editors
Maria-Novella Kienzle-Focacci Maneesh Wadhwa
Photon 2001 International Conference on the Structure and Interactions of the Photon Including the 14th International Workshop on Photon-Photon Collisions
Photon 2001 International Conference on the Structure and Interactions of the Photon Including the 14th International Workshop on Photon-Photon Collisions
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editors Maria-Novella Kienzle-Focacci University of Geneva, Switzerland Maneesh Wadhwa Basel University, Switzerland
Photon 2001 International Conference on the Structure and Interactions of the Photon Including the 14th International Workshop on Photon-Photon Collisions Ascona, Switzerland
2 - 7 September 2001
V | b World Scientific w l
New Jersey • London • Sine Singapore • Hong Kong
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PHOTON 2001 Proceedings of the International Conference on the Structure and Interactions of the Photon, Including the 14th International Workshop on Photon-Photon Collisions Copyright © 2002 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.
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PREFACE
PHOTON2001, an International Conference on the Structure and Interactions of the Photon, organised by the University of Geneva, was held at the Centro Stefano Pranscini on Monte Verita, Ascona, Switzerland, from the 2nd to the 7th of September 2001. The conference is the 14th in a series that started in Paris in 1973. The conferences were originally devoted entirely to the physics of photon-photon collisions, but since 1995 the scope has been extended to include also single photon interactions which have been extensively studied in recent years at the HERA ep collider at DESY, Hamburg. As is customary in this series, only plenary talks were given. These were grouped into sessions on: Photon Structure (8), Jets and Inclusive Hadron Production (13), Charm and Beauty Production (10), Total Cross-Sections and Diffraction (16), Resonances and Exclusive Channels (23) and Future Projects and Related Topics (8). The number of 15 minute talks given in each session is shown in parentheses. Out of a total of 78 talks, 58 were experimental and 20 theoretical. Conference summary talks of 45 minutes were given by Armin Boehrer (experiment) and Maria Krawczyk (theory). The majority of new experimental results presented were from LEP and HERA, but important contributions came also from detectors at lower energy high luminosity colliders such as BELLE and CLEO. Particularly impressive were the huge statistics of the preliminary data on gamma gamma collisions from BELLE. Other experimental highlights were new experimental results from HERA and LEP (open b-quark production in 7p and 77 collisions and inclusive production of IT0 at high pr in 77 collisions) that seem to pose a serious challenge to the predictive power of perturbative QCD. Hints for the production of the so-far-unobserved 775 meson were shown. The first results in coherent photon-photon and photon-pomeron collisions from the RHIC heavy ion collider at Brookhaven were presented. In the future, important results in this domain are expected from heavy ion collisions in the LHC collider at CERN. In two other talks the possibility for detection of tagged 77 interactions in pp collisions at the LHC were reviewed. The current status of the real photon collider within the TESLA linear electron accelerator project was also described. The Centro Stefano Franscini is situated in 'sub-tropical Switzerland' on the sunny western shore of Lake Maggiore. In the early years of the 20th Century, the summit of Monte Verita was home to a commune seeking an
v
VI
outdoor way of life, a vegetarian diet, simplicity, nature and free love. One visitor during this period, seeking therapy for a nervous disorder was Hermann Hesse. Other visitors to Ascona around this time included Carl Gustav Jung, Erich Maria Remarque, Paul Klee, Hans and Sophie Tauber Arp and Alexi Jawlensky. In 1927 the Monte Verita Hotel was built by Emil Fahrenkamp. During this period, Ascona became an important meeting point for many artists of the 'Bauhaus' school. After the second world war, Jorge Semprun could restore his health in the Ascona and Locarno surroundings. In 1956 Baron von der Heydt, the then owner of Monte Verita, left the property to Canton Ticino. In 1989 a private foundation including Canton Ticino, the Town Council of Ascona and the Swiss Federal Institutes of Technology in Lausanne and Zurich was established with the aim of creating a cultural and scientific centre on Monte Verita. In 1992 the present Centro Stefano Franscini was founded. The 90 participants at the Conference were able to benefit the excellent conference facilities, clear air, splendid views and good food provided by the Centro Stefano Franscini. During the excursion to the Brissago Islands, they were also able to appreciate the fine weather, a very interesting visit to a unique botanical garden, and the convivial Conference Dinner sandwiched between two memorable concerts of Good Time Jazz provided by local musicians. We should like to thank Claudia Lanfranchi for the warm and efficient organization of our life in the Center. Shivani Wadhwa and Peggy Argentin for their continous kindness and Patrick Deglon for his ability in solving computers problems. The sponsorship of the Conference by Hewlett-Packard, Victorinox, the Swiss National Science Foundation, CERN, ETHZ and the Societe Academique de Geneve is gratefully acknowledged.
