two-photon width of the r)c performed in twophoton collisions are in good agreement with the ones obtained in pp annihilations 2 1 . The situation is different for the \c2- The measurements of the
319 Table 2. The most recent results on the two-photon width of mesons, charmonia, radial excitations and glueball candidates, (t the value is given times the decay branching ratio)
Resonance 77'(958) a 2 (1320)
4(1525) Vc (2980) 7?c(2980) Xc2(3555) Xc2(3555) Xc2(3555) Xc2(3555) Xco(3415) 77(1440) f2(1750) 3^(1752) 4(1752) fo(1500) fo(1710) £(2230) £(2230) £(2230)
Experiment L3 L3 L3 L3 DELPHI L3 L3 OPAL BELLE CLEO CLEO L3 L3 L3 BELLE ALEPH ALEPH CLEO CLEO L3
Final state +
7T 7T~7 7r+7r_7r°
K°K° 9 chan. 3 chan. 9 chan. i+r-y l+l-J +
_
+
7r 7T 7r 7r~
K^K±7rT K°K° 7T+7T 7T° 7T + 7r _ 7r 0 ir+ir~ +
7r 7T~
K°K°
3PC
o-+ 2++ 2++ 0-+ 0-+ 0-+ 2++ 2++ 2++ 2++ 2++ 0-+ 2++ 2++ 2++ 0++ 0++ 2++ 2++ 2++
r i 7 7 4.17±0.10±0.27 keV 0.98±0.05±0.09 keV 0.085±0.007±0.012 keV 6.9±1.7.±0.8keV 13.0±2.7.±5.0 keV < 2.0 keV 1.02±0.40±0.15 keV 1.76±0.47±0.37 keV 0.84±0.08±0.10 keV 0.53±0.15±0.23 keV 3.76±0.65±1.81 keV 0.199^0.52 keV 0.049t±0.011±0.013 keV 0.29+±0.04±0.02 keV 0.27 t ±0.02±0.04 keV < SlOt eV < 550* eV < 2.5* eV < 1.3+ eV < 1.4+ eV
Ref. 9 17 19 26 23 26 28 27 20 25 25
10 19 17 16 29 29 22 22 19
two-photon width of the Xc2 performed in two-photon collisions and using the J / ^ T decay mode are significantly higher than the values measured in pp annihilations 2 1 . The reason for this could be due to a systematic effect affecting the two-photon measurements based on the J/V'T decay mode. As a matter of fact, this new measurement by CLEO is surely not affected by the same systematic effects and is in better agreement with the measurements obtained in pp annihilations. The first measurement of the two-photon width of the Xco is obtained by CLEO 2 5 . The result is reported in Table 2 and is obtained using the 7r+7r~7r+7r- decay mode. An indication for the formation of the Xco is present in the KgK^ mass spectrum presented by BELLE 2 0 . If confirmed, it will be interesting to have the possibility to perform a completely independent measurement of the two-photon width of the Xco-
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6
Conclusions and outlook
The study of resonances and exclusive channels is a very interesting and active field of research. A remarkable progress on the study of resonance formation in two-photon collisions has been achieved in the last few years. Data from the LEP collider at CERN and CESR at Cornell allowed to improve significantly the precision on the two-photon widths of several resonances, to identify some radial excitations and to search for glueball candidates. New high luminosity e + e~ machines have been built and are now starting their data taking. The first results from BELLE at KEK and KLOE at LNF represent a good sign for the future and new projects like CLEO-c 30 are welcome. The most relevant recent results on resonance formation in two-photon collisions are summarized in Table 2 and represent an important contribution to meson spectroscopy and glueball searches. Acknowledgments I would like to acknowledge all the organizers of Photon2001 for the very nice and friendly atmosphere we had in Ascona. I would like to thank in particular G. Bali, co-convener of this session, M.N. Focacci-Kienzle, J.H. Field, M. Wadhwa for the very constructive discussions and suggestions. References 1. S. Braccini, Resonance formation in two-photon collisions, Acta Physica Polonica 31 (2000) 2143 and hep-ex/0007010. 2. G. Debreczeni, these proceedings. 3. D. Haas, these proceedings. 4. K. Grzelak, these proceedings. 5. T. Barillari, these proceedings. 6. A. Chen, these proceedings. 7. B. Echenard, these proceedings. 8. G. Lanfranchi, these proceedings. 9. L3 Collab., Phys. Lett. B 418 (1998) 399. 10. I. Vodopianov, these proceedings. 11. A. V. Anisovitch et al., Eur. Phys. J. A 6 (1999) 247. 12. A. Boherer, these proceedings. ^ 13. G. Bali, these proceedings. 14. C. Amsler, these proceedings. 15. M. Levtchenko, these proceedings.
321
16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
S. Hou, these proceedings. L3 Collab., Phys. Lett. B 413 (1997) 147. C. R. Miinz, Nucl. Phys. A 609 (1996) 364. L3 Collab., Phys. Lett. B 501 (2001) 173. S. Uehara, these proceedings. Particle Data Group, D. E. Groom et al., Eur. Phys. J. C 15 (2000) 1. CLEO CoUab., Phys. Rev. Lett. 79 (1997) 3829; CLEO Collab., Phys. Rev. Lett. 81 (1998) 3328. G. Polok, for the DELPHI CoUab., note submitted to this conference. N. Fabiano, these proceedings. H. Paar, these proceedings. L3 CoUab., Phys. Lett. 461 B (1999) 155. OPAL CoUab., Phys. Lett. 439 B (1998) 197. L3 CoUab., Phys. Lett. 453 B (1999) 73. ALEPH CoUab., Phys. Lett. 472 B (2000) 189. D. Cassel, these proceedings.
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6 Future Projects and Related Topics
Session Convenors: S. Soldner-Rembold, F. Kapusta and V. Serbo
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P H O T O N COLLIDER AT TESLA V.I. TELNOV Institute of Nuclear Physics, 630090 Novosibirsk, and DESY, Hamburg, Germany E-mail:[email protected]
Russia
Photon colliders (77, 7e) are based on backward Compton scattering of laser light off the high energy electrons in linear colliders. Recently the Technical Design Report of the linear collider TESLA has been published. In this paper physics program, possible parameters and some technical aspects are discussed.
1
Introduction
Recently, the ECFA Panel in Europe and the Snowmass Study on Future of High Energy Physics in US have recommended the linear collider on the energy about 500 GeV as the next large HEP project. The unique feature of the e+e~ Linear Colliders is the possibility to construct on its basis a Photon Collider using the process of the Compton backscattering of laser light off the high energy electrons. x~ 4 This option is considered now for all linear colliders projects. In March 2001 the Technical Design of the linear collider TESLA on the energy 90-800 GeV has been published. 5 The Photon Collider has been included in the project, though many technical aspects, especially the laser system, should be developed in the next 2-3 years. So, it is very likely that in about one decade physicists will get a new very powerful instrument for study of matter: e + e~, 77, 7e, e _ e _ collider. Discussion of the photon collider scheme and basic principles can be found elsewhere. 2- 6 In this paper physics, parameters of the TESLA photon collider and possible laser schemes are discussed shortly. 2
Physics
Physics in e + e~ and 77, 7e collisions is quite similar, however, reactions are different and can give complementary information. Some phenomena can best be studied at photon colliders due to better accuracy (larger cross sections or unique reactions, such as 77 —> Higgs) or due to larger accessible masses: a single resonance in 77 and 7e or a pair of light and heavy particles in 7e collisions. As we will see below the 77 luminosity in the high energy part of spectra at TESLA can be about 30 % of the e + e~ luminosity. Taking into account that typical cross sections in 77 collisions are higher than those in e + e~
325
326
collisions by about one order of magnitude 4 ' 8 , 5 the number of "interesting" events at the photon collider will be even higher than in e + e _ collision. So, it is quite clear from general considerations that Photon Collider can complement in an essential way the physics program of the TESLA e + e _ mode. A short list of physics processes for the photon collider is presented in Table 1. 7 More detail consideration of the physics program at photon colliders can be found elsewhere. 7,s Table 1: Gold-plated processes at photon colliders Reaction Remarks ho bb,77 M Tiho < 160 GeV ho WW{WW*) 140<M h o < 190 GeV ll180<Mh 0 < 350 GeV ZZ(ZZ") 77" ho 77 —> H, A —» bb 7 7 ^ / 7 , xtxT, 11 -» S[it\ 7e •
H+H-
-*?
77 -» W+W~ 7 e _ —» W~ue 77 -+ WW + 77 —* tt
Me- < 0.9 x 2Eo - Af-o WW{ZZ)
7 e _ —• ibi/e
77 —» hadrons 7e~ —» e~X and veX 19 -+ qq, cc 77 —» J/ip J/ip
3
M.SSM. heavy Higgs supersymmetric particles tt stoponium anom. W inter., extra dim. anom. W couplings strong WW scattering anom. t-quark interactions anom. Wtb coupling total 77 cross section struct, functions gluon distr. in the photon QCD Pomeron
Parameters of the Photon collider at TESLA
The parameters of the photon collider at TESLA for the energy of electron beams 2£b = 200, 500 and 800 GeV are presented in Table 2. For comparison the e + e _ luminosity at TESLA is also included. It is assumed that the electron beams have 85% longitudinal polarization and that the laser photons have 100% circular polarization. The thickness of the laser target is one Compton scattering length for 2EQ = 500 and 800 GeV and 1.35 scattering length for 2EQ = 200 GeV, so that k2 ss 0.4 and 0.55, respectively (k is the e —» 7 conversion coefficient). The laser wave length is 1.06 /xm for all energies. The distance between conversion and interaction points is b = ^ay for 2EQ = 500 and 800 GeV and b = 27
327 Table 2: Parameters of the photon collider at TESLA.
2£o,GeV scat
500 200 800 1.06/1.8 1.06/4.5 1.06/7.2 1.35 1 1
2 2 N/1010 2 az [mm] 0.3 0.3 0.3 14.1 14.1 14.1 frep x nb [kHz] 2.5/0.03 2.5/0.03 2.5/0.03 •yex/y/W-6 [m-rad] 1.5/0.3 1.5/0.3 1.5/0.3 px/y [mm] at IP 140/6.8 88/4.3 69/3.4 ax/y [nm] b [mm] 2.6 2.1 2.7 Lee(geom) [1034 cm-'s" 1 ] 48 12 W Lee(z > 0.65) 0.03 0.07 0.095 (GeV) 122 670 390 77, w> L^(z > 0.8z m , 77 ) [1034] 0.43 1.7 1.1 732 440 W-7e, max (GeV) 156 1.3 L 7e (* > 0-8zm,7e ) [1034] 0.94 0.36 :ii [10' cm-'-'s-1! 5.8 1.3 3.4
0.6
0.8
1
Z-W„/2E„
Figure 1: 7 7 luminosity spectra at TESLA(500). Solid line for total helicity of the two photons 0 and dotted line for total helicity 2.
below include nonlinear effects in the Compton scattering. 10 Corresponding parameters f2 = 0.15,0.2,0.4 for 2E 0 = 200,500,800 GeV, respectively. From Table 2 one can see that for the same energy L 7 7 (z > 0.8z m ) « ( l / 3 ) L e + e _ . Simultaneously with 77 collisions there are also 7e collisions with somewhat lower luminosity, so one can study both types of collisions simultaneously. Residual electron-electron luminosity is very small due to the beam repulsion.
328
The normalized 77 luminosity spectra for 2E0 = 500 GeV and 800, 200 GeV are shown in Fig. 1 and Fig. 2, respectively. The luminosity spectra are decomposed in two parts: with the total helicity 0 and 2. Fig. 1 shows also TESLA(200)
TESLA(800)
0.6
0.8
z-W„/2E.
Figure 2: The 7 7 luminosity spectra at TESLA for 2E0 = 800 and 200 GeV (for Higgs(115)) 0.9
0.9
<*7.
0.8
1
L.
•
'
0.7
I
•
'
'
1
'
U U
0.7
R-lto.-u.l/a^-IW
0.6
0.5
0.4
0.4
0.3
\\,
no cut
R-llu,- -^/"ov-%.J
0.6
0.5
0.3
J
0.2
h
R<0.5 ^~~fi: C
0.2
0.4
0.6
\' 0.8
l-W* /2E,
no cut
0.1
0
• 1
R<0.i|
0.2
0.1
0
•
0.8
C
0.2
0.4
•
-
_^Z,^; 0.6
0.8
1
z-W^ /2E,
Figure 3: Left: normalized 7e luminosity spectra at TESLA(500) when the photon collider is optimized for 7 7 collisions and there is e —» 7 conversion for both electron beams. Right figure: there is e —> 7 conversion only for one electron beam and the distance between interaction and conversion point is 1.05cm, 5 times larger than for the left figure.
luminosity spectra with additional cuts on the longitudinal momentum of the produced system, which suppress the low energy luminosity to a low level. In the case of only two jets one can restrict the longitudinal momentum using the acollinearity angle between jets (H —• bb,TT, for example). The normalized 7e luminosity spectra for 2EQ = 500 GeV and parame-
329 ters from Table 2 are shown in Fig. 3-left. For dedicated ye experiments one can convert only one electron beam, increase the distance between the conversion and the interaction points and obtain the ye luminosity spectrum with suppressed low energy part, Fig. 3-right. The 77 luminosity distributions, including all their polarization characteristics, can be measured using processes 77 —• l+l~ (I = e, fj,). The 7e luminosity can be measured using the process 7 e _ —» 7 c - . 5 4
LASERS-OPTICS
The photon collider at TESLA requires the laser with wavelength about 1 /mi, the flash energy 5 J, duration 1.5 ps and the repetition rate 14 kHz.
Figure 4: Optical trap (storage ring)
Ring-cavity optics for e to Y conversion of one electron beam side view
M
adaptive optics other opt. elements
laser M (T-0.01)
Figure 5: Ring type external optical cavity
All parameters are reasonable for exception of the repetition rate (average power). To overcome this problem each light pulse at TESLA will be used
330
many times. Two schemes are considered. In the first scheme, 9 ' 5 Fig.4, each laser bunch is used for the e—> 7 conversion about 12 times. The laser pulse is sent to the interaction region where it is trapped in an optical storage ring. This can be done using Pockels cells (P), thin film polarizers (TFP) and 1/4wavelength plates (A/4). The maximum number of cycles is determined by reflection coefficients of mirrors and attenuation in the Pockels cell. In the second scheme, u'9>12>5 an "external" optical cavity is used. Using a train of low energy laser pulses one can create in the external cavity (with one mirror having small transmission) an optical pulse with an energy higher than in a laser pulse by a factor Q (cavity quality factor) and this pulse collides with electron bunches many times. As result the required laser power can be lower than in the one-pass case by factor of 50-100. In the next two-three years a design of the photon collider (interaction region, laser system and specific elements of a detector) should be done. Physics program will be further developed, main processes have to be studied with realistic simulation. The work has been partially supported by the INTAS 00-00679 grant. References 1. I.Ginzburg, G.Kotkin, V.Serbo, V.Telnov, Pizma ZhETF, 34 (1981) 514; JETP Lett. 34 (1982) 491. 2. I.Ginzburg, G.Kotkin, V.Serbo, V.Telnov, Nucl. Instr. k Meth. 205 (1983) 47. 3. I.Ginzburg, G.Kotkin, S.Panfil, V.Serbo, V.Telnov, Nucl. Instr. kMeth. 219 (1984) 5. 4. V.Telnov, Nucl. Instr. kMeth.A 294 (1990) 72; 355 (1995) 3. 5. TESLA Technical Design Report, Part VI, Ch.l. Photon collider at TESLA, DESY 2001-011, ECFA 2001-209, TESLA Report 2001-23, hepex/0108012. 6. R.Brinkmann et al., Nucl. Instr. kMeth. A 406 (1998) 13, hep-ex/9707017. 7. E. Boos et al., Nucl. Instr. hMeth.A 472 (2001) 100, hep-ph/0103090. 8. V.Telnov, Int. J. Mod. Phys. A 13 (1998) 2399, hep-ex/9802003. 9. V.I. Telnov, Nucl. Instr. kMeth. 472 (2001) 43, hep-ex/0010033. 10. M. Galynski, E. Kuraev, M. Levchuk, V. Telnov, Nucl. Instr. &cMeth. 472 (2001) 267, hep-ph/0012338. 11. V. Telnov, Nucl. Phys. Proc. SuppL, 82 (2000) 359, hep-ex/9908005. 12. I. Will, T. Quest, H. Redlin, W. Sandner, Nucl. Instr.&Meth. A 472 (2001) 79 .
C H A R G E A S Y M M E T R Y IN e + e ~ , 7 P , 7 e COLLISIONS ILYA F . G I N Z B U R G Sobolev Institute
of mathematics SB RAS, Pr-t Koptyuga Novosibirsk, 630090, Russia E-mail: [email protected]
\,
I discuss problems considered recently and some to be studied in the future: Phases of ITIX scattering, resonances in e + e - —• e + e ~ ir+Tr~, e+e~ KK, e+e~ cc, possible CP violation with t-quarks in cy —• eti. Possible discovery of the odderon in diffraction type process "fp —> ir~*~ir~X. Breaking of quark-hadron duality. Weighted structure functions in DIS. Study of possible strong interaction in the Higgs sector via cy -> eW+W~.
The charge asymmetry of reaction products is a powerful tool for many problems of particle physics. It can be of different origin: • The CV violation in a process or a decay. • Specific charge content of an initial state (e.g. quark content of proton). • Interference of production mechanisms giving final state T (like 7r+7r~ or qq pair) with the same particle content but with opposite C-parity. We consider here mainly the last one. In all the cases the key to charge asymmetry is connected to photons (with definite - negative - C-parity). A well-known example is a forward-backward asymmetry of the muons produced in the e+e~ collisions at Z resonance. A vector current (photon exchange mainly) produces a C-odd system while an axial current in Z exchange produces a C-even system. The observed charge asymmetry in charm photoproduction 1 mixes the second and the third mechanisms. Two particle final s t a t e s . We start with production of two-particle systems T, i.e. e+e~ —> e+e~ T, ej -> eT, jp —> TX with T = TT+TT~ or cc or W+ W~, ... and describe kinematics in terms of the pion case. First, let pi and P2 be momenta of collided particles, s = (pi + P2)2, 2-axis is directed along collision axis, transverse components of momenta are orthogonal to pi and P2 both. Next, p± are momenta of ir^, with energies e± and longitudinal momenta p±z. We define z± = (e± +P±z)/y/s,
k=p++p-,
W = M = Vk? , r = p+ - p- . (1)
The charge asymmetry is that over r^ —> —r^. We consider it studying distributions in components of rM, determined via light cone variables for pions, z± and the relative transverse momentum of pions in their c.m.s. p±: S = z+-z-,
v = p2+±-p2_±-
£ k i = (pj.k ± ), (p± = r± - £k x ) . (2)
331
332
Here £ and v denote forward-backward (or longitudinal) and transverse asymmetry respectively. These variables are related to the polar and azimuthai angles in the c.m.s. of produced system T as £ oc cos 9, v = ^W\p_L\sm9cos(j).
e+e~
—> e+e~ 7r + 7r _ , TVK scattering, resonances, etc.
Developing proposals of ref.2, we calculated the charge asymmetry of pions in the process in a form suitable for the real experimentation 3 . This asymmetry corresponds to an interference between the amplitudes given by diagrams of fig. 1. Pi^ p'} ~~' q^ Z C-even (7r+7r, ) =>• i C P ga* +
^ T * * ? ^ C-odd (TT+TT-)
( )« ^ v . PX «2 „, -Pa • ~P2
pi T
; fil
tr.
Figure 1. The two-photon and bremsstrahlung production of pion pairs
In the helicity basis for the 7*7* —> TT+TT~ subprocess the charge asymmetric part of distribution in pion phase space dT^ (in the inclusive set-up) reads as ^ -
= [G++Re(F:M++)
+ G—FU(F;M-J)
+ G0+fie(F;M0+)] .
(3)
fll fl-jr
The coefficients d are calculated in refs. 3 , 4 . (The process e+e~~ -> 7r+7r~7 gives also a charge asymmetry in pion distribution due to interference of diagrams with ISR and FSR. It is separated from our process by cut in value of missing mass Mm = (pe+ + pe~ — p+ — p _ ) 2 with Mm ss 0 for the process e+e~~ -> 7r+7r~7 and relatively large Mm for our process.) At low effective dipion mass this asymmetry is directly connected to the sand p-phases of the elastic 7T7T scattering. At higher energies these observations should help to separate different models for resonances having two-pion and two-photon decay modes. For instance, it can give us some new information about /O(980) and / 2 (1270) mesons etc. To get an idea about magnitude of charge asymmetry just as S/B, we consider a toy model with 5-wave given by only QED + /o(980) at I^o = 100 MeV and with additional phase shift 1? (giving effect of possible a state) + pion form factor for P-wave. At suitable kinematical cuts the asymmetry in K « £ and v together with charge symmetric background (solid lines) are comparable with pure QED effects (dotted, etc. lines) in fig. 2.
333 10 "|»"i»"|
. r
^ r : —™*s.
-
^~
,_ > .
!"" |"-i|-.i| ]»» T T T 1 difft/dW J dAff,/dW dAo»/dW i 10"' i dAo,/dW + f„ r-0.1 G«V. * a&ojavi + / „ r - o . i G«v, * dflo»/dW x 10"' +• rB
"T
I""
I
GeV I'
"'1
1
1
1J
: | :
, ^ H n z ::-
V
•
i 1000 W. in MeV
1200
Figure 2. The charge asymmetries due to (p, /o(980)) interference.
Related topics.
• The eqs. 3 describe charge asymmetry of kaons in the process e + e — e e K+K~ as well. At MKK ~ 1 GeV this asymmetry is given by the phase difference between amplitudes of cf> meson and mysterious /o(980) + ao(980) mesons production. • e+e~ —>• e+e~ cc, e+e — —>• e+e~bb, e*y —> ebb. These quarks are produced mainly via resonance states (near the threshold). Therefore, the study of charge asymmetry in these processes (perhaps, in LEP data) can help to discover new C-even (with J = 0 and 2) cc and bb resonances. (The similar analysis of HERA data can be useful for such discovery also.) • e*y —>• eti. Effects of the New Physics are expected to be well visible in interactions of (very heavy) t-quarks. The study of charge asymmetry in the process will be a new effective tool for a study of possible CV violation effects related to the New Physics. The quark-hadron duality will work here well since t-quark decays before formation of bound state. The equation for muons describing charge asymmetry in QED is changed here due to contribution of the Z boson exchange axial current from the bremsstrahlung diagram. Besides that, at large transverse momentum of the scattered electron a contribution from the t-channel Z boson exchange with its axial current should also influence on a charge asymmetry. These effects should be studied in details to separate them from effects of true CV violation related to the New Physics. The effect of axial Zti anomaly (due to Z-boson) can also be observed at small transverse momenta of the electron. +
Possible discovery of t h e odderon in jp —>• TV+TV~X.T Let us remind that the Pomeron and odderon are considered as the t—
334
channel Regge-pole type objects that have identical vacuum quantum numbers except the only difference: in contrast to the C-even Pomeron, the odderon has negative C, similar to the photon. The Pomeron describes elastic and total cross sections at high energies. The odderon is responsible e.g. for the difference a*°' — a^ at high energies. (In QCD treatment the Pomeron and the odderon are based on two-gluon and d-coupled three-gluon exchanges in ^-channel respectively). The data and BFKL calculations show that the Pomeron intercept aip(O) > 1. There is no reliable information on the odderon intercept, the estimations vary with the paper preparation date (a o (0) = 0.94 -> 0.96 -> 1 ->?). The odderon remains an elusive object till now. It is not seen in the difference app — <jpv at present accuracy. The 7p collisions at HERA provide the best place for the discovery of the odderon. Indeed, an initial photon has definite C-parity. Thus, the high energy diffractive production of C-even meson M in process •yp -> M + X is completely governed by an odderon exchange (X - proton or proton remnant) 6 . The cross sections of these processes at small p± were calculated with some "plausible" assumptions (in particular, it was assumed that the odderon is just around the corner in avv — app data) 6 . The discovery of the odderon via study of charge asymmetry in the photo production of cc pairs was proposed in ref.8. The charge asymmetry is caused by an interference between C-odd system (Pomeron exchange) and C-even system (odderon exchange) production. However, even the Pomeron mediated cc production cross section is small. The efficiency of c-quark recording is not high. Last, the obtained interference term contains a small factor Re \ileiir(an>-ao)/2
= sin[7r(aip-ao)/2].
(4)
All these things make it difficult to discover the odderon in this very approach. We propose to search for the odderon using similar charge asymmetry in the high energy diffractive type process •yp —• TT+TT~P* at HERA 7 (p* denotes proton or its excitation). Here the observable effect should be much bigger than the direct odderon-induced production of C-even resonances, and dependence on hypothesis about odderon-proton coupling is smaller. The C-odd and C-even states of dipion are produced via Pomeron and odderon exchanges respectively. For the first discussion we consider for Pomeron only p{770) and for odderon / 2 (1270). An interference of these mechanisms beings a charge asymmetry in the momentum distribution of pions. We present the Pomeron contribution in a simple approximation KA
_ „™<*u>/2 nr~
/W^-BRP,
/2WBr(R ~» 7T+7T )mRTR 2 2 H ^{M -m R + imRrR)
JX
335
The odderon contribution is similar (with different intercept value and additional factor i in front). The slope parameter for / 2 is unknown, we use in estimations Bf ta Bp. Factor £,£ depends on helicity A of produced resonance R, its spin J and initial photon polarization vector e. For the p and f2 meson production in the states with helicity 1 we have respectively MS1/
2v / 3(erl),
MS2/
= 2\/l5(erj_)£.
(6)
The interference between the amplitudes with even Ac=+ — Ac = _ gives forward-backward asymmetry, while the interference between amplitudes with odd Ac=+ - Ac=- gives transverse asymmetry . The forward-backward asymmetry can be considered either in the form A*£"B similar to partial wave analysis (remind that £ = cos 8) or in other form: APW
•^FB
J idal ( | do) , A%B = J idol ( | \t\da
(7)
Our numbers refer to v ^ ~ 200 GeV (HERA). The diffractive p production (Pomeron exchange) was measured as a(-yp —> pp*) ~ 5pb. The estimations of ref.6 give ao(SYP -> hp*) « 20 nb (odderon exchange) - with uncertainty related to hypothesis about value of odderon coupling to proton. The p mesons are produced mainly in the same helicity state as an initial photon (s-channel helicity conservation - SCHC). We assume the same SCHC, i.e. A = 1 for the / 2 production. In this case main charge asymmetry is a forward-backward one (and ApB = 2AFWB). It is shown in fig. 3. We see that 0.25 0.225 0.2 0.175 0.15 0.125 0.1 0.075 0.05 0.025
L o c a l F—B a s y m m e t r y Af B (M)
Figure 3. The AV^B for the pj ji production. Solid and dotted lines: ajp —OLQ = 0 and 0.1.
with the choice for averaging the dipion mass interval 1.2 GeV < M„.+„.- <
336
1.4 GeV, the observable effect should be about 0.15-0.2 for A^B and 0.3-0.4 for A^FB. (This value can be enhanced using reasonable cut from below in fc_i_.) The new data reported at this conference show that the cross section of J2 production at least twice lower than those predicted in ref.6. Even with damping by factor 6 (more than for ir° production) above numbers must be decreased by a factor 2.5, provided good enough perspectives for observation. Note, that according to data, the SCHC violating amplitude of p production can be of ~ 30% (that is ~ 10% in cross section). With SCHC violating amplitudes for / 2 production added, one can expect that the transverse asymmetry will be of the same order of magnitude. Other mechanisms of fa production contribute to the effect weakly. • The p, co trajectories for production of C-even resonances contribute much less than the odderon expectations 6 , o-p,u(lP —* hP*) ~ 0.1 nb. • The Primakoff effect contribution (7^ —¥ (77* —• f2) ® (p —> 7*p)) is concentrated at very low total transverse momenta of produced pion pair. Its interference with the Pomeron can be eliminated by a proper lower cut in k± 6 . The interference between Primakoff and bremsstrahlung mechanisms in the electroproduction of dipions (like that in e+e~ —> e+e~ 7r+7r~) is much lower than discussed here since bremsstrahlung production of C-odd dipion is much lower than that via Pomeron. In this respect the paper 9 is off the point. Breaking of quark—hadron duality. It is assumed usually that for the heavy quarks the quark-hadron duality works well (at least in average). However, the crucial feature of the obtained results was a strong enhancement of an interference term due to final state interaction (formation of resonances). It changes the effects dramatically. The main source of observed £>-mesons is a decay of cc resonances. That are J = 1 states of cc system, produced via bremsstrahlung production for e+e~~ collision or a Pomeron exchange for -yp case. In the same region J = 0 and perhaps J = 2 states of this cc system should be produced via twophoton production or an odderon exchange respectively. All these resonances are not very narrow. The overlapping of these resonances should give essential contribution to the charge asymmetry as it was discussed for pions. Would be above duality valid, the main asymmetry in e+e~ -t e+e~ cc will be transverse one (just as for muons in the process e + e~ ->• e+e~ /j,+p,~)3. For the 7p collision this asymmetry will be suppressed by a small factor (4), obtained in ref.8. In reality for resonans production we expect picture that is similar to pion pair production. In the e+e~~ collisions essential charge asymmetry will be forward-backward one. In the -yp collisions the small factor (4) is eliminated because of additional phase shift given by a product of two
337 Breit-Wigner factors related to different resonances. Therefore, a charge asymmetry makes clear breaking of quark-hadron duality due to final state interaction even for heavy quarks. Weighted structure functions Here we consider a deep inelastic scattering of electron with momentum pe on the proton with momentum pp (DIS). Let us denote the sums of momenta of all positively charged and all negatively charged particles by p± and corresponding light cone variables z± respectively. Now we describe charge asymmetry with the aid of variables £ and v, determined by eqs. (2). The suggested weighted structure functions (WSF) are described via data in the same manner as usual structure functions (SF) for DIS but with charge odd weight factor like £ for each event. (Certainly, the standard polarization analysis can be added to these definitions.) In the standard language they are W^{p,q)
= 2n2^2 x
fdiz<X\Jv(0)]\p>ei^
(8)
J
with charge odd operator Rc (longitudinal or transverse). Note that with the weight £, effects of proton charge gives negligible contribution in the result, since Xj are small for secondaries j flying along initial proton. Useful points of the W S F . • The (multi) gluon exchange effects cannot be seen in the standard SF W3. Indeed, for this exchange with proton, W3 corresponds to interference of C-even (Pomeron-like) exchange and C-odd (odderon-like) exchange, producing in the collision with photon final states with opposite C-parity. Therefore, this contribution disappears in the standard SF (see ref. 10 for lowest order) and it remains in the WSF. • At large transverse momenta of scattered electron the difference of the cross sections for left-hand and right-hand polarized electrons (like W3) depends on vector and axial currents Jv and J A as daL - daR oc Re(J^JA),
(9)
where Jy is roughly determined by only 7* intermediate state and J A is given by Z exchange only. In this case we deal with the interference of final states given by hard Pomeron exchange but with initial states of opposite C-parity. According to our experience in Higgs physics at pe± > 30 GeV these contributions become close to each other. This interference disappears in the standard SF and it remains in the WSF.
338
Strong interaction in Higgs sector. ~ye —>•
eW+W~
Possible strong interaction in the Higgs sector can be seen as that of longitudinal W's and, in particular, in the process 77 -t WLWL- The experience with 77 —> n+ir~ makes the following picture the most probable: strong interaction modifies weakly the cross section near the threshold in comparison with its QED value but the phase of the amplitude reproduces that of strong interacting WLWL scattering and it can be not small. It makes strong interaction in the Higgs sector badly observable in the cross sections below expected masses of WW resonances, about 1.5-2 TeV but one can expect to see it even at relatively low energy of TESLA (0.8 TeV) using discussed charge asymmetry in cy —• eW+W~. The charge asymmetry in this process is caused by an interference of two-photon and one-photon production (as in e+e~ —¥ e + e~ 7r+7r~) and by interference of photon and Z boson exchanges. The different interferences dominate in different regions on final phase space (depending on transverse momentum and energy of scattered electron). I am thankful to organizers for support of my participation in the Conference. This paper is also supported by grants RFBR 99-02-17211, RFBR 00-15-96691, INTAS 00-00679 and grant 015.02.01.16 Russian Universities. References 1. E. Cuautle, G. Herrera, J. Magnin, A. Sanches-Hernandez. hep-ph/0005023 2. V.L. Chernyak, V.G. Serbo. Nucl. Phys. B 67, 464 (1973) 3. I.F. Ginzburg, A. Schiller, V.G. Serbo. Eur. Phys. J. C 18, 731 (2001) 4. M. Diehl, T. Gosset, B. Pire. Phys. Rev. D 62, 073014 (2000). 5. I.F. Ginzburg, D.Yu. Ivanov. Nucl. Phys. B 388, 376 (1992) 6. E.R. Berger, A. Donnachie, H.G. Dosch, 0 . Nachtmann et al.. Phys. Rev. D 59, 014018 (1999), Eur. Phys. J. C 9, 491 (1999), Eur. Phys. J. C 14, 673 (2000) 7. I.F. Ginzburg, LP. Ivanov, N.N. Nikolaev. In preparation. 8. S.J. Brodsky, J. Rathsman, C. Merino. Phys. Lett. B 461, 114 (1999) 9. M. Galynsky, E.A. Kuraev, P.G. Ratcliffe, B.G. Shaikhatdenov. hep-ph/0003061 10. T. Jaroszewicz, J. Kwiecinski, M. Praszalowicz. Z. Phys. C 12, 167 (1982)
S T R U C T U R E OF T H E COULOMB A N D U N I T A R I T Y C O R R E C T I O N S I N T H E e+e~ P A I R P R O D U C T I O N A T RELATIVISTIC N U C L E A R COLLISIONS
R.N. LEE AND A.I. MILSHTEIN Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia E-mail: [email protected]; [email protected] V.G. SERBO Novosibirsk State University, 630090 Novosibirsk, Email: [email protected]
Russia
We analyze the structure of the Coulomb and unitarity corrections to the single e+e~ pair production as well as the cross section an for the multiple pair production in collision of ultra-relativistic nuclei. In the external field approximation we consider the probability of one pair production at fixed impact parameter p between colliding nuclei. We obtain the analytical result for this probability at p ~S> l/me. The energy dependence of this probability as well as that of
1
Introduction and main results
Recently the processes of e+e~~ pair production in ultra-relativistic nuclear collisions, especially at the RHIC and LHC, were discussed in numerous papers. T h e charge numbers of nuclei Z\ = Z 2 = Z and their Lorentz factors 71 = 72 = 7 are given in Table 1. T h e cross section of one pair production in the Born approximation was obtained many years ago l'2 and reads 28 crBorn = 7ZT ao [L3 - 2.198 L2 + 3.821 L - 1.632] ,
(1)
ZY7T
{ZiaZ2af °o =
—2
1 ,
a = —
,
L = ln(7i72),
(2)
where m is the electron mass. Here we consider the case I > 1 . Since cross section (1) is huge (see Table 1), a pair production can be a serious background for many experiments. Besides, it is also important for the problem of beam lifetime and luminosity of colliders (see review 3 ) . It means t h a t t h e various corrections t o t h e Born cross section, as well as t h e cross section an for n-pair production, are of great importance. At present, there are a lot of incorrect statements in papers devoted to this subject (the
339
340 Table 1. Results for relativistic heavy-ion colliders
Collider
Z
^Coul 0Born
0-unit, 0Born
36.0
-25%
-4.1%
3000
227
-14%
-3.3%
3700
0.872
-1.06%
-0.025%
7
OBorn [kb]
RHIC, Au-Au "79
108
LHC, Pb-Pb
82
LHC, Ca-Ca
20
corresponding references and critical remarks can be found in 4>5'6). In the present paper we try to clarify some principal points in this problem a . Since the parameter of the perturbation series Za may be not small, the whole series in Za has to be summed. Fortunately, there is another small parameter 1 / L < 0 . 1 , therefore, it is sufficient to calculate corrections in the main logarithmic approximation only. The exact cross section for one pair production can be written as 0\ - OBorn + CTCoul + ^unit •
(3)
The Coulomb correction acoui corresponds to multi-photon exchange of the produced e± with nuclei (Fig. la). In the main logarithmic approximation
Figure 1. Feynman diagrams for the Coulomb and unitarity corrections
the Coulomb correction was calculated in
4
28
-ecu. = ^
°°
1
[/(Zia) + f(Z2a)] oQL> , /(*) = x 2 £ n=l
. ^
(4)
'
The accuracy of this calculation is determined by the omitted terms Accoui/^Bom ~ {ZiflOt)2/L2. This accuracy is better than 0.4% for the RHIC and LHC colliders. The size of the Coulomb correction is given in Table 1. "More details can be found in our e-print hep-ph/0108014.