John H. Field Maria Novella Kienzle-Focacci Maneesh Wadhwa
COMMITTEE
International Committee
Programme Committee
S. J. Brodsky (SLAC) M. Erdmann (Karlsruhe) F. C. Erne (NIKHEF) V. S. Fadin (Novosibirsk) J. H. Field (Geneva) D. Hitlin (CALTECH) S. Iwata (KEK) F. Kapusta (LPNHE Paris) U. Karshon (Weizmann) R. Klanner (DESY) M. Krawczyk (Warsaw) D. J. Miller (UC London) H. P. Paar (UC San Diego) G. Pancheri (Frascati) S. Soldner-Rembold (CERN) V. I. Telnov (Novosibirsk) A. Wagner (DESY) P. M. Zerwas (DESY)
M.N. Kienzle-Focacci (Geneva) C. Amsler (Zurich) R. Eichler (PSI) Z. Kunszt (ETHZ) M. Pohl (Geneva) L. Tauscher (Basel) Local Organising Committee M.N. Kienzle-Focacci (Chairwoman, Geneva) P. Achard (Geneva) P. Deglon (Geneva) M. Wadhwa (Basel) P. Argentin (Secretary, Geneva) C. Lafranchi (CSF)
VII
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CONTENTS
Preface
v
Committee 1
vii
P h o t o n Structure
Measurement of the Hadronic Photon Structure Function F% at LEP2 R. J. Taylor Study of the Hadronic Photon Structure Function with the DELPHI Detector at LEP I. Tyapkin Measurement of the Charm Structure Function of the Photon at LEP A. Csilling New Analysis of LO Parton Distributions of the Real Photon — Preliminary Results P. Jankowski
3
7 14
19
The Structure of Real Photons at HERA A. Valkdrovd
23
Structure of Virtual Photons at HERA K. Sedldk
29
Charm and the Virtual Photon at HERA B. J. West
35
Summary of the Structure Function Session at Photon 2001 R. Nisius
39
2
Jets and Inclusive Hadron Production
Inclusive 7r° and K^ Production in Two-Photon Collisions at LEP P. Achard
49
Fragmentation in Diffractive Deep Inelastic Scattering at HERA D. Traynor
53
ix
X
Photoproduction of Neutral Strange Hadrons at ZEUS S. Boogert
58
Di-Jet Production in Photon-Photon Collisions at y/s^ from 189 to 209 GeV T. Wengler
62
A Measurement of the Dijet Cross Section in Two-Photon Collisions at LEP2 J. Masik
67
Measurement of Isolated Prompt Photon Production in Photon-Photon Collisions at <JsZ = 183 - 209 GeV with the OPAL Detector at LEP J. Lillich
71
Substructure of Jets at HERA M. Vazquez
75
Measurement of Z/7* Production in Compton Scattering of Quasi-Real Photons I. Fleck
80
Combining Next-to-Leading Order QCD Calculations and Parton Showers B. Potter and T. Schorner
84
Interference Terms and Contribution of 7^ in the Electron-Proton Collision U. Jezuita-Dgbrowska
88
QCD Tests with Jets at HERA T. Schorner
3
92
Charm and Beauty Production
Heavy Quark Production in 77 Collisions J. Chyla
103
Inclusive D*-Meson Production in Two-Photon Collisions at LEP A. A. Sokolov
109
Inclusive J/^f Production in Two-Photon Collisions at LEP A. A. Sokolov
113
XI
Heavy Flavour Production in Two-Photon Interactions V. P. Andreev
117
Heavy Quark Production at HERA in kr Factorization Supplemented with CCFM Evolution H. Jung
122
Charm Production in Deep Inelastic Scattering and Diffraction at HERA W. Erdmann
128
Bottom Production at HERA M. Turcato
134
Heavy-Flavoured Jets at HERA S. Padhi
140
4
Total Cross-sections and Diffraction
Study of e + e - Annihilation into Hadrons at VEPP-2M V. F. Kazanine et al.