341
The unitarity correction <7unit has terms ~ (ZiaZ2a)2t-n~1')2. The calculation of the unitarity correction as well as an for n > 2 differs considerable in two interesting cases: A) Zi>2a
L2 ,
(5) (6)
n>2,
C 3 = 0.264,
C 4 = 0.066,
C 5 = 0.0176.
(7)
These results can be directly applied to Ca-Ca collisions at the LHC with Za = 0.15. In particular, we find that the unitarity correction is small (see Table 1) and that a2 — 0.11 b which corresponds to 27 000 events per second with the production of two e + e~pairs. Our result an oc Ln for n > 2 differs considerable from the incorrect results an oc L2n of 7 and an oc L3n of 8 . The case B is considered in Sect. 4. The results are given in Table 1. 2
External field approximation
For 7 ^> 1 it is possible to treat the nuclei as sources of the external field and calculate the probability of n-pair production P„(p) in collision of two nuclei at a fixed impact parameter p. The corresponding cross section an is obtained by the integration over the impact parameter: an = J Pn(p) d2p. For the sake of simplicity we consider the process in the frame where the nuclei perform the head-on collision with the same Lorentz factors 71 =72 = 72.1
Calculation of Pi (p) in the Born approximation
The lowest order for the probability Pi (p) is given by the Born approximation denoting as P B ( P ) - It plays an important role in further consideration. For a few particular values of 7 the function PB (p) was calculated numerically in Refs. 10 ' 11 around mp ~ 1 . For mp ^> 1, this function was approximated in Ref. 3 by a simple expression - , ,
14 (ZxaZ2a)2
/
0.68i72\2
,
2
/cA
This expression looks very convenient for fast estimates of various quantities. That is why Eq. (8) is widely cited and used in many papers (see, for example, Refs.
12,7,13,10,14,15,16,8)
W e
find
Qut^
h o w e v e r )
t h a t
Eq^gj
ig i n c o r r e c t
.
in
342
fact, there are two scales in dependence of PB{P) on p: in the region of relatively small impact parameters, 1
PB(P)
= IT* ( Z l (^j" ) 2 t 2ln 7' - 3 ln (mp) ] ln (mp)'
(9)
while in the region of relatively large impact parameters, 7 < mp
The most important distinction between Eq.(8) and our result is a quite different dependence of PB(P) on 7 for 1
Wj
1 7 —
Wj<m7,
pj
u>i
m
(11)
Then these photons collide and produce a pair, therefore, PB(P) = f dnidn2 5 ( P l -p2-p)
a^(W2),
W2 = 4 Wl w 2
(12)
where the cross section of the process 77 —> e + e . The further simple integration leads to (9), (10). 2.2
Average number of pairs n(p) and a?
We introduce now the average number of the pairs produced in collision of two nuclei at a given p: 00
fi(p) = $ > p n ( p )
(13)
71=1
and the artificial cross section: oo
/
n(p) d2p = ^
n<J
n
(14)
n=l
The quantity n(p) can be expressed in the closed form (see Refs. 17
343 corrections with respect to one of the nuclei, and a^c is the Coulomb corrections with respect to both nuclei. In the main logarithmic approximation they were obtained in 5 ' 6 o% = ~
[f(ZAa)
+ f(ZBa)}
a0L2,
a%c = ±- f(ZAa)f(ZBa)
a0 L (15)
where the function f(x) is given in (4). It is clearly seen that, within accuracy of calculation, the sum 0% + a^c coincides with the Coulomb correction (4) to o\. It means that the Coulomb corrections to ay and to o\ are the same in contrast with the opposite statements in Refs. 17 ' 18 ' 19 . 2.3
Factorization of Pn(p) and unitarity correction
In a set of publications 7.13>20.21 jt was argued that the factorization of the multiple pair production probability is valid with a good accuracy
Pn(p) = I ^ e - W .
(16)
Strictly speaking, such a factorization does not take place due to the interference between the diagrams corresponding to the permutation of electron (or positron) lines (see, e.g., 9 ) . Nevertheless, one can show that this interference gives the contribution which contains at least one power of L less. Therefore, in the leading logarithmic approximation we can use expression (16). Let us represent the cross section o\ of one pair production as follows a1=aT
+ a u n i t = f n(p) d2p - f [l - e " f i ^ ] n(p) d2p.
(17)
The main contribution to ar comes from p > 1/m. As for ffUnit, the main contribution to it comes from p ~ 1/m. If Z\^,OL ~ 1, then the exact n(p) at p ~ 1/771 differs essentially from the Born result PB{P)3
T h e case A: Z1>2a < 1, (Z1aZ2a)2
L < 1
In this case it is possible to use -PB(P) instead of the exact function n{p), expand the exponent exp(—n) in unitarity correction and omit it in 2). As we argued above, the function P B ( P ) at rap < 7 and L » 1 has the form PB(J>)
= {ZiaZ2a)2
F{mp) L
(18)
with the universal function F(x) independent of Zi>2 and 7. We extract this function (see Fig. 2) from the numerical results in 10 for the case 7 = 3400.
344
It follows from (9) that the asymptotic form of the function F(x) at x >• 1 reads 56 In a; (19) • a s y m p (*) = 2 2 97T a;
'
Figure 2. The function F{x) from Eq. (18) vs. x = mp (solid curve) and its asymptotic form Fa.symp(x), Eq. (19) (dashed curve).
Using this function, we obtain in the case A the unitarity correction to the one-pair production cross section in the form (5) and the cross sections for the n-pair production (n > 2) in the form (6) with Cn = 4 / n\ Jo 4
The case B : [ZxaZ2a)2
Fn(x)xdx.
(20)
L ~ 1
If (Z1aZ2a)2 L ~ 1, but (ZiaZ2a)2 (Z 1 ) 2 a) 2 L < 1 , then we can neglect the Coulomb effects in n(p) but should keep the exponent in Eq.(16). It gives the result similar to Eq. (6) for an with the replacement 27T
Cn -)• C n (7, Zi, 2 ) = - r / n\ J0
f°°
Fn(x) exp[-{ZiaZ2a)2
L F(x)} xdx .
(21)
For unitarity correction we have /•OO
CTunit = -27rCTo L / Jo
F(x) {1 - exp[-{ZiaZ2a)2
LF(x)]}
xdx .
(22)
If (ZiaZ2a)2 (Zit2a)2L ~ 1, then we should use in Eq. (16) the function n(p) calculated exactly with respect to the parameters Zit2a. The function n{p) as well as PB{X) was calculated numerically in 22 for the particular
345 case 7 = 100, Z = 79. Using these results, we find that the exact value of ^unit/o'Bom equals —4.1% , while the result without Coulomb effects is —6.4%. Analogously, using the recent numerical results of K. Hencken (private communication) for n{p), we find that the exact value of ^unit/oBo™ for the case 7 = 3400, Z = 82 is equal to -3.2%. Acknowledgments We are very grateful to K. Hencken for sending us the numerical data cited above. V.G.S. would like to thank A. Baltz, F. Gelis, L. McLerran, and A. Peshier for useful discussions during his stay in BNL. This work is partially supported by Russian Foundation for Basic Research (code 99-02-17211 and 01-02-16926) and by Foundation 'Universities of Russia' (code 015.02.01.16). References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
L.D. Landau, E.M. Lifshitz, Phys. Z. Sowjet. 6, 244 (1934). G. Racah, Nuovo Cim. 14, 93 (1937). C. Bertulani, G. Baur, Phys. Rep. 163, 299 (1988). D.Yu. Ivanov, A. Schiller, V.G. Serbo, Phys. Lett. B 454, 155 (1999). R.N. Lee, A.I. Milstein, Phys. Rev. A 61, 032103 (2000). R.N. Lee, A.I. Milstein, Phys. Rev. A A 64, 032106 (2001). G. Baur, Phys. Rev. D 41, 3535 (1990). M.C. Giiglu, Nucl. Phys. A 668, 149 (2000). A.J. Baltz, F. Gelis, L. McLerran, and A. Peshier, nucl-th/0101024. K. Hencken, D. Trautmann, G.Baur, Phys. Rev. A 51, 1874 (1995). M.C. Giiclu et al., Phys. Rev. A 51, 1836 (1995). G. Baur, Phys. Rev. A 42, 5736 (1990). M.J. Rhoades-Brown, J. Weneser, Phys. Rev. A 44, 330 (1991). A. Alscher, K. Hencken, D. Trautmann, G.Baur, Phys. Rev. A 55, 396 (1997). G.Baur, K. Hencken, D. Trautmann, J. Phys. G: Nucl. Part. Phys. 24, 1657 (1998). M.C. Giiglii et al., Ann. of Phys. 272, 7 (1999). B. Segev, J.C. Wells, Phys. Rev. A 57, 1849 (1998); physics/9805013. A.J. Baltz, L. McLerran, Phys. Rev. C 58, 1679 (1998). U. Eichmann et al., Phys.Rev. A 59, 1223 (1999). C. Best, W. Greiner, G. Soff, Phys. Rev. A 46, 261 (1992) K. Hencken, D. Trautmann, G. Baur, Phys. Rev. A 51, 998 (1995). K. Hencken, D. Trautmann, G.Baur, Phys. Rev. C 59, 841 (1999).
T H E G A U G E B O S O N A N O M A L O U S I N T E R A C T I O N S VIA P R O C E S S e ~ 7 -+ W ~ i / . T H E L E P T O N D E C A Y M O D E . DMITRIY A. ANIPKO, ILYA F. GINZBURG, ALEXEY V. PAK Sobolev Institute of mathematics SB RAS, prosp. Koptyuga 4 and Novosibirsk State University, ul. Pirogova 2 Novosibirsk, 630090, Russia E-mail: [email protected] We study possibilities to measure the triple anomalous W-boson couplings to photon in the cy ->• Wv process via its lepton decay channel with the simplest signature. We found that in the study of the quadruple momentum A one can limit himself small region in phase space. The way to find this region is proposed. The obtained estimates for A at TESLA project are roughly twice better then contemporary ones for e+e~ mode. For anomalous magnetic momentum the discussed mode gives no improvements as compared e+e~ mode.
Study of anomalous interactions of gauge bosons (beyond the Standard Model - SM) is an essential part of the program of Linear Colliders (LC), in both e + e~ mode and in e'y and 77 modes (Photon Colliders) 1 , 2 . The e + e~ mode of the LC has been studied thoroughly 3 . The process e'y —> Wv was considered in respect of Photon Collider program in 19844 first. The anomalous gauge boson interactions in ee —>• WW, 77 —> WW, e'y —»• Wv were studied in the papers 5 , 6 neglecting backgrounds, W-boson decay and with spectra, polarization and luminosity which are far from modern understanding. The advantages of the e'y -> Wv process as compared with e+e~ -> WW are: (a) a much higher cross section which does not fall with energy (where effect of anomalies grows) as compared with decreasing with energy a(e+e~ —• WW); (b) here only 7WW anomalies influence, while in e+e~ ->• WW the ZWW anomalies influence too, that demand more complex analysis of final state, reducing possible accuracy. We parameterize the effective lagrangian with the aid of standard anomalous parameters Afc and A - anomalous magnetic and quadruple momenta of W-boson respectively as e[W\„W»Fv
- W\FVW»V
+ (1 + Afc)W t M W„F'" / + ^ - W ^ W ^ F ^ ] . m w
Some important features of the e'y —>• Wv
346
reaction are seen
347
through analysis of helicity amplitudes for the process and its cross section. • Since Weu vertex enter only left hand polarized fermions, the cross section is proportional to (1 - 2Ae) where Ae is a degree of the electron longitudinal polarization. Thus, with variation of mean electron helicity one can measure the right current admixture in that vertex in a new region of W virtualities. • In our problem, to discover anomalous effects, they are supposed to be small. Therefore, the observable variations of cross sections are only linear in Ah and A. The view for helicity amplitudes shows that for the left hand or right hand polarized photons both anomalies (in Afc and A) can be seen in cross sections while for unpolarized photons the linear in A effects are canceled. Therefore, the photon circular polarization is an essential parameter in the simulation. The considered observable processes contain additional diagrams as compared to e-y —)• Wv with subsequent decay. Thus, the muon decay channel contain diagram in which an initial photon interact with muon after W decay. We classify the channels of reaction in accordance with observable parmuon (electron) channel 1 2 ej —*• W~ve cy —> W~ve I
4/i(e)i/ M
I
T - channel
quark channel
e-y -» W~ve
I
e7 -> W~ue
TVT
4-
4-
qq
vr + hadrons Table 1. W decay channels.
ticle and its origin, Table 1. We distinguish, for example, two muon channels, channel 1 corresponds to direct W decay into fj,D, and channel 2 corresponds to cascade decay to muon plus neutrinos with intermediate r state. We consider only the first two channels with the single observed particle, either muon or electron. For definiteness, we discuss mainly the muon decay channel. Event selection cuts. We impose two constraints on muon escape angle 0 and its transverse momentum px: 1. 7T - 0O > 0 > 0O = 10 mrad. 2. P± > P±0 = 10 GeV. The first cut corresponds to the TESLA detector expected angular limitation. The second cut allows to exclude many background processes. We found that the reasonable (not very strong) increasing of 0o and pxo influence our results only weakly. The background processes are those in which either muon is the only particle that can be observed or where some other charged particles or photons
348 cannot be detected due to their small escape angles. These are: 1. The processes in which all the final particles can be observed, in principle — ej -+ e/j,+/j,~, cy -*• eZj (Z ->• up). The transverse momentum conservation exclude these processes at our event selection cuts. 2. The processes that include neutrinos in a final state — e*f -4 e r r (r ->• fi), cy -> eZZ [Z -4 uv, Z -> fip,), e'y -4 vWZ (Z -* vD, W -» fj,v), (W+ -* t+vt, W~ -> ju/„). e 7 _> eW~W+ 3. The processes caused by initial state different from ideal due to conversion mechanism. There are e~e~ ->• vW~e~ collisions with residual electrons in the photon beam, 77 —• W~W+ process with beamsstrahlung photons or with photons from multiple electron scattering on laser photons. The processes of the last two groups cannot be excluded in principle. Our analysis shows that the considered anomalies will be extracted with the best efficiency from the regions of muon momentum plane (PL,P±) which are close to the boundaries of the phase space permissible in a reaction. The detailed analysis shows that all the processes of second and third groups have very small cross section in these regions and, therefore, can be neglected. To the moment, we considered with simulation only backgrounds, the e7 -* Wv collisions with low energy photons from multiple electron scattering. Main parameters. The electron longitudinal polarization is 2Ae = —0.85, luminosity value in e~f mode is given as the one fourth of the one in e+e~ mode 2 f jCejdt — (1/4) f £e+e-dt. Different signs of photon circular polarization values are accounted. We assume main parameter for e —¥ 7 conversion x = 4.8 (which responds to Ee — 500 GeV). Shape of the high energy part of the photon spectrum depends weakly on details of conversion, the beam size and laser flash energy. We used here the spectra from papers 4 , 9 . On the contrary, shape of low energy part strongly depends on all these details and cannot be defined now reliably and photons here will be almost unpolarized. To imitate this part of spectrum we use in the collision point the low energy part of energy spectrum of backscattered photons given in the conversion point and assume these photons to be unpolarized. We found that these low energy photons don't change the results significantly. To account electron initial state radiation we used a formula for effective electron spectrum from papers 7 , 8 . Calculations. We calculated distribution of produced muons over components of their momentum d2a/(dpndp±) in SM and with anomalies using CompHEP package 10 for symbolic calculations. For the /^-channel 2 the distribution on r-momentum was calculated with CompHEP (just as for channel 1) and the result was convolved with easily calculated distribution of muons
349 from r decay considering r decay branching ratio (17%). This procedure allow us to avoid an analysis of phase space for 5 final particles. This approximation is affordable since r-lepton width is very small. We found that final distributions on muon momentum for these two channels are similar. Computed distributions within the SM and with anomalous interactions are used to calculate the Statistical Significance (SS) value oc _ N(SM+anom)
~
^SM
VNSM in separate cells of the phase space. At the first step we fixed values A = A s j m = 0.1 or Afc = Afcsjm = 0.1 and calculated SS. A typical distribution of SS is shown at the Figure 1. It is strongly non-homogeneous. The best estimates can be found out by joining
Figure 1. A map of SS in p±, p\\ plane for , / s = 800GeV, A 7 = —1, Ak = 0.1, X = 0.
of the phase space cells that bring maximum SS value. To find these regions (examples are shown at Figure 2) we used a following algorithm: 1. Random choice of a phase space cell. 2. SS recalculation for the area with/without the concerned cell. 3. Area changes confirmation in a case of SS increase. These regions depend on sign of photon helicity. The areas that are responsible for A detection belongs to a small phase space region. The essential feature of these areas is that their reduction to the borders of the phase space reduce SS only a little (10-20%). With this reduction the intersection of areas,
350 1
S
Transversal momentum, GeV
Photon A7 = + 1
250
y/see
5
Transversal momentum, GeV
250
= 500 GeV, A = Xsim, Afe = 0
Figure 2. Phase space areas (in muon p±,p\\
plane) that bring the best SS value - in grey.
responsible for two considered anomalies, become small. It means that Ak and A can be measured practically independently. At the second step we obtain the ultimate values of the anomalous parameters achieved in the process by linear extrapolation with confidence level CL (fixed by convention) via equations like Aexp
= \8im{Li
h J O O)
The quantity y/N$M in denominator of definition of SS corresponds this very limit of discovery of anomalies when their influence on cross section is small. While consider the e-channel, some new backgrounds should be added to the analysis of the \x channel. However, their effect is estimated as a very small in the areas responsible for anomalies. Therefore, in estimates we can consider both e and fi channel by doubling of number of events obtained for fj, channel. We present results for these two channels in Table 2, assuming CL=1 - to compare our results with those for the e+e~ channel 3 . We considered c.m.s. energy for the basic ee system = 130,500,800 GeV. The numerical inaccuracy of the obtained results is less than 5%. Final notes. Let us enumerate our plans related to ej -t Wv process. 1. Despite the estimates showed that the backgrounds influence weakly to the results, we will simulate these processes. The goals are to get more precise data and receive experience for more complex processes. Due to estimated small influence of backgrounds to result, their description can be simplified by approximations like those used in the description of the second muon channel (convolution of production and decay distributions).
351
fCdtJb-1
A«> GeV 130 500 800
e7 e7 e+e~ e7 e+e~
100 125 500 250 1000
A 3.3-lO" 2 2.5 • 10" 4 5.9 • 10" 4 1.7 - 1 0 - 4 3.3 • 10- 4
Afc
1.2-10- 3 1.0-lO" 3 3.3 • 10" 4 1.0-10~ 3 1.9 • 10- 4
Table 2. The ultimate values of Ak and A obtainable from cy —>• Wv reaction (e and \i channels) and those from e+e~ —»• WW
2. We will add events with r hadron decay to the result. Since the muon distributions in ^-channels 2 and 1 are similar and m r <S M\y, we expect that one can use here the obtained data for muon channels. It will be tested by simulation of some separate channels of hadronic r decay. This data are expected to improve estimates noticeably. 3. The W-boson quark decay must be simulated and is expected to influence the results significantly. This paper is supported by grants RFBR 99-02-17211, 00-15-96691 and INTAS 00-00679. D.A. and I.G. acknowledge organizers for support. References 1. I.F. Ginzburg, G.L. Kotkin, V.G. Serbo, V.I. Telnov, Nucl. Instrum. Methods 205, 47 (1983); I.F. Ginzburg, G.L. Kotkin, S.L. Panfil, V.G. Serbo, V.I. Telnov, Nucl. Instrum. Methods, A 219, 5 (1984); Zerothorder Design Report for the NLC, SLAC Report 474 (1996); 2. TESLA TDR, v. VI 3. TESLA Report 2001-23, DESY, 2001 4. I.F. Ginzburg, G.L. Kotkin, S.L. Panfil, V.G. Serbo. Nucl. Phys. B 228, 285 (1983) (E: B 243, 550 (1984)) 5. E. Yehudai Phys. Rev. D 45, 33 (1990) 6. S.Y. Choi, F. Schrempp. Phys. Lett. B 272, 149 (1991) 7. E.A. Kurayev, V.S. Fadin. Yad. Fiz. 41, 733 (1985) 8. M. Skrzypek, S. Jadach. Z. Phys. C 49, 577 (1991) 9. I.F. Ginzburg, G.L. Kotkin Eur. Phys. J. C 13, 295 (2000) 10. A. Pukhov, E. Boos, M. Dubinin, V. Edneral, V. Hyin, D. Kovalenko, A. Kryukov, V. Savrin, S. Shichanin, A. Semenov. CompHEP User's manual, hep-ph/9908288.
TAGGING TWO-PHOTON PRODUCTION AT THE LHC KRZYSZTOF PIOTRZKOWSKI Universite catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve E-mail: [email protected] Several aspects of tagging two-photon interactions at the LHC, as separation from pomeronpomeron events or control of the tagging efficiency, are shortly discussed.
Recently, a method of tagging two-photon interactions at the LHC has been proposed [1]. The method is based on the measurement of very forward protons using detectors similar to those planned for measurements of the elastic pp scattering at the LHC [2]. In two-photon processes protons are scattered at very small angles, comparable to the beam angular divergence at the interaction point (IP). The scattered protons can however be measured when a significant fraction of the initial proton energy is carried away by a photon. In such a case these protons are more strongly deflected by the beam-line magnets and can be detected in the socalled Roman pots installed far away from the IP and close to the proton beam. The detectors are capable of measuring the distance and angle of the scattered proton with respect to the proton beam at a given location. The distance in the horizontal plane measures then the proton energy loss, hence the tagged photon energy. Other measured variables are used to reconstruct the proton scattering angle [1]. The particles produced via yy fusion are registered in the CMS detector, for example. The tagging efficiency is determined by minimum distance between the detector sensitive edge and the proton beam. For small beam widths, a 1 mm minimum detector approach is usually required to ensure enough space for the beam steering [2]. If recently advocated detector location is considered [1,3], some 240 m from the IP, the 1 mm distance corresponds to a minimum tagged photon energy of 70 GeV, that is to 1% of the beam energy. If the maximum tagged energy of 700 GeV and, the maximum virtuality, Q2max = 2 GeV2, of the colliding photons are assumed, one obtains the tagged effective luminosity spectra as a function of the yy center of mass energy W (see Fig. 2 in [1]). The double tagging corresponds to the case when the two scattered protons are detected, whereas the single tagging occurs when only one proton is detected. In such a case, however also those two-photon events are tagged where one proton does not survive the interaction. In fact, these inelastic two-photon events have even higher effective luminosity than the nominal, elastic events, and the luminosity available for the tagged two-photon collisions is significant - for example, it reaches 1% of the pp luminosity for W > 100 GeV. One should note also that the luminosity spectrum extends to very large W, even beyond 1 TeV.
352
353
The tagging efficiency depends on the detector closest approach, and the 1 mm approach assumed above in fact requires an edgeless detector, i.e. a detector which is sensitive right from its mechanical edge. This might be considered too optimistic and instead one can conservatively consider a 2 mm distance between the detector sensitive edge and the beam. In Fig. 1 the luminosity spectra and their integrals (= probability of YY collisions per &pp collision) are shown for that case, demonstrating that the single-tagged spectrum is modestly affected, whereas the low W part of the double-tagged spectrum is as expected suppressed. This shows that the tagging efficiency does not critically depend on the closest approach to the proton beam.
/dWS.
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Figure 1. Tagged photon-photon luminosity spectrum % and its integral jwo dW S-n, assuming double tags (shaded histograms) and single tags, for all events (solid line) and for elastic events (dashed line); all for a 2 mm closest approach.
The ultimate resolution of the scattered proton momenta is determined by the beam properties at the IP, its transverse cross-section and divergence [1]. For the high luminosity running, and providing the detector spatial resolution in the 10-20 pm range, the W resolution of about 5 GeV (for double tags) and the proton p T resolution of about 120 MeV are expected. Good resolution of p T is essential for separating two-photon and pomeron-pomeron (IPIP) events which otherwise are indistinguishable. Separation power at high luminosity is limited and therefore only effective when the pomeron-pomeron cross-section is not much bigger than the two-photon one. However, for special running conditions and using only double events one can achieve better separation. In Fig. 2 the distribution of the product of two proton transverse momenta squared is shown where a 1000 times bigger IPIP cross-section has been used. This indicates the ultimate value of the separation power.
354 m 8000
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Two-photon exclusive production of lepton pairs is an excellent monitoring tool of the tagging efficiency and its energy scale. In Fig. 3 the invariant mass of the singletagged muon pairs exclusively produced within acceptance of the CMS tracking system is plotted using the LPAIR event generator [4]. Such events can be selected using a standard CMS di-muon trigger and used off-line for a number of systematic studies, including also the luminosity normalization and the contribution of the inelastic production, or the accidental tagging. Figure 3. Invariant mass distribution § ' * »
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355
W it becomes weaker resulting in incoherent production (~Z2) at large W. Tagging YY interactions is however not practical in this case. It is then restricted to a large W domain where the coherent interactions are much suppressed and YY luminosity is small. Situation is very different for the proton-ion collisions, where the scattered proton can be detected in the same manner as in the pp case, and the single-tagged luminosity is high, especially below W = 100 GeV where the enhancement is still significant. For example, almost 50% of the proton-Argon luminosity LpAr is available for yy collisions at W > 50 GeV, and LpAr itself can reach values above 1031 cm'V 1 . The luminosity of the tagged YY events at medium W might be therefore comparable to that in the pp collisions whereas the relative amount of IPIP background is smaller. In addition, tagging inpA collisions can be used to check YY event selection in the AA collisions. /dWS.
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In conclusion, a few new aspects of tagging two-photon production at the LHC discussed in this paper confirm feasibility of tagging, and provide a strong motivation for further, more detailed studies. References 1. 2. 3. 4. 5.
K. Piotrzkowski, Phys. Rev. D 63 (2001) 071502(R). TOTEM Collaboration, Technical Proposal, CERN/LHCC/99-07. A. Faus-Golfe et al, h e p - e x / 0 1 0 2 0 1 1 . J.A.M. Vermaseren et al, Proc. Physics at HERA, vol. 3, Hamburg, 1991. For example, see G. Baur et al, h e p - p h / 0 1 1 2 2 1 1 .
Fast luminosity measurement at 77 collider using 77 —• 4 leptons process N. Arteaga, C. Carimalo, W. da Silva, P. Kapusta LPNHE, IN2P3 - CNRS Universites Paris VI et VII, 4 Place Jussieu, Tour 33, Rdc, 75252 PARIS Cedex 05, FRANCE We present an exact computation of the amplitudes of the process 77 —• 4 leptons corresponding to diagrams with the exchange of a space-like photon. We have developed a Monte-Carlo generator and we show some relevant distributions for this process. A rate of four detected muons at a 77 collider is also evaluated.
1
Introduction
We already computed the diagrams with the exchange of a space-like photon, using an approximation based on the impact factor method 1>2 . We here compute all associated amplitudes taking into account all terms in the photon propagator. This allows us to now quantify numerically the approximation used in previous papers 1 , 2 , 3 . The results are presented in fig 1 where the terms L(EPS—),L(EPS+) correspond to the transverse part of the photon propagator, L(T-Z) is the main term computed with the impact factor method and L(T+Z) the remaining term. We can see that the previously neglected terms are several orders of magnitude below the main contribution.
2
Discussion of 4 lepton events topology
In order to discuss the topology of 77 -¥ 4 leptons events we have developped a Monte-Carlo generator. The diagrams with the time-like exchanged photon are not included, but their contribution is expected negligible at very small angle. Fig 2 shows that most of events are produced at very small angle due to the low values of the photon transfer. Lepton pairs are mainly produced backward-forward. The energy distribution is also an important observable (fig 2). The energy distribution of one outgoing lepton is almost uniform and the sum of the energies of two nearest muons is a constant and equal to the energy of the incoming photon.
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358
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We know that the cross section 4 l e P t o n s at high incoming photon energy surpass the cross section <j 77- * 2 l e P t o n s because the production of 4 leptons leads to a constant cross section (see fig 3 and ref 4 ). Using our Monte-Carlo generator the energy distribution of outgoing electrons after a frontal collision between an ultra high energy photon and an infrared photon is shown fig 3. This almost uniform energy distribution is different than the well-known 2 leptons energie distribution and may help to distinguish the two process. 4
Fast luminosity measurement at small angle
A question remains since a long time : is it possible to use the process 77 —^ 4 leptons for a fast luminosity measurement? There are several constraints. The outgoing leptons are produced at very small angle of mrad order typically, a region where there are a lot of sources of particules produced as for example coherent pair creation or beamstrahlung (see T D R 5 ) . This background is strongly correlated with the optic design. The expected number of events is computed with the formula : Nevt = L 7 7 j 0 Z - Z m 2ZdZ / j | f(x, y)f{x, f) f L n o r m / C U T S da 77 "-* 41 ^ 0 " 8 where the function / is the Compton spectrum (see 5 ) The number of events is strongly dependent of the detection angle. A rate'of 10~ 4 event per second with four muons detected between 12 and 20 mrad is expected (see fig 3). An other important physical source of background is the coincidences between our signal and one lepton coming from the 77 -> 2 leptons process. In order to evaluate these potentially dangerous events we have to know the 77 luminosity distribution at invariant 77 mass near two muon mass which requires a MonteCarlo simulation of the photon beam at very low energy. Here we modify the theoretical Compton distribution in agreement with the ref 5 . The results are correct only for high 77 invariant mass because the distribution at low invariant 77 mass is not known yet. So we just give a lower limit of this kind of background. Fig 3 shows that this number of events may not be negligible.
5
Outlook
From the theoretical point of view, we have to compute the time-like diagram in order to estimate its contribution at large angle and the interference between the time-like and space-like diagrams. From the experimental point of view we need more topological studies with our Monte-Carlo generator in order to find some relevant topological differences
359
Figure 3: Energy distribution of outgoing leptons after a cosmic collision and expected rates for the signal and the background for a 77 collider.
between leptons coming from 77 -> 2 leptons or 77 —>• 4 leptons. For the fast luminosity measurement it will be very difficult to use 77 -> 4 leptons process for measuring luminosity but before giving strong conclusions we have to study carefully all sources of leptons and their contributions at small angle. For this we need a detailed simulation of the beam of photons, especially in the low energy range. References 1. C. CARIMALO, A. DA SILVA, F. KAPUSTA Nucl. Phys. B 82, 391 (2000) (Proc. Suppl). 2. C. CARIMALO, A. DA SILVA, F. KAPUSTA PHOTON 2000 International Conference on the Structure and Interactions of the Photon. AIP CONFERENCE PROCEEDINGS, VOL 571. 3. E.A KURAEV, A SCHILLER and V.G SERBO Nucl. Phys. B 256, 189 (1985). 4. Lee SANGJIN Phys. Rev. D 58, 043004 (.) 5. TDR on Photon Colliders http://www.desy.de./ telnov/tdr/ggtdr.ps.gz
G E O M E T R I S A T I O N OF E L E C T R O M A G N E T I C FIELD A N D T O P O L O G I C A L I N T E R P R E T A T I O N OF Q U A N T U M MECHANICS FORMALISM
N.N.Semenov
O. A. OLKHOV Institute of Chemical Physics, 4 Kosygin Street, Moscow, 117977, Russia E-mail: [email protected]
We consider interacting electromagnetic and electron-positron fields as a nonmetrized space-time 4-manifold. The Dirac and Maxwell equations is found to be a relationships expressing topological and metric proprieties of this manifold. A new equation for the weak interaction is proposed that explains geometrical mechanism of CP-violation.