147
Total Cross Section in Two-Photon Collisions at LEP M. N. Kienzle-Focacci
152
Total Cross-Section Measurement in 77 Collisions at Very Low Q2 at LEP2 A. Nygren et al. Impact Factors of Virtual Photons at NLO V. S. Fadin
158
162
Measurement of the Hadronic Cross-Section of Double Tagged 77 Events at ALEPH G. Prange
166
Double-Tag Events in Two-Photon Collisions at L3 Experiment
170
C. H. Lin Measurement of the Hadronic Cross-Section for the Scattering of Two Virtual Photons at OPAL M. Przybycierl
174
XII
High-Energy Asymptotics of Photon-Photon Collisions in QCD V. T. Kim et al.
178
Investigation of Pomeron- and Odderon-Induced Photoproduction of Mesons Decaying to Pure Multiphoton Final State at HERA T. Berndt
182
Diffractive p° Production at HERMES K. Lipka
186
Diffraction at High and Low Q2 at HERA P. D. Thompson
191
Leading Baryon Production at HERA K. Borras
197
Coherent Photon-Pomeron and Photon-Photon Interactions in Ultra-Peripheral Collisions at RHIC F. Meissner
203
Total Cross-Sections R. M. Godbole, A. Grau and G. Pancheri 5
207
Resonances and Exclusive Channels
Cross Section Measurement of fi Pair Production at -y/s = 161-208 GeV in 77 Collisions at LEP with L3 213 G. Debreczeni Cross Section Measurement of r Pairs in Two-Photon Collisions with the L3 Detector at LEP2 D. Haas and M. Wadhwa
217
Measurement of the Cross-Section for the 77 —>• pp Process at y/s = 183-189 GeV at LEP T. Barillari
223
Proton-Antiproton Pair Production in Two-Photon Collisions at BELLE A. Chen A and E° Production in Two-Photon Collisions at LEP B. Echenard
'
227 231
XIII
The Analysis of 7r+7r~7r° Production in Two-Photon Production M. Levtchenko Resonance Formation in 7r+7r~7r° Final State in Two-Photon Collisions at BELLE S. R. Hou
235
241
The Transition of Virtual Photons into Pseudoscalar Mesons P. Kroll
245
"Glueballs": Results and Perspectives from the Lattice G. S. Bali
249
Meson Resonances in Proton-Antiproton Annihilation C. Amsler
263
Radiative Decays of Basic Scalar, Vector and Tensor Mesons and the Determination of the P-Wave qq Multiplet A. V. Anisovich
259
Measurements of KK Production and \ci Production in Two-Photon Collisions S. Uehara
263
Detection of -¥ ao(980)7, / 0 (980)7 and —>• T77, TT Monte Carlo as an uncertainty with which we are able to describe the corresponding data samples. Certainly, there are some other sources of systematics in the measurements, but their influence is estimated as much lower. The correlation
12
fcr 0.5 3
• DELPHI LEP2 o DELPHI LEP1 * OPAL o L3 A ALEPH
0Ml<X 0.1 the measurement is well described by Monte Carlo models and perturbative QCD calculations but for x < 0.1 the predictions are lower than the data both in the directly measured region and after the extrapolation.