All numerous a t t e m p t s of the electromagnetic field geometrisation were based on concept "pointlike sources-extended field". 1 ' 2 ' 3 But we had recently shown t h a t the free Dirac field can be considered as a curved nonorientable closed connected space-time 4 - m a n i f o l d . 4 ' 5 ' 6 Its fundamental group consists of four gliding symmetries and the Minkowski space appears as the manifold covering space. Taking this into account we now suggest a new approach to the electromagnetic field geometrisation and this approach inevitably means a new topological interpretation of the q u a n t u m mechanics m a t h e m a t i c a l formalism. We suppose t h a t interacting Dirac and Maxwell fields can be considered as a single closed connected nonmetrized 4-manifold. Electric a n d magnetic fields appear within such approach as components of the curvature tensor of the manifold covering space and the Dirac spinors appear as basic functions of the manifold fundamental group representation. Above concept differs from the one of general theory of relativity by two m a i n points: we geometrise not only the field but the field sources also and we represent the field and its sources not as a riemannian 4-space (object with difinite shape) but as a nonmetrized 4-manifold (object without definite shape). We start with the known equations for interacting clasical electromagnetic and electron-positron fields 7 p, *7i( ^ oxi
1- ieAx)^
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After contraction over q and / we obtain Rik - Rik,q
-
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4
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362 2. Covering space of this manifold is a conformal pseudoeuclidean space. 3. Potentials Au is defined by t h e connectivity of this space Tjt {ieAk = T^). 4. Electric a n d magnetic field components are defined by the components of the covering space curvature tensor Rn, (ieFik = Rik)5. Dirac spinors appear as basic functions for the manifold fundamental group representation. One comment in conclusion. Replacing a "wave-particle" by a nonmetrized space-time manifold does not mean " m o r e determinism" for t h e q u a n t u m object description a n d the topological approach does not introduce any hidden variables and does not therefore contradict the Bell a n d von N e u m a n n theorems. 9 ' 1 0 We now show t h a t , in a one-particle approximation adopted in this work, weak interaction can be represented as a manifestation of the torsion in the covering space of a 4-manifold representing field a n d its sources. In due time, Einstein a t t e m p t e d at including electromagnetic field into a unified geometrical description of physical fields by "adding" torsion to the R i e m a n n i a n s p a c e time curvature, which reflects the presence of a gravitational field in general relativity. n Since the curvature of covering space corresponds now t o t h e electromagnetic field, we shall a t t e m p t t o include weak interaction into the topological approach by including torsion in this space. Let us first consider the case where the electromagnetic field is absent, i.e., the curvature of covering space is zero. A space with torsion b u t without curvature is called the space with absolute parallelism. u T h u s , the challenge is t o determine how does free-particle equation change if the interparticle interaction is due only to the torsion, which transforms the pseudo-Euclidean covering space into a space with absolute parallelism. Let us denote the torsion tensor by S* m ; then the problem can be formulated as follows. It is necessary t o "insert" the tensor Sfm or some of its components into free-particle equation so t h a t the resulting equation remains invariant about the Lorentz transformations a n d does not contradict to experimental d a t a . Among the spaces with torsion, there are so-called spaces with semisymmetric parallel translation 1 2 . T h e torsion tensor Sfm for such spaces is defined by the antisymmetric part of connectivity a n d can be represented in the form Sfm = S,Akm-SmAf.
(8)
Here, Si is a vector and Af is the m a t r i x of rotation group representation. T h e vector Si has the property t h a t the infinitesimal parallelogram remains closed upon parallel translation in the hyperplanes perpendicular t o this vector. One m a y thus assume t h a t in the presence of vector Si the spatial isotropy breaks in such a way t h a t the isotropy is retained only in the indicated
363 hyperplanes. Assume t h a t the translational symmetry is retained along Si, while the s y m m e t r y of free-particle equation is retained in the hyperplanes perpendicular to this vector. Consider the ip -field t h a t transforms according to a two-dimentional representation of the Lorentz qroup and let's B^ will be the connectivity corresponding to (8) for this representation. T h e n we can finally write down the equation for ip as i
2
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- igB»)i,
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Here, the ip is a two-component spinor, a^ are the Pauli matrices, g is an interaction constant and summation over \i and v are going with a p s e u d o Euclidean metric. Evidently, Eq.(9) violates both spatial and time symmetry. T h e question of how does Eq.(9) account for the other properties of weak interaction and how does it relate to the results of the standard model of electroweak interaction will be considered in detail elsewhere. 1
References 1. 2. 3. 4.
5.
6. 7. 8. 9. 10. 11.
12.
H.Weylin Gravitation und Electrizitat, (Preuss.Akad.Wiss, Berlin, 1918). N.P. Konopleva, H.A. Sokolic, Nucl.Phys. 72, 667 (1965). M. Daniel, C M . Viallet, Rev.Mod,Phys. 5 2 , 175 (1980). O.A. Olkhov, in Proceedings of the 7th International Symposium on Particles, Strings and Cosmology, Lake Tahoe, California, 10-16 December 1999, p.160. e-print quant-ph/0101137. O.A.Olkhov in Thesises of the International Seminar on Physics of Electronic and Atomic Collisions, Klyasma, Moscow region, Russia, 12-16 March 2001, p.28 quant-ph/0103089 O.A.Olkhov, Chem.Phys.Reports, (to be published). S.Schweber in An introduction to relativistic quantum field theory, (Row, Peterson and Co., Evanstone, 111., Elmford, N.Y. 1961). P.A.M. Dirac in General theory of relativity, (John Wiley and Sons, N.Y.Sydney-Toronto, 1975) I.S. Bell, Rev.Mod.Phys.38, 447 (1966). J.V. N e u m a n n in Mathematische grundlagen der quantenmechanik, (Verlag von Julius Springer, Berlin, 1932). A.Einstein in Riemann Geometric mit Aufrechterhaltung des Fernparallelismus, (Sitzungsber: preuss. Akad. Wiss. phys-math, K l , p.217, 1928). J.A.Schouten in Tensor analisis for physicists, (Oxford, 1952).
P H O T O N S A N D QCD AT LHC W I T H ATLAS S. TAPPROGGE Helsinki Institute of Physics, CH 1211 Geneva 23, Switzerland E-mail: [email protected] The measurement of direct photon production will give important input to QCD studies at LHC, especially in providing constraints on parton densities in the proton in an as yet uncovered kinematical region. In addition, measurements of the strong coupling constant should be possible.
1
Motivation
The LHC will allow QCD studies to be performed at very high energy in proton-proton collisions at i / i = 14 TeV, with a design luminosity of L = 1034 c m _ 2 s _ 1 , including precision tests and measurements in an as yet unexplored kinematic region. A detailed understanding of QCD is important for almost all physics processes to be studied at the LHC, as the production mechanisms are mostly controlled by QCD. There will a broad programme of QCD measurements to be performed at LHC, for more details see the recent reviews x'2 and 3 . In this contribution, after a brief overview of the ATLAS detector, the expected performance of ATLAS for photon measurements will be discussed and an overview of various physics measurements with direct photons be given. 2
The ATLAS detector
The ATLAS detector 4 is one of the two general purpose detectors for LHC. It will have silicon pixel and silicon strip detectors mounted close to the interaction region, allowing robust tracking and precise vertex measurements. They are followed by a transition radiation tracker providing electron identification. The tracking detectors are surrounded by a 2 T solenoid, which is located in front of the calorimetry (liquid Argon (LAr) based for the e.m. part and a combination of scintillator based and LAr based sampling calorimeters for the hadronic part). The muon measurement is performed by a stand-alone system with air-core toroid magnets and muon detectors. The detector has been optimized for precision measurements within the Standard Model and searches for the Higgs boson(s) and for physics beyond the Standard Model. Precise measurements of leptons, photons and 6-jets are
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going to be performed over the range |?7| < 2.5, whereas the coverage for jets and for missing ET extends up to I77I = 5 (with calorimetry only). An additional challenge is to provide an efficient trigger system, which has to reduce an interaction rate of 109 Hz to about 100 Hz going to mass storage. More information on the expected detector performance can be found in 3 .
3
ATLAS performance for photon measurements
The experimental challenge is to achieve a good efficiency for photons while providing at the same time an excellent rejection against jets. The ratio of the inclusive jet cross-section to the direct photon cross-section is about 10 3 (for M < 0.7 and 100 < pT < 500 GeV). The left part of Figure 1 shows the dependence of the jet rejection on the transverse energy ET, indicating that due to the very fine grained LAr calorimeter a rejection of 3 • 10 3 can be obtained for ET > 40 GeV. As the right part indicates, this is achieved for an efficiency for photons of about 80 % (at low luminosity L — 10 33 c m - 2 s - 1 ) over the relevant pseudo-rapidity range. In order to reach this efficiency, conversions in the material of the inner detector have to be recognized and reconstructed (the probability for a conversion to occur is between 20 % and 40 %, depending on 77).
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4
Physics measurements
The production of photons can provide sensitivity to the gluon density in the proton, via the QCD Compton graph: qg —> q~f. Background processes producing photons include qq —> (77 and fragmentation contribution (q —> 97). In addition, the production of jets containing a leading 7r° can lead to fake photon signatures. In order to suppress the contribution from photons produced in fragmentation processes, an isolation cut is applied. The usual scheme uses a fixed cone around the photon direction and demands that any additional energy is below a certain threshold (which might depend on the photon energy). An alternative prescription (S. Prixione, see 2 ) uses cones of variable size (and threshold depending on the cone size) and has the advantage to give cross-sections which are not depending on the fragmentation contribution. An isolation prescription will also improve the experimental rejection of fake jet signatures. In the results presented above, only a detailed shower shape analysis in the calorimeter has been performed. In the left part of Figure 2 the cross-section for direct photon production as a function of the photon transverse momentum pip is shown, based on a leading order calculation. Due to the high value of the LHC luminosity, huge samples of direct photon events can be expected, e.g. for 30 f b - 1 more than 2 • 104 events having a photon with pip > 500 GeV are expected.
367
4-1
Constraints on the gluon density
The hard scattering scale is given at leading order by the square of the transverse momentum of the photon (Q2 = (pj) 2 ). A minimal p j of 40 GeV corresponds to Q2 > 103 GeV2 and together with |?7| < 2.5 implies a lower limit on Bjorken x of x > 5 • 10~ 4 . The upper limit on x depends on the maximal transverse momentum of the photon and thus is given by the available statistics. For a value of 500 GeV the upper limit is x < 0.2. This kinematic coverage on the gluon density can be compared to HERA, where for Q2 > 10 3 GeV2 only the range x > 0.01 is kinematically accessible. As the right part of Figure 2 shows, the dependence of the photon+jet cross-section on the fractional momentum xyj: xlj
= -j= \PT^
+ PTje^}
(1)
(as determined from the measured photon and the measured jet) is sensitive to the shape of the gluon distribution and should allow to distinguish between various parametrisations. 4-2
Measurement of the strong coupling constant
A determination of the strong coupling constant as can be obtained using the ratio H of the cross-sections for inclusive jet production and inclusive photon production (for a more detailed discussion see S. Frixione in 2 ):
HPT) = P-Ip-
(2)
dpTj dpT7 At first order, this ratio is proportional to as and dependencies on the parton distribution functions should cancel, thus avoiding the usual correlation between the size of the gluon density and the value of as. 4-3
Systematic
uncertainties
For all measurements using photons, important experimental uncertainties will be given by the knowledge of the absolute energy scale (the aim is to know this to 0.1 %), the rejection against fake photon signature and uncertainties in the subtraction of the remaining background. Most likely however, in many cases theoretical uncertainties like the knowledge of the size of higher order corrections might be the dominating source of uncertainties. As mentioned above, in most cases the statistical accuracy will be negligible.
368 5
Conclusions
Studies of QCD processes at the LHC will provide further tests of QCD, being the theory of strong interactions, at the energy frontier of 14 TeV. The expected performance of the ATLAS detector will allow in addition precision measurements of QCD processes to be performed. Measurements of direct photon production should lead to improvements in the knowledge of the proton structure (esp. for the gluon density) in an as yet unexplored kinematical region and possibly also to measurements of the strong coupling constant up to large scales. References 1. S. Catani et al., Report of the QCD working group at the LHCC workshop on 'Standard Model physics (and more) at the L H C , preprint hepph/0005025 (2000). 2. S. Catani et al., Report of the QCD/SM working group at the Les Houches workshop on 'Physics at TeV colliders', preprint hep-ph/0005114 (2000). 3. ATLAS collaboration, ATLAS Detector and Physics Performance Technical Design Report, CERN/LHCC 99-14 and 99-15 (1999). 4. ATLAS collaboration, ATLAS Technical Proposal, CERN/LHCC 94-43 (1994).
7 Summary
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S U M M A R Y OF P H O T O N 2001 ARMIN BOHRER Fachbereich Physik, Universitat Siegen, 57068 Siegen, Germany E-mail: [email protected] MARIA KRAWCZYK IFT UW, Hoza 69, 00-681 Warszawa, Poland E-mail: [email protected] This article summarizes the experimental and theoretical results presented and discussed at the International Conference on the Structure and Interactions of the Photon, PHOTON 2001, in Ascona. 1
Introduction
The photon, the first and best known gauge boson, is a fundamental particle with pointlike couplings to charged fundamental particles. In high energy hadronic processes, however, the photon may behave like a hadron. The study of the structure and the interaction of the photon in soft, semi-hard and hard hadronic processes turns out to be a rich field of investigation and test of the strong interaction. Detailed studies are performed especially at e + e~ colliders and now also with ep interactions. Different in their initial state, processes at LEP and HERA add to give a common understanding of the photon and its interaction. This is rounded off by specific, detailed and complementary results at low energy colliders also discussed at this conference. In this summary we present the highlights of the conference PHOTON 2001 as seen by the two authors. For further details we refer the reader to the individual presentations or the group summaries of the conference and references therein. 2
Theoretical Framework
The soft high-energy processes involving photons, a bulk of events, can be described in the VDM-type models using a framework of Regge Theory, while in the hard processes the perturbative QCD works; the semi-hard processes corresponds to the case where both Regge approach and pQCD are applicable. In both, hard and semi-hard processes the notion of the partonic structure of the photon is useful and it is clear that in such processes the photon may participate directly or via its partonic agents (the resolved photon processes).
371
372
The standard DGLAP approach to describe hard processes involving photons, like DIS on the photon and large px jet (particle) production in 77 or 7p collision, is based on the collinear approximation where terms with large log Q2 or logpy are summed up. The leading and next-to-leading (LO and NLO) calculations exists for many quantities, also all existing paxton parametrizations for the photon were obtained in such an approach. For semi-hard processes, e.g., DIS at small x, there appear other large scale and corresponding large logarithms have to be summed to all orders. Resummation of large logl/a; terms can be obtained using BFKL or CCFM evolution equations. In both of the latter approaches the pt of the initial parton cascade is not ordered; the basic ingredients are the unintegrated parton densities to be convoluted with appropriate matrix elements with the initial parton being off-shell. These approaches were presented during this conference, being superior in some cases to the standard DGLAP approach in the description of the data. In many respects the approaches used to describe photons are similar to ones used for a hadron, e.g., proton. One should be aware, however, that the possible direct coupling to a pointlike parton influences significantly the whole picture. The Parton Model prediction can be derived for F ^ from the basic process 7*7 -4 qq giving a logarithmic dependence on Q2. The corresponding DGLAP evolution equations, which take into account additional QCD radiation processes are inhomogeneous, and in principle (unfortunately not in practice due to appearance of singularities) can be solved without any input (asymptotic solution). Basic ideas and results can be found in recent reviews 1 ' i ' ° . 3
Structure Functions
The (hadronic) structure function F% of the (real) photon is measured in the hadron production processes in unpolarized e + e _ collisions from the single-tagged events. The negative momentum transfer squared of the photon emitted by the tagged lepton is equal to q2 = — 2Et&gEi)eam(l — cos9). The second lepton stays undetected so the corresponding momentum transfer squared p2 = —P2 is small. The process then can be viewed as a deep inelastic electron-photon scattering (DIS e7 ), where a quasi-real photon (with "mass squared" p2) is probed by a virtual photon with high virtuality Q2 = —q2. The differential cross section can be expressed as d 2 ae 7 ^ex/dzdQ 2 = [(1 4- (1 - y)2)F](x,Q2) - y2F2(x,Q2)]2na2/xQ2 with 2 2 2 x m Q /(Q + W ) and the inelasticity y « 1 - ( E t a g / £ b e a m ) cos2 6>tag. In most cases y is small and the term with F"[ can be neglected. Some
373
experiments correct their results for it, with the increased precision of the measurement the correction should become mandatory, as it was noted at the conference. The ej cross section given above is used to extract the structure function F£(x,Q2) primarily related to the quark densities in the photon q^ixiQ2), see Ref. 4 and Ref. 3 . The measurements of i ^ at LEP reached x as low as 10~ 3 and cover a range of (Q 2 ) from about 2GeV 2 to more than 750 GeV2 (even above 1000 GeV2 for Q 2 -dependence). All existing data are shown in Fig. 1 as a function of x, the new data obtained at the highest Q2 by OPAL and DELPHI groups 5 , e are shown in the last diagram. The logarithmic rise with Q2 seen in data is predicted by the theory. It appears already in the Parton Model QCD modifies this rise softly (logarithmically). In Fig. 3 the evolution with Q2 is shown for various x regions (DELPHI) in comparison with other data, MC predictions and with few parametrizations. The data (Fig. 1) are nicely described by the GRV-HO and SaS-lD parton parameterizations for a real photon; with the present precision the Q2 dependence data (Fig. 3) start to challenge existing parton parametrizations and MC models. Note, that all parametrizations for photon were obtained from data collected before 1997. The full present set of over two hundred data points is being used in a new LO fit to F% based on DGLAP evolution equation 7 . The updated parton parametrization for a real photon can be used to describe hard processes induced by the real photons at LEP and HERA, where some discrepancies are being observed (see Sec. 3 and 4). This new parametrization will be important also for studies of potential of future linear colliders, especially the photon colliders (see Sec. 7). An extraction of F*[ by fitting its components (QPM, VDM and RPCresolved photon contribution) separately, rather than a regularized unfolding, may lead to a better measurement; the estimated uncertainties increase but are more reliable, as stated by DELPHI 6 . It has been pointed out at the conference, however, that improvements are still to be made: where precision is high by including the P2 dependence or statistics is low by combining all four LEP experiments. Note that if P2 differs from zero, we deal with a virtual photon, which has the three states of polarization: two transverse(like a real photon) and one longitudinal (called also scalar) ones, see Sec. 3.1 where the importance of the resolved 7£ contribution are discussed. The charm contribution to the photon structure function i ^ , denoted F%c, can be obtained from the DIS e7 data from the sample with charmed hadrons. The updated result of OPAL, which identifies charm by exclusive reconstruction of a D* meson (see also below), strengthens their previous finding that for x < 0.1 the predicted hadron-like contribution is lower than
374
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the measurement 8 , see Fig. 3. A confirmation of the difference by the other LEP experiments is desirable. More data are needed to constrain the gluonic content of the photon in such measurements. A first measurement has also been performed by OPAL of the process e7 -> eZ/7* where the centre-of-mass energy of the eZ/7*-system y/§ is equal or larger than the Z mass 9 and found to be in agreement with MC predictions. 4
Hard Inclusive Processes
Hard production of jets (single jet and dijets) or particles at LEP and HERA are used as a complementary method to probe the "structure" of the pho-
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ton 10 . The hard scale Q is then provided by a large px of produced jets or particles. The part of momentum carried by a partonic constituent of the photon, x-f, is at LO equal to x. Direct, single-resolved (for LEP also doubleresolved) photon processes contribute, and can be separated at LO by using the fact that in the resolved one the remnant jet carries away a part of the' invariant mass available in the 77 or jp collision. For dijets at HERA the variable be reconstructed from the pseudorapidity 77 and transverse momentum ET of the jets, as x 7 = ( ^ e " ^ ' + E$a''e^*''')/\2yEe). Similarly x^ relevant for LEP measurements (photon-photon collisions) can be obtained. The implementation of NLO in the event simulation for jet production is in progress as was reported at this conference, where a systematic method for combining NLO QCD calculation with the parton was presented 12 . Special emphasis was recently put on the study of the (soft) underlying events (sue), especially important for the double-resolved contribution. Inclusion of multiple parton interaction (MIA), parametrized as in pure hh collision, usually improves the agreement with data. The structure of jets, forming sub jets, has been investigated at HERA u , where samples of different gluon purity have been obtained in events with charm quarks. The subjet structure is predicted by QCD as a function of the jet resolution parameter. The results are consistent with perturbative QCD and consistent with findings in hadronic Z decays at LEP. Further tests of
376
QCD such as the measurement of a s give values compatible in precision with other measurements or better 13 . Both at LEP (see Ref. 14 for reviews) and HERA inclusive hadron production has been studied intensively. Predictions from MLLA, e.g., average charged multiplicity, Gaussian shape of the distribution in £ = — ln(phadron/Pbeam) and the dependence of the maximum £* on Q2, were shown at this conference for HERA and found in very good agreement with the data both in deep inelastic and diffractive scattering processes, respectively, proving also the universality of the fragmentation functions. Such studies were performed for charged particles inclusively, for strange particles and particles versus anti-particles 15 (see also Ref. 16 for similar studies in charmed jets at HERA). 4-1
Jets
• Dijets at LEP Present measurements of dijet events at LEP, from a ~ 600 p b _ 1 data sample collected, concentrate on the separation of the direct and (single)resolved contribution to investigate the gluon content of the real photon 17>18, which is not tightly constrained by the F% data. Comparisons with the NLO calculations and the Monte Carlo models PYTHIA and HERWIG are made by OPAL for ET, and r) as well as x± distributions (see Fig. 4). The MC predictions for both parton parametrizations, GRS or SaS-lD, are too low by 20% for small a;7 and small ET indicating a too low gluon content in the photon. To study the effects of the underlying event the data sample is divided into samples where xjj or x~ < 0.75 and > 0.75, giving data sets with different single- and double-resolved fraction. Similar studies were also performed by DELPHI 1 8 for ET and jet profile distributions. Jet profiles turn out to be very sensitive to the presence of possible MIA effects. PYTHIA with MIA (default setting) and HERWIG with MIA (sue=20%, i.e., in 20% of the simulated double-resolved events a soft underlying event was included) are favoured. The OPAL and DELPHI data, for which comprehensive studies and Monte Carlo comparisons have been presented, are consistent with each other. Note however that comparisons to the NLO QCD calculation were made on parton level only 17 and it had been pointed out previously that hadronization corrections are important. The differential cross section in E3tet and 77 need corrections of 10% to 20%. However, for the distributions in x7, very sensitive to the hadronisation, the corrections may be even higher.