1
Introduction
The charm component of the photon structure function, F^,., has been measured by OPAL at LEP2 by applying the well established method of exclusive D* reconstruction to deep-inelastic electron-photon scattering events. The determination of F^c exploits the fact that the differential cross-section as function of Q2 and Bjorken x is proportional to F2C(x,Q2). 1 Due to the large scale established by their masses, the contribution to F^ from charm quarks can be calculated in perturbative QCD, and predictions have been evaluated 2 at next-to-leading order (NLO) accuracy. F^c receives contributions from the point-like and hadron-like components of the photon structure, with the hadron-like component dominating at very low values of x and the point-like part accounting for most of F]c for x > 0.1. The preliminary results presented here 3 extend the earlier measurement 4 of F^c using basically the same analysis strategy. It is based on 654.1 p b _ 1 of data for e + e~ centre-of-mass energies from 183 to 209 GeV, recorded by the OPAL experiment in the years 1997-2000. 2
Data selection
The most important cuts used in the selection of deep-inelastic electronphoton scattering events containing a D* are summarised below. "On leave of absence from KFKI Research Institute for Particle and Nuclear Physics, H-1525 Budapest, P.O.Box 49, Hungary
14
15 •
I
i
'
'
'
i
•
•
'
i
'
-+- OPAL preliminary — fit: 60.3 +10.3 signal events HH wrong-charge combination
40 35 30 25 20 15 10 5 °
0.14
0.15
0.16
0.17
0.18
0.19 0.2 Am [GeV]
Figure 1. Distribution of the difference between the D* and D° candidate masses. The data are shown as points with statistical errors, while the histogram represents the combinatorial background estimated using events with wrong-charge combinations for the decay products of the D* mesons. The curve is the result of the fit to the data.
1. An electron candidate must be present with an energy _Etag > 0.5.Eb and a polar angle in the ranges 33 < 6>tag < 55 mrad (SW) or 60 < 0tag < 120 mrad (FD), corresponding to 5 < Q2 < 100 GeV 2 . 2. Double-tag events are eliminated by requiring that the sum of all energies in the SW and FD detectors opposite to the tag are below 0.25£t> 3. An exclusively reconstructed D* candidate must be present with a transverse momentum p® > 1(3) GeV for SW(FD)-tagged events and a pseudorapidity \rp | < 1.5. The D* meson must decay into D°7r with the D° decaying into the charged particles K7r or 'KTCK-K. Figure 1 shows the difference between the D* and D° candidate masses for both decay channels combined. A clear peak is observed around 0.145 GeV, the mass difference between the D* and the D° mesons. An unbinned maximum likelihood fit to this distribution gives 60.3 ± 10.3 signal events above the combinatorial background from deep-inelastic electron-photon scattering events e + e~ —> e + e~qq with q—uds. The expected background from all other processes that potentially contain D* mesons in the final state is found to be negligible using Monte Carlo simulations. Figure 2 shows the distributions of two global event quantities, Q2 and Wyis, and two variables related to the kinematics of the D* candidates, p® and
16 i i i l i i i I i i i l i i i l
|35 '30 25^ 20 IS 10
a)
i - 1 - OPALpreBm.• - - HERWIG I I HW scaled UZ& H W P L Vermaseren
0.
Figure 2. Data distributions compared to the HERWIG and Vermaseren predictions. For HERWIG several predictions are shown: the full prediction, the point-like component alone (HW PL), and a superposition of the HERWIG point-like prediction together with a scaled hadron-like prediction, denoted by HW scaled.
\rjD* |. The data are compared to the absolute predictions of the HERWIG6.1 5 and Vermaseren 6 leading order Monte Carlo programs. To get a better description of the data, the hadron-like component of the HERWIG prediction has been fitted to the xJp = 2pJp /WVis distribution shown in Figure 3 while keeping the point-like part fixed, resulting in a scale factor of 6.6 ± 2.7. There are several possible sources for this difference. The NLO prediction itself has a significant uncertainty due to variations of the charm quark mass and the renormalisation and factorisation scales, the gluon distribution of the photon has large experimental errors, and uncertainties in the shape and the modelling of the p® distribution can change the efficiency for the selected events. This scaled HERWIG prediction, also shown in Figure 2, is used to estimate the signal selection efficiency. The difference between the results obtained with the scaled and the original HERWIG models is taken into account as a systematic uncertainty.