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•Jet and dijets production at HERA in photoproduction and DIS e p events At HERA using the jet data, parton densities of the proton and of the photon can be constrained. The structure of the real photon (photoproduction, Q2 < 1 GeV 2 ) and of the virtual photon (electroproduction or DIS ep events with Q2 > 1 GeV 2 ) have been studied, including direct and resolved photon contributions. In the resolved virtual photon processes at HERA the variable Q2 is the virtuality (mass squared) of the photon, which structure is tested by large px jets or particles, pT 3> Q2. For the first time a partonic content of 7£ was included in the analysis of the HERA data, see below. On the other hand interference terms, which may be important, as it was addressed in 19 , were omitted in the analysis. HI and ZEUS have measured cross section for the photoproduction of inclusive jet as well as dijet as a function of 77 and ET 20- The ZEUS and HI data are in nice agreement with each other in most observables (after correction for different cuts) and with the calculations for inclusive jet production, see Fig. 5-left and center, where HI data are shown. However for dijets event ZEUS finds a deficit at low x7 (even for large ET sample) indicating that more
378
Figure 5. Left and Centre: The jet cross sections for HI data in comparison with the NLO calculations for different parton parametrizations 2 0 ; Right: The dijet cross section (ZEUS) as a function of |cos#*|, from 2 0 .
gluons are needed in the photon. It is demonstrated in Fig. 5-right, where the angular distribution is presented for various subprocesses. The HI dijet data differ here from the ZEUS measurements and do not show a discrepancy with the NLO predictions. It was pointed out that the NLO calculations for cuts chosen for dijet events by ZEUS (e.g., different E™m for the two jets) should be more reliable 10 . The partonic content of the virtual photon has been investigated at HERA in dijet events, confirming the main In p^/Q2 dependence of the parton densities for 7* predicted by the theory (already by Parton Model). This behaviour leads to a suppression of the cross section with growing Q2 for a fixed pr value (range). ZEUS results, in form of a ratio of the cross sections for events with x > 0.75 and x < 0.75, are presented in Fig. 6-left (below similar ratio for subsample with charm will be shown). The ratio, plotted as a function of Q2 for various ET ranges, shows disagreement with HERWIG predictions (with SAS1D, GRV). HI data in two similar samples were compared with HERWIG MC predictions based on the direct 7* and on the resolved j? contribution. When in addition the contribution due to the partonic content of the longitudinally polarized virtual photon is included in analysis 21 , the description of the data is improved. Here also the CASCADE Monte Carlo based on CCFM evolution was applied - it gives prediction even closer to the data (Fig. 6-right), however the Q2 dependence is not well reproduced 2 1 .
379 • HI Preliminary
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Figure 6. Left: The ratio of cross sections R = a(x^ < 0.75)/cr(a 7 > 0.75), from ZEUS, as a function of Q2 2 1 ; Right: Dijet cross section for the HI data, the dark (light) histogram represents the direct 7* (direct plus the resolved j^.) contribution of HERWIG. The full line stands for the sum of the direct 7* and of j ^ , and 7^ resolved photon contributions of HERWIG; the dashed line is CASCADE prediction 2 1 .
4-2
Prompt Photons
At the Tevatron, HERA and recently also at LEP collider the prompt (isolated) photon production has been studied 22>23. While for pp collisions the DO data agree with the NLO predictions, CDF observes an excess at low photon px, similar as in measurements at lower centre-of-mass energy in hadronhadron collisions, see Fig. 7-left. The kt smearing for initial partons helps to describe data. The run II at Tevatron may clarify the situation, see also 24 where plans of future measurements of prompt photons at LHC are discussed. Note, that such processes are sensitive to the gluonic content of the proton. At the ep-collider HERA the photoproduction of the prompt photon plus jet were measured by the ZEUS group recently (in previous publications ZEUS 25 dealt with prompt photons only; then, their data showed slight disagreement with the NLO calculation in the r\ distribution for small y sample 2 6 ) . In this new measurement a direct photon sample, ie. with x1 ~ 1, was used to
380
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extract the (fct), ~ 2 GeV, in the proton 2 7 . The new OPAL measurements of the inclusive production of the isolated photon in the process 77 ->• 7X needs a if-factor of 1.85 to describe the data (Fig. 7-right) 2 3 . 4-3
Hadron Production
In Fig. 8 px spectra for TT0 and Ks in two-photon collisions are presented as measured by L3. The data show the expected exponential behaviour for small px, for px > 1.5 GeV a power law p^,3 with B « 4 indicates a simple underlying 2 body -> 2 body process. The spectra are also compatible with NLO calculation or PHO JET prediction (which are similar) for momenta up to a few GeV. Beyond 5 GeV, where data only for TT° are available a clear disagreement is seen: the NLO prediction lies below the data points (Fig. 8-a), PHO JET exceeds the measurements while PYTHIA is below (not shown) 2 8 . It was pointed out that further tests for charged pions are welcome. 5
Charm and Beauty Production
Heavy quark production provides important tests of QCD. It gives complementary to jets information on partonic densities in the photon. Although the large quark mass should allow for reliable perturbative calculations in
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QCD, discrepancies are observed for the heavy quark productions, especially for b production, at all colliders. The question may appear on a limitation of the standard calculation based on a DGLAP evolution, both for massless and massive approaches used in the calculations. It has been pointed out at this conference that a recently developed CASCADE program based on the CCFM evolution equations using unintegrated parton distributions reproduces the b production cross section at the Tevatron 2 9 . CASCADE also reproduces most charm and bottom distributions at HERA, unfortunately it has not been applied for 77 processes. For beauty production the QCD predictions are expected to be more reliable than for charm, but are still limited by the smaller cross section. More considerations for a better description of in the b sector were debated (e.g., possible need of additional terms 3 0 ) . It was emphasized 31 that care should be taken, whether comparisons are performed for B meson spectra or b-jet spectra, with the latter being more closely related to the partons. A clear, non-ambiguous signal for charm quark production is the presence of a D*+. This gold-plated signature has been exploited by all four LEP and both HERA collaborations. The leptonic decay has been used by ALEPH (/j* for charm), L3 (fi* and e* both for charm and bottom) and OPAL ( ^ f o r bottom). Though these analyses rely on the momentum spectrum as theoretical input, the statistics is substantially increased as compared to the D* + analyses 3 2 ' 3 3 . The b measurements at HERA rely on the inclusive semileptonic decays, using electrons or muons in dijet events. This signature is combined either with the requirement of a large p " ' to a jet (exploiting the
382
Figure 9. Left: Differential cross section for D* production obtained by LEP experiments in comparison with NLO QCD calculations, Centre: Charm production in 77 collision; Right: Summary of open charm and bottom production at e + e _ colliders in comparison with NLO QCD calculations 32 .
effect of the large b quark mass), or the secondary vertices (profiting from the lifetime of the B mesons). 5.1
Heavy Flavour Production at LEP
As discussed above for jets the production of heavy flavour in two-photon collisions is dominated by two processes, the direct and the single-resolved process. Both contribute in equal shares to heavy flavour final states at LEP 2 energies. The LEP experiments, ALEPH, DELPHI, L3, and OPAL, agree among themselves and with the theoretical expectation, which e.g., predicts a flat distribution in pseudorapidity for D* production. In transverse momentum distribution the measurements are close to the NLO QCD prediction based on a massive quarks approach, while there is some scatter among data, Fig. 9right. The experiments measure the fraction of direct and single-resolved contribution on a 10% level and confirm the prediction of NLO calculations 3 1 . The charm cross section as function of W 77 (Fig. 9-centre) shows a steeper rise as compared to (7(77 ->hadrons), see Sec. 5. With mCharm = 1-2 GeV the agreement with NLO QCD calculation is very good and also shows that the contribution from the resolved process dominates at high W 7 7 4 3 . The present status of the measurements for the total e + e~ -¥ e + e~cc, bbX
383 ZEUS 1996+97 Preliminary
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Figure 10. Charm in photoproduction (ZEUS). Left: Data for charm and non-charm jets; Centre: Results for dijets for with a reconstructed D* meson in comparison with the HERWIG model for x-, distribution (a) and with a parton level NLO QCD calculation (b); Right: The cosfl* distributions for dijets events with additional cuts; direct and resolved 7 samples in comparison with the PYTHIA model 1 6 .
cross section is summarized in Fig. 9-right. The importance of the resolved photon contribution is obvious for both charm and bottom production. The results are compared to NLO calculations, and good agreement is seen for charm production while a large discrepancy (3-4 a) is observed for bottom. Bottom production is measured by L3 using the fact, that the momentum as well as the transverse momentum of leptons with respect to the closest jet is higher for muons and electrons from bottom than for background, which is mainly charm. The total bottom production cross section is extracted correcting for detector efficiency. Note a large sensitivity of the cross section to the value of heavy quark mass. The same findings on agreement with theory, but with the studies restricted to the muonic channel, come from OPAL. This experiment also investigated the XT = 2pr/WviB distribution, where pr is the transverse momentum of the muon with respect to the beam axis; the shape of the MC simulation is found compatible with the data 3 2 .
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5.2
Heavy Flavour Production at HERA
The charm production (jets and D* mesons) are measured by HI and ZEUS both for a real and virtual photon interaction with a proton. Although such processes are dominated by the photon-gluon fusion, which directly probes the gluon content of the proton (or the pomeron for the diffractive events) they also offer opportunity to study the resolved photon contributions. The cross section as measured by ZEUS in photoproduction as a function of pseudorapidity for charm and non-charm jets are shown in Fig. 10-left. The failure of the NLO QCD to describe the data in the forward hemisphere is evident. The difference of shape and normalization can not be explained by the fragmentation, not included in the simulation 16 . A similar effect is seen in Fig. 10-centre; HERWIG and NLO QCD fail to describe the data for low a;7, where the resolved photon contribution dominates. Nevertheless, checking the underlying dynamics by the cosf9* distribution, with additional cuts (e.g., MJJ > 18 GeV), separately for direct (large a;7) and resolved (low x1; gluon exchange) enriched samples, good agreement with the PYTHIA simulation is found, see Fig. 10-right. For the virtual photon the ratio of low to high a:7 in dijet events as function of Q2 (Fig. 11-left) was measured by ZEUS, and suppression with
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Figure 12. Left: ZEUS data for rapidity distribution for b in photoproduction in comparison to PYTHIA and CASCADE 29 ; Right: Comparison of measured b production cross section at HERA to NLO QCD calculation as function of Q2 3 6 .
Q2 was found, weaker however than for the all-flavours case 3 4 . Suppression with growing Q2 is observed also in HI data for D* production, see Fig. 11centre. In DIS e p events the measurements of HI and ZEUS for D* production for the total cross section and the differential distributions in p%* and r/D* are nicely described by CASCADE. The HVQDIS Monte-Carlo, traditionally used in ep-scattering for heavy flavour production, fails in describing the forward (rjDt) range giving too low cross section (Fig. 11-right), similarly problem is seen in photoproduction events (Fig.lO-left). The total cross section for b production has been studied both in photoproduction, and in DIS ep events. ZEUS results for photoproduction are presented in Fig. 12-left for a distributions of the n coming from b-quark decays. There is an agreement with CASCADE prediction, except in the forward direction. Here the fct-factorization may break down 2 9 . Note, that in this region xp is here rather large, while a;T is small. The visible cross section and the total cross section from Monte Carlo simulations have been used to convert the b quark cross section from restricted p r and 77 ranges to form the Q2 and y distributions. The standard (DGLAP) NLO QCD calculations give results being lower than the measure-
386
H1 prel(96-97)
DELPHI J^ Diffractive Resolved
I0
2.5
5
7.5
10 12.5
15
17.5 20 22.5
Figure 13. Left: DELPHI data for differential cross section d) Right: HI data for da/dp^.(J/i>) in compared to MC 29 .
25
P,2(GeV2)
P,', (GeV/c)"
33
;
ments as shown in Fig. 12-right; CASCADE is above these calculations, but still somewhat below the data 3 6 .
5.3
Inclusive J/ip Production
In two-photon collisions at LEP a first look to fi+n~ + X has been given, where the muons are the decay products of the 3/tp, as shown in Fig. 13 33-left. DELPHI finds 36 ± 7 events in the muonic decay. The pr spectrum allows for the separation of the resolved (gluon exchange) and diffractive process (pomeron exchange). The latter fraction is found to 26 ± 22%. A precise measurement may help understand the total 77 cross section. Recently 37 , it was proposed that a comparison with theoretical calculations of 3/tp plus two jets may show, if colour octet production is important as it was found at Tevatron and at LEP in e + e~ annihilation events. In continuum events taken by BaBar (SLAC) close to the T(4S) both cross section and polar angular distribution of inclusive 3/tp production favour NRQCD fragmentation with the colour octet model 3 8 . The production of 3/ip at HERA (HI) is also shown in Fig. 13-right in agreement with the CASCADE model.
387
6
Total Cross Sections for 77 and 7*7*. Diffraction
Pure perturbative QCD can not describe soft and semi-hard inclusive processes at very high energy. The old, very well known and successful framework for soft phenomena is based on the Regge models, with exchange of Pomeron and Reggeons. The Pomeron is a complicated object with vacuum quantum numbers; its exchange governs the elastic and diffractive processes at high energies or at small x. Other processes and quantities, such as the difference of the total cross sections for pp and pp collisions, is thought to be related to the exchange of the Odderon, a partner of the Pomeron but with opposite C and P quantum numbers. There are various attempts to apply the perturbative QCD to the small x regions. Simple models based on the two-gluon and three-gluon exchange to represent Pomeron and Odderon exchange. Important progress has been obtained recently in this field, new theoretical and experimental results were presented 39>40>41>42. For a consistent description at small x in the BFKL approach, the impact factors of 7* at NLO are needed 3 9 . The advantage of the impact factors is that they can be calculated from first principles in the perturbative QCD (the photon-Reggeon interaction). The only place at present to test Odderon exchange processes is the HERA collider. A dedicated study of photoproduction with exclusive production of mesons decaying into photonic final states - with even or odd number of photons (from two to five photons) - has been performed by HI and no sign of an Odderon contribution was found 42 . 6.1
Cross Section <777
The reliable description of the process 77 —> hadrons is very important not only from the theoretical point of view, but also since this process gives the bulk of background at future linear colliders. This cross section,
388 3200
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' 1'
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^ ^ P ^ P p ^ * 1 1 IjT
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• L3 *OPAL D PlutO ATPC-2Y
oMD-1
20 10 A(OiV)
"w^GeV]10
Figure 14. Left: Measured total cross sections for pp, pp, and (rescaled) 7p, 77 Right: LEP data for
41
;
to describe the data (Fig. 15-left) and it would appear that data for (7(77 -*• hadrons) are overestimated by about 10%. Effects of resummation were also studied 41 . A DELPHI measurement of the a7»7» for very low Q2 double-tag events, important for a reliable estimation of the cr77, was also presented 4 4 , see Fig. 15-right for results.
6.2
Cross Section
CT7.7.
In the virtual photon collisions, 7*7* ->• hadrons, with large virtualities of both photons, Q?~ Q\, a large scale Q\~ Q\ ~ Q2, allows for a clean test of perturbative QCD in Regge limit. Such measurements with the aim to test the BFKL picture, as DGLAP evolution is suppressed for Q\~ Q\, were performed by the LEP experiments 4 5 , 4 6 , see Fig. 16-left for results 4 5 . It is shown that LO BFKL can not describe the data, however, when the NLO corrections to BFKL expressions in the BLM optimal scale setting were implemented 40 a good agreement is found (Fig. 16-right).
389 1000
- EMM Phod c o n s t a n t / pM„=1.5GeVko=0.4A=0 ; GRV ( l o w e r ) p,„i,=2 GeV k 0 = 0 . 6 6 A not 0/
900 L G R S ( t o p ) 800 700
15 < W < 60 GeV
-
G R S p l - , = 1 . 5 l < 0 = 0 . 6 6 A =0 P,™,, c o n s t a n t
/
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--T-
300 r
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—
STIC+VSAT Data V VSATDota GVDM Model VDM+Cont Model
L E P 2 - L 3 189 GeV and 1 9 2 - 2 0 2 GeV L E P 2 - O P A L 189 GeV
10
10
it? Q*(GeV)
Vs ( GeV)
Figure 15. Left: Two-photon cross section cr^ versus \/s in various models Right: The DELPHI data for very low Q2 double-tag events ** .
41
;
Data f r o m LEP2 V S „ _ = 1 8 9 - 2 0 9 GeV •
L3
< t f > - 1 6 0eV
O OPAL <0*> - 18 GeV NLO BFKL S ^ t f - 4 x Q * t v - 1 . 1 7 4 LOBFKL S«=tf-10x0" a,=1.545 LO 060X NLOOBOX
..
:
^^S..
Y^/^)"2)
Y=log(S„/)
Figure 16. Cross section for 7*7* -)• hadrons as function of Y = In W^/Q2. Left: The LEP 2 data, by ALEPH, L3 and OPAL, in comparison to PYTHIA 4 5 (the OPAL and L3 data are extrapolated to the acceptance range of ALEPH), Right: Comparison of the LO and NLO BFKL predictions to L3 and OPAL data 4 0 .
390
6.3
Diffraction at Low and High Virtuality of the Photon at HERA. DVCS
Various models of diffraction exist (e.g., pure soft Regge exchange models, the resolved Pomeron model 47 and dipole models 48 ) and they can be tested by comparison of distributions in specific processes. The diffractive production of vector mesons were measured in the photoproduction and DIS e p events at HERA. The photoproduction of vector mesons are shown in Fig. 17-left, where a steeper rise with energy is observed for heavy mesons as compared to light mesons 4 9 . For electroproduction the vector meson production ratios as a function of Q2 were used to test the flavour independence hypothesis: p : w : cj) : 3/ip=9:l:2:8, or (slightly modified ratios predicted in pQCD). For the light vector mesons the data scale with (Q2 + m 2 ), while the ones for 3/ip do not. In Fig. 17-right the rate for the p production as a function of Q2 is presented in a form of the ratio R = OL/O-T, and found to be in agreement with QCD 4 9 . The Deeply Virtual Compton Scattering (DVCS) process, 7*p -> 7p, is an exclusive analogue to the prompt 7 production in DIS ep : 7*p -)• 7X. In DVCS scales are different: Q2 is much larger than (p^) 2 , and |i| is smaller than 1 GeV 2 . This process can be described in terms of the skewed parton distributions, which can be treated as a generalization of the standard parton densities. The results of measurements at HERA (HI) for the DVCS cross section as a function of Q2 and W are presented in Fig. 18. In the HERMES experiment at HERA polarized e ± beams collide with the (gas) targets. The exclusive diffractive p production in DIS ep events was analyzed. The results for O-(J1P —> pp) are shown in Fig. 19 for two Q2 samples ((Q 2 ) « 2 and 4 GeV 2 ). The quark exchange subprocess dominates for smaller Q2 events, while gluon exchange mechanism starts to be important at larger Q2. Spin effects in p electroproduction were studied with the conclusion that s-channel helicity conservation is slightly violated. The double-spin asymmetry were also studied 50 (for DIS and photoproduction) and results were interpreted in terms of GVMD.
7
Exclusive Channels and Resonances in 77 collisions
Study of pure leptonic final states in 77 collision were performed to test QED (up to 0(ai)) but also to demonstrate the understanding of the detectors. The remarkable number of new results on exclusive hadronic final states presented during the conference, some of them from new high luminosity low energy colliders, leads to better understanding of strong interaction at low
391 ZEUS
15
A ZEUS 94 T ZEUS 95 • ZEUS (prel.) 96/97 • HI 95/96 10
5
"
- CTEQ(5M) MRST(99)
-
udnT
jr*
0 1
i
\
t
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i
i
i
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15
20
i
25 2
Q [GeV 2 ]
Figure 17. Left: Photoproduction of vector mesons at HERA and fixed target exp. Right: The ratio R = OX/
•
Xl
c &
? 10
15
i V 0
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I I DVCS(FFS) fifiSJ DVCS(DD) W = 75 GeV 111 < I OeV2
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10
25
50
75
W
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125
[GeV]
Figure 18. Cross sections for DVCS as function of Q2 and W, from HI
49
energies. If a large momentum scale is involved in the reaction, then we can use pQCD assuming factorization of the amplitude into a perturbative and non-perturbative part 51 . In Refs. 52 the meson distribution amplitude were constrained from study of transition 7*7 -> TT, 77,77'. Radiative decay ampli-
392 —!—1 I I I I II—'•*"• 1
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tudes for various particles, among them the decays TT,T},T]' -4 7*7, lead to reconstruction of pion and photon wave functions 53 . Production of particles containing heavy quarks is of special interest; results obtained at e + e~ colliders (see below) and at HERA for the production of excited P-wave charm mesons 54 were discussed during the conference. One of the basic open question of QCD is the existence of the glueballs, a bound state of gluons. The two-photon process is a powerful anti-filter for glueballs. The lattice simulation 55 of the quenched glueball spectrum was preformed with first promising results for nf=2. 7.1
Lepton and Hadron Pairs
Lepton pair production e + e~ -» e+e~l+£~ (t = fj,, r) have been measured by L3 at LEP 2 as function of centre-of-mass energy and of W 7 7 . Limits on a possible anomalous coupling of the r have been given 56 . New LEP 2 results on pion and kaon pair production were presented 57 and compared with the QCD-inspired calculation of Brodski and Lepage (Fig. 20). ALEPH and DELPHI find good agreement for kaon pairs both in normalization and shape of the distribution in scattering angle cos 9* and W^. For the pions the shape of the distributions all agree, while for the normalization, sensitive to nonperturbative input, neither the experiments nor experiments versus theory agree. The production mechanism for dibaryon production was tested by OPAL
393 •
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i
i
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i
i
i
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i
i I
pcos9*| < 0.6 C< +t4H 'i* til H3J j[
• DELPHI preliminary ° A L E P H preliminary • —— Brodsky & Lepage —
W^ [GeV] Figure 20. Differential cross section for 77 to two charged kaon ond pion pairs, respectively as function of W 7 7 as measured by DELPHI and ALEPH 57 .
and Belle in pp and by L3 in AA final states. The dibaryon mass spectra as function of W11 (from the dimensional counting rule ~ s~" is expected) prefer the quark-diquark model (n = 4) rather than the three-quark model (n = 6). The measurements are in agreement with previous measurements, though all predictions tend to lie below the data 58 . 7.2
Exclusive Meson Production and Glueball Search
The results are manifold and involved. The branching ratios, production as function of the virtuality of the photon and form factors of specific mesons are interesting on their own, but also constrain the gluonium content of the particle. The determination of the spin and helicity of resonances has been performed, showing that for the tensor mesons the multiplet is understood, while for the scalars the situation is more unclear. Possible mixture of states complicates the interpretation and the isolation of the best glueball candidate 59 - 60 . 7.3
Charmonia and Bottomonia
Extraction of r 7 7 (rj c ) was investigated in the 7r + 7r - K + K~, 2(K + K~), KsK+7T~ and 2(7r+7r~) decay modes by DELPHI. While the combination of the first three channel results in a two-photon width o f l 3 . 0 ± 2 . 7 ± 5 . 0 keV and is compatible, though somewhat higher, with previous measurements, the non-observation of the Ait decay leads to an upper limit of 3.8 keV 6 0 .
394 M
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Figure 21. Mass difference m(e+t--y)-m{e+t-)forxc0 -> J/V> events as measured by Belle 6 2 .
,J\
\
, A, .
3400 3600 M (4*r) (MeV)
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.
3800
Figure 22. Invariant mass distribution of four charged pions as measured by CLEO 6 1 .
The CLEO Collaboration presents a first observation of the Xco m twophoton collisions 6 1 . A result of r 7 7 (xco) = 3.76 ± 0.65 ± 1.81 keV is extracted in the 7r+7r-7r+7r~ decay mode. Belle shows that the Xco is present in the KgKs mass spectrum as well 62 . Belle also measures the Xc2 production in the J/V>7 decay mode (Fig. 21), CLEO presents a first measurement from the 7r+7r~7r+7r- decay mode (Fig. 22). Both results are lower, but in agreement with previous results in two-photon collisions and larger than the results from pp collisions. As pointed out 61 the ratio r 7 7 (x c o)/r 7 7 (xc2) is a good QCD test with small theoretical uncertainties and could provide a measurement of a s , but the calculations of the C ( a | ) term for the Xc states are badly needed. A first search for the % meson in two-photon collisions was performed in ALEPH 63 , the bottomonium ground state being still undetected. The observation of one % candidate (m = 9.30 ± 0.02 ± 0.02 GeV/c 2 ) compatible with background gives upper limits of 57eV and 128eV for r 7 7 (r/b)xBR for decays to 4 and 6 charged particles, respectively. 8
F u t u r e P r o j e c t s and R e l a t e d Topics
The two-photon collisions at the future LHC collider may turn out to be important for the search of the Higgs boson, as addressed in the presentation 6 5 . The coherent photon-pomeron and photon-photon interactions appear already in ultraperipheral collisions at RHIC; a clear p° signal was observed in the 7r+7r_ invariant mass spectrum 66 .
395 Relativistic nuclear collisions at LHC and RHIC were studied in 6 7 . In particular the Coulomb and unitarity corrections to the single e + e~ pair production as well as the cross section an for the multiple pair production were obtained in an analytic form. Some of the results differ from results published by other authors, The Born cross section for e + e pair production is given by: _ 28 (ZiZ 2 a 2 ) 2
r
3
2.198 L2 + 3.821 L- 1.6321
with L = ^(7172), where 7, and Z, are the Lorentz factors and the charges of the colliding nuclei. The cross sections for this process at LHC and RHIC are huge, so the pair production can be a serious background. The control of this background may turn out important for a good beam lifetime and luminosity of the colliders. In Table 1 results forCTBomare given together with corrections (calculated for small 1/L in the main logarithmic approximation).
Tcible 1. Results for relativistic heavy-ion colliders {Z\ = Zi = Z and 71 = 72 = 7)
Collider
Z
7
<7Born [kb]
gCoul CBorn
°unit OBorn
RHIC, Au-Au
79
108
36.0
-25%
-4.1%
LHC, Pb-Pb
82
3000
227
-14%
-3.3%
LHC, Ca-Ca
20
3700
0.872
-1.06%
-0.025%
Very important for the investigations and the understanding of the photon and its interactions are planned e + e~ Linear Colliders (LC) at large CM energy (500, 800 GeV or higher), in particular the Photon Collider (PC) option based on Compton backscattering of laser light off the high energy electrons. Such 77 and ej collider has unique properties as it was discussed in Refs. 68 ' 69 (with particular emphasis on the TESLA PC 7 0 - 7 1 ). Cross sections are higher than for corresponding processes in e + e _ collision, accessible masses are larger and there are unique reactions, such as 77 ->H. Since the 77 luminosity in the high energy part of spectra at TESLA can be about 30 % of the e + e~ luminosity (see also Ref. 72 for a fast luminosity measurements study) the number of "interesting" events at the photon collider will be even higher than in e + e~ one. A short list of physics processes for the photon collider is presented in Table 2 7 1 .
396 Table 2. Gold-plated processes at photon colliders Reaction 77 —> ho —• bb, 77 7 7 -<• ho -> WW(WW) jj^ho ->ZZ(ZZ*) 77 -+ H, A —• bb
7 7 - / 7 , x,+xr> # + # 77 - S[ft] 7e -> e X? 77 — W+W~ 7e~ —• W~ve 77 -+ W W + WW(ZZ) 77 —* tt 7e~ —• tbve 77 —• hadrons 7e~ —• e~X and i^X 75 — qq, cc 77 —»• J / ^ J/ip
Remarks MhQ < 160 GeV 140 < Mho < 190 GeV 180 < Mho < 350 GeV M.SSM. heavy Higgs supersymmetric particles tt stoponium Me- < 0.9 x 2E0 - M+o anom. W inter., extra dim. anom. W couplings strong WW scattering anom. t-quark interactions anom. Wtb coupling total 77 cross section struct, functions gluon distr. in the photon QCD Pomeron
The unique feature of a 7e collider is the possibility of the measurement of the structure function for the real photon (not quasi-real as presently), in particular the spin-dependent structure functions, not measured so far. The future of exclusive particle production measurements at charm and bottom factories (CLEO-c, BaBar and Belle experiments) were also discussed at the conference. E.g., at CLEO-c the high statistics and high precision measurements allow progress in measuring branching ratios, form factors, decay constants, CKM matrix parameters etc. 64 . 9
Conclusion
Plenty of new high quality data involving photons in hadronic processes have been analysed after PHOTON 2000 at LEP and HERA, as well as from experiments at Tevatron, RHIC, VEPP-2M, DAPHNE, CESR, KEKB and SLAC. An impressive progress in the measurements is accompanied by improvements in the theoretical descriptions of hard, semi-hard and soft hadronic processes involving photons. Also pure QED processes were studied, relevant for present and future colliders. Processes with photons provide simple tests of new theoretical ideas, like
397 e.g., non-commutative QED; in future conferences of the PHOTON series, we certainly will learn more about these new possible interactions of the photon so that we finally understand "what are light quanta". Acknowledgements It is pleasure for us to thank the organizers of the conference PHOTON2001, especially Maria Kienzle and Maneesh Wadhwa, for a nice atmosphere and perfect organization in the beautiful site of Ascona. Armin Bohrer thanks the Bundesministerium fur Bildung und Forschung of Germany (grant BMBF 05 HE 1 PS A8) for the financial support. Maria Krawczyk is grateful to the organizers of the conference and the Polish Committee for Scientific Research (grant 2P03B05119 (2002)) for the financial support. References 1. Proceedings of the International Conference on the Structure of the Photon (PHOTON 2000), Ambleside (2000), Eds.: A. Finch, New York, American Institute of Physics. 2. A. de Roeck, Survey in High Energy Physics, Vol.16, 49 (2001). 3. R. Nisius, Phys. Rep. 332, 165 (2000); M. Krawczyk et al., Phys. Rev. 345, 265 (2001); M. Whalley, J. Phys. G27, 12A1 (2001); M. Erdmann, Springer Tracks in Modern Physics 138 (1997), Heidelberg, Springer. 4. R. Nisius, these proceedings and private communication. 5. R. Taylor, these proceedings. 6. I. Tyapkin, these proceedings. 7. P. Jankowski, these proceedings. 8. A. Csilling, these proceedings. 9. I. Fleck, these proceedings. 10. M. Wing, these proceedings. 11. M. Vasquez, these proceedings. 12. B. Potter, these proceedings. 13. T. Schorner, these proceedings. 14. A. Bohrer, Phys. Rep. 291, 107 (1997); I.G. Knowles and G.D. Lafferty, J. Phys. G23 731 (1997). 15. D. Traynor; S. Boogert, these proceedings. 16. S. Padhi, these proceedings. 17. T. Wengler, these proceedings. 18. J. Masik, these proceedings.
398 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55.
U. Jezuita-Dabrowska, these proceedings. A. Valkarova, these proceedings. K. Sedlak, these proceedings. M. Begel, these proceedings. J. Lillich, these proceedings. S. Tapprogge, these proceedings. J. Breitweg et al. [ZEUS Collaboration], Phys. Lett. B 472, 175 (2000). M. Fontannaz et al., Eur. Phys. J. C 21, 303 (2001); A. Zembrzuski and M. Krawczyk, Phys. Rev. D 64, 114017 (2001). S. Chekanov et al. [ZEUS Collaboration], Phys. Lett. B 511, 19 (2001). P. Achard, these proceedings. H. Jung, Phys. Rev. D 65, 034015 (2002); DESY-01-136, hepph/0110034 and these proceedings. J. Chyla, these proceedings. S. Frixione, these proceedings. V. Andreev, these proceedings and private communication. A. Sokolov, these proceedings. B. West, these proceedings. W. Erdmann, these proceedings. M. Turcato, these proceedings. M. Klasen et al, Nucl. Phys. B 609, 518 (2001). S. Passaggio, these proceedings. V. Fadin, these proceedings. V. Kim, these proceedings, S. Brodsky et al., hep-ph/9901229v3, V. Kim et al., hep-ph/9911241. G. Pancheri, these proceedings. T. Berndt, these proceedings. M. Kienzle, these proceedings. A. Nygren, these proceedings. G. Prange,these proceedings. C. H. Lin, M. Przybycieri, these proceedings. G. Ingelman and P. Schlein, Phys. Lett. B 152, 256 (1985). K. Golec-Biernat and M. Wiisthoff, Phys. Rev. D 59, 014017 (1999). S. Kananov, these proceedings. K. Lipka, these proceedings. G. P. Lepage and S. J. Brodsky, Phys. Rev. D 22, 2157 (1980). P. Kroll, these proceedings. A. V. Anisovich, these proceedings. U. Karshon, these proceedings. G. Bali, these proceedings.
399 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70.
G. Debreczeni; D. Haas, these proceedings. K. Grzelak, these proceedings. T. Barillari; A. Chen; B. Echenard, these proceedings. C. Amsler, these proceedings. S. Braccini, these proceedings. H. Paar, these proceedings. S. Uehara, these proceedings. A. Bohrer, these proceedings. D. Cassel, these proceedings. K. Piotrzkowski, these proceedings. F. Meissner, these proceedings. V.G. Serbo, these proceedings. V. Telnov, these proceedings. I. Ginzburg, D. Anipko, these proceedings. R. Brinkmann et al. (Eds.), TESLA Technical Design Report, DESY2001-011 (2001) 71. B. Badelek et al. (Eds.) [ECFA/DESY Photon Collider Working Group], part VI, appendices, chapter 1. The Photon Collider at TESLA, hepex/0108012; Proceedings of Photon Collider Workshop, Hamburg (2000), Eds.: R.D. Heuer et al, Nucl. Instrum. Methods A 472, 1 (2001); 72. W. da Silva, these proceedings
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8 Miscellaneous
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ADRESSES OF PARTICIPANTS P. Achard
DPNC, Geneva University 24, quai Ernest-Ansermet 1211 Geneve 4, Switzerland pablo. achard@cern. ch
C. Amsler
Physik Institut, Universitat Zurich Winterthurerstr. 190, 8057 Zurich, Switzerland [email protected]
V. Andreev
EP Division, CERN 1211 Geneve 23, Switzerland valer i. andreev® cern. ch
D. Anipko
Dept. of Physics, Novosibirsk State University Pirogova 2, 630090 Novosibirsk, Russian Federation [email protected]
A. Anisovich
Theory Division, Petersburg Nuclear Physics Institute Orlova Rosha 1, 188300 Gatchina, Russian Federation aanisovi@iname. com
G. Bali
Dept. of Physics and Astronomy Glasgow University, University Avenue G12 8QQ Glasgow, United Kingdom [email protected]
T. Barillari
High energy Physics, Colorado-Boulder University 2575 Sand Hill Rd 94025 Menlo Park CA, United States [email protected]
M. Begel
Physics and Astronomy, Rochester University Box 500 Fermilab, 60510 Batavia IL, United States [email protected]
T. Berndt
Dept. of Phys. and Astronomy Kirchhoff Institute for Physics Schroederstrasse 90, 69120 Heidelberg, Germany [email protected]
403
A. Boehrer
Fachbereich Physik, Siegen University Emmy-Noether-Campus, 57068 Siegen, Germany armin. boehrer @cern. ch
S. Boogert
Nuclear and Particle Physics, Oxford University Keble Road, 0X1 3RH Oxford, United Kingdom [email protected]
K. Borras
ZEUS Experiment, DESY Notkestr. 85, 22603 Hamburg, Germany [email protected]
S. Braccini
Laboratori Nazionali di Frascati - INFN Via Enrico Fermi 40 00044 Frascati (Roma), Italy [email protected]
D. Cassel
Lab. of Nuclear Studies, Cornell University Newman Laboratory, 14850 Ithaca NY, United States [email protected]
A. Chen
Dept. of Physics, National Central University Wu-Chuen li, 320 Chung-Li, Taiwan [email protected]
J. Chyla
Elementary Particule Physics, Institute of Physics ASCR, Na Slovance 2, Prague 8, Czech Republic [email protected]
S. Collins
Dept. of Physics and Astronomy Glasgow University, University Avenue G12 8QQ Glasgow, United Kingdom [email protected]
A. Csilling
EP Division, CERN 1211 Geneve 23, Switzerland [email protected]
G. Debreczeny
Faculty of Natural Sciences Eotvos Lorand University Pazmany Peter, 1117 Budapest, Hungary gergely. debreczeny @cern. ch
P. Deglon
DPNC, Geneva University 24, quai Ernest-Ansermet 1211 Geneve 4, Switzerland [email protected]
A. Dizdar
Dept. of Physics, Siegen University Walter Flex Str. 3, 57072 Siegen, Germany [email protected]
B. Echenard
DPNC, Geneva University, Geneva University 24, quai Ernest-Ansermet 1211 Geneve 4, Switzerland [email protected]
W. Erdmann
Institut for Particle Physics, ETH Zrich WLGA E18, 5232 Villigen-PSI, Switzerland [email protected]
F. Erne
NIKHEF, Postbus 41882 1009 DB Amsterdam , Netherlands [email protected]
N. Fabiano
Dept. of Physics, INFN Perugia Via A. Pascoli, 06100 Perugia, Italy [email protected]
V. Fadin
Siberian Branch of Russian AS Institute of Nuclear Physics, Lavrentiev av., 11 630090 Novosibirsk, Russian Federation v. s. fadin@inp. nsk. su
J. H. Field
DPNC, Geneva University, Geneva University 24, quai Ernest-Ansermet 1211 Geneve 4, Switzerland [email protected]
A. Finch
Dept. of Physics, Lancaster University Bailrigg, LAI 4YZ Lancaster, United Kingdom [email protected]
I. Fleck
Faculty of Physics, Freiburg University Hermann Herder Str. 3, 79104 Freiburg, Germany [email protected]
406
S. Frixione
Theoretical Physics, LAPP Chemin de Bellevue 74941 Annecy-le-Vieux - France stefano. frixione@cern. ch
I. Ginzburg
Theoretical Physics Sobolev Inst, of Mathematics Prosp. Ac/Koptyug, 4 630090 Novosibirsk, Russian Federation [email protected]
K. Grzelak
Institut of Experimental Physic Warsaw University, Hoza 69 00-681 Warsaw, Poland [email protected]
D. Haas
DPNC, Geneva University 24, quai Ernest-Ansermet 1211 Geneve 4, Switzerland [email protected]
J. Hess
Dept. of Physics, Siegen University Emmy-Noether-Campus 57072 Siegen, Germany [email protected]
S. Hou
Institute of Physics, Academia sinica P717, 11529 Nankang, Taiwan [email protected]
P. Jankowski
Inst, of Theoretical Physics, Warsaw University Hoza 69, 00-681 Warsaw, Poland [email protected]
U. Jezuita-Dabrowska
Inst, of Theoretical Physics, Warsaw University Hoza 69, 00-681 Warsaw - Poland [email protected]
G. Jikia
Dept. of Physics, Freiburg University Hermann Herder Str. 3 79104 Freiburg, Germany [email protected]
H. Jung
Dept. of Physics, Lund University Professorsgatan, 22100 Lund, Sweden [email protected]
S. Kananov
High Energy Physics, Tel Aviv University Ramat Aviv, 61390 Tel Aviv IL, Israel [email protected]
F. Kapusta
LPNHE-Paris, CNRS-IN2P3 4, Place Jussieu, Tour 33 RdC, BP200 75252 Paris, France kapusta@in2p3. fr
U. Karshon
Particle Physics, Weizmann Institute Herzl, 76100 Rehovot , Israel [email protected]
V. Kazanine
Siberian Branch of Russian AS Institute of Nuclear Physics, Lavrentiev 630090 Novosibirsk, Russian Federation kaz anin@inp .nsk.su
M.-N. Kienzle-Focacci
DPNC, Geneva University 24, quai Ernest-Ansermet 1211 Geneve 4, Switzerland [email protected]
V.Kim
High Energy Physics Division St.Petersburg Nuclear Physics Inst. Orlova Roscha 1 188300 Gatchina, Russian Federation [email protected]
M. Krawczyk
Faculty of Physics, Warsaw University Hoza 69, 00-681 Warsaw, Poland [email protected]
P. Kroll
Fachbereich Physik, Wuppertal University Gaussstrasse 20, 42097 Wuppertal, Germany [email protected]
G. Lanfranchi
Laboratori Nazionali di Frascati - INFN Via Enrico Fermi 40 00044 Frascati (Roma), Italy [email protected]
M. Levtchenko
High Energy Physics. Dept. - PNPI 188350 Gatchina - Russian Federation [email protected]
J. Lillich
Dept. of Physics, Freiburg University Hermann Herder Str. 3 79104 Freiburg, Germany [email protected]
C.H. Lin
EP/LE Division - CERN 1211 Geneve 23, Switzerland linch@mail. cern. ch
J. Masik
Dept. of High Energy Physics Institute of Physics, ASCR Na Slovance 2, 18221 Praha, Czech Rep. [email protected]
S. Matsumoto
Dept. of Physics, Chuo University Kasuga; Bunkyo-ku, 112-8551 Tokyo, Japan [email protected]
R. McNeil
Dept. of Physics and Astronomy Louisiana State University 202 Nicholson Hall 70803 Baton Rouge LA, United States [email protected]
F. Meissner
Nuclear Science Division Lawrence Berkeley Laboratory 1 Cyclotron Rd, MS70-319 94704 Berkeley CA, United States [email protected]
P. Mermod
DPNC, Geneva University 24, quai Ernest-Ansermet 1211 Geneve 4, Switzerland [email protected]
K. Negodaeva
HERMES Collaboration, DESY Notkestrasse 85, 22607 Hamburg, Germany [email protected]
A. Ngac
Dept. of Physics, Siegen University Emmy-Noether-Campus, 57068 Siegen, Germany [email protected]
R. Nisius
EP Division, CERN 1211 Geneve 23, Switzerland [email protected]
A. Nygren
Dept. of Physics, Lund University Box 118, 221 00 Lund, Sweden nygren@mail. cern. ch
O. Olkhov
Theoretical Physics, Institute of Chemical Physics Kosygin Street 4, Moscow - Russian Federation [email protected]
H. Paar
Dept. of Physics, California San Diego University 9500 Gilman Drive, 92093 La JoUa CA, United States [email protected]
S. Padhi
ZEUS Experiment, DESY Notkestrasse 85, 22607 Hamburg, Germany [email protected]
G. Pancheri
Laboratori Nazionali di Frascati - INFN Via Enrico Fermi 40, 00044 Frascati (Roma), Italy [email protected]
S. Passaggio
Sezione di Genova, INFN Via Dodecaneso 33, 16146 Genova, Italy [email protected]
K. Piotrzkowski
Louvain University Chemin du Cyclotron 2 1348 Louvain-la-Neuve, Belgium [email protected]
B. Poetter
Theory, Max-Planck-Institut Foehringer Ring 6, 80805 Muenchen, Germany [email protected]
G. Prange
Dept. of Physics, Siegen University Emmy-Noether-Campus, 57068 Siegen, Germany [email protected]
M. Przybycien
Faculty of Physics, Mining and Metallurgy University Al. Mickiewicza 30, Krakow , Poland mar iusz. pr zyby cien@ifj .edu. pi
T. Schoerner
Experiment HI, Max-Planck-Institut Foehringer Ring 6, 80805 Muenchen, Germany [email protected]
410
K. Sedlak
Institute of Physics Academy of Sciences of the Czech Rep Na Slovance 2, 18221 Praha 8 - Czech Rep [email protected]
V. Serbo
Dept. of Physics, Novosibirsk State University Pirogova Str. 2 630090 Novosibirsk, Russian Federation [email protected]
W. da Silva
LPNHE- Paris 6 University 4, Place Jussieu, Tour 33 RdC, BP 200 75252 Paris, France [email protected]
A. Sokolov
IHEP Pobeda, 142284 Protvino, Russian Federation [email protected]
S. Tapprogge
CERN 1211 Geneve, Switzerland [email protected]
R. Taylor
Dept. of Physics and Astronomy University College London, Gower Street London WC1E 6BT, United Kingdom [email protected]
V. Telnov
Siberian Branch of Russian AS Institute of Nuclear Physics, Lavrentieva 11 630090 Novosibirsk, Russian Federation [email protected]
P. Thompson
School of Physics, Birmingham University Edgbaston, Birmingham B15 2TT, United Kingdom [email protected]
D. Traynor
Dept. of Physics, Queen Mary, London University Mile End Road, London E l 4NS, United Kingdom [email protected]
M. Turcato
Padova University, INFN Via Marzolo 8, 35131 Padova, Italy [email protected]
411
I. Tyapkin
JINR Dubna, Moscow, Russia Federation [email protected]
S. Uehara
KEK - High Energy Accel. Research Org. Oho 1-1, 305-0801 Tsukuba, Japan [email protected]
A. Valkarova
Institute of Particle and Nuclear Physics Charles University, V Holesovickach 2 180 00 Praha, Czech Republic [email protected]
M. Vasquez
Dept. of Theoretical Physics Universidad Autonoma de Madrid Facultad de Ciencias (Cantoblanco) 28049 Madrid, Spain [email protected]
I. Vodopianov
High Energy of Physics Petersburg Nuclear Physics Institute, Orlova Roscha 188350 Gatchina, Russia Federation [email protected]
M. Wadhwa
Dept. of Physics, Basel University Klingelbergstrasse 82, 4056 Basel, Switzerland [email protected]
T. Wengler
EP Division - CERN 1211 Geneve 23, Switzerland t hor sten. Wengler @ cer n. ch
B. West
Dept. of Physics and Astronomy University College London, Gower Street London WC1E 6BT, United Kingdom [email protected]
M. Wing
ZEUS Experiment, DESY Notkestrasse 85, 22607 Hamburg, Germany [email protected]. de
N. Zimine
Laboratory of High Energy, JINR (Dubna) 6 Juliot Curie, Dubna, Moscow, Russia Federation [email protected]
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413
PICTURES
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AUTHOR INDEX
A P. Achard, p. 59 C. Amsler, p. 263 V. P. Andreev, p. 127 D. A. Anipko, p. 356 A. V. Anisovich, p. 269
B G. S. Bali, p. 259 T. Barillari, p. 233 T. Berndt, p. 192 A. Bohrer, p. 299, 383 S. Boogert, p. 68 K. Borras, p. 207 S. Braccini, p. 325
C D. G. Cassel, p. 307, 311 A. Chen, p. 237 J. Chyla, p. 113 A. Csilling, p. 24
D G. Debreczeni, p. 223
E B. Echenard, p. 241 W. Erdmann, p. 138
F N. Fabiano, p. 303 V. S. Fadin, p. 172 I. Fleck, p. 90 G I. F. Ginzburg, p. 341 K. Grzelak, p. 289
H D. Haas, p. 227 S. R. Hou, p. 251
J P. Jankowski, p. 29 U. Jezuita-Dabrowska, p. 98 H. Jung, p. 132
K U. Karshon, p. 319 V. F. Kazanine, p. 157 M. N. Kienzle-Focacci, p. 162 V. T. Kim, p. 188 M. Krawczyk, p. 383 P. Kroll, p. 255
418
L G. Lanfranchi, p. 278 M. Levtchenko, p. 245 J. Lillich, p. 81 C. H. Lin, p. 180 K. Lipka, p. 196
M J. Masik, p. 77 F. Meissner, p. 213
N R. Nisius, p. 49 A. Nygren, p. 168
O O. A. Olkhov, p. 369
P H. P. Paar, p. 293 S. Padhi, p. 150 G. Pancheri, p. 217 K. Piotrzkowski, p. 362 B. Potter, p. 94 G. Prange, p. 176 M. Przybycien, p. 184
S T. Sch6rner, p. 102 K. Sedlak, p. 39 V. G. Serbo, p. 349 W. da Silva, p. 366 A. A. Sokolov, p. 119, 123
T S. Tapprogge, p. 374 R. J. Taylor, p. 13 V. I. Telnov, p. 335 P. D. Thompson, p. 201 D. Traynor, p. 63 M. Turcato, p. 144 I. Tyapkin, p. 17
U S. Uehara, p. 273 V A. Valkarova, p. 33 M. Vazquez, p. 85 I. Vodopianov, p. 284
W T. Wengler, p. 72 B. J. West, p. 45
This volume reports on all aspects of high energy photon interactions using both photon and proton targets. Significant new results from the LEP and HERA experiments as well as from CLEO II and BELLE are presented. These data are confronted with diverse theoretical models. In particular, predictions of QCD in both the perturbative and the non-perturbative sector are extensively discussed. The prospects for gamma—gamma physics at future high energy colliders are also reviewed.
World Scientific www. worldscientific. com 5011 he