17 n T T i ] i i i i | i i i i •[ r i i i | i i i i | i i i i | i i i i | i i i i I'T-i i i | i i .
0
0.25
Figure 3. The measured xjj! caption of Figure 2.
3
0.5
0.75
1
1.25
1.5
1.75
2
2.25
distribution compared to the predictions described in the
Results
Table 1 summarises the cross-section of D* production in deep-inelastic electron-photon scattering measured in the kinematic region defined by the event selection. The total cross-section for cc production in deep-inelastic electron-photon scattering, shown in Figure 4a), is the result of an extrapolation to the whole kinematic region using the HERWIG scaled model. The value of the charm structure function of the photon, - F ^ x , (Q2))/aem, averaged over the corresponding bin in x, shown in Figure 4b), is obtained using the ratio F%c(x, (Q2))/aem/cr(e+e~ —* e + e _ c c X ) given by the NLO 2 calculation. All models and predictions shown in Figure 4 are in good agreement with the measurement for a; > 0.1, where the purely perturbative point-like process is dominant and both the experimental and the theoretical uncertainties are moderate. On the other hand, for x < 0.1 the measurement lies more than two stan-
Table 1. The cross-section <xD measured in the restricted region, compared to Monte Carlo predictions. The numbers in parentheses refer to the point-like and hadron like components.
OPAL HERWIG HW scaled Vermaseren
0.0014 < x < 0.1 4.7 ± 1 . 3 ± 0 . 9 1.02 (0.65 + 0.37) 3.10 (0.65 + 2.45) 0.84
0.1 < x < 0.87 3.0 ± 0.9 ± 0.4 2.05 (2.02 + 0.03) 2.23 (2.02 + 0.21) 2.81
18
;
OPAL preliminary a) NLO (Laenen el al.) LO HERWIG Vermaseren
IOO
50 r
• i
0
0.1
0.2
0.3
0.4
0.5
1 O,
i
hh (BetheHeitler) cross-section. Those contributions appear provided that the centremass energy of the 7*7 system, W, fulfills a condition W > 2m/,. Apart from the update of the GRV'92 results (with the differences described above) another fit was done including extra charm contribution to the F£. Namely separate J / $ meson evolution has been added on top of the 3 flavour DGLAP equations. At scale Q2j/^, fitted as other parameters, J / ^ evolution starts with input densities: xvj/\j,(x, Q2j/^) = Nj^xaj^"(l — X)PJ/* . There is no input gluon and no extra point-like charm density and the Bethe-Heitler charm contribution is held. We formally add an extra Kj/y factor to account for heavier charmed mesons. Fits of the parameters of both models to the F2 experimental points were performed with use of the MINUIT procedure. We got three results. Two in case of the simple GRV'92 update - 'update 2' with Ql = 2 GeV2 ^ Ql, 'update 0.25' with Ql = Ql = 0.25 GeV 2 , and one with extra J / * contribution - 'update + J / * ' . In case of the GRV'92 parametrization x2 (X2 per data point) equals 250 (3.73) when one calculates it for the 67 data points used in '92. At present for 220 experimental points we get: GRV'92 476 (2.16), 'update 2' - 298 (1.35), 'update 0.25' - 296 (1.34) and 'update + J / * ' - 277 (1.23). Table 1 gives fitted parameters for each model. As the only independent input distributions in the updates are v„ and Vj/y we fitted K • Nv and KjxfNjiy. rc's and N's could be separated thanks to the constraint on the number of valence quarks in each meson: JQ v7r(x,Ql) = / 0 vj^(x,Q2j,^,) — 1. Through the energy-momentum sum rule constraint we could check the consistency of our results. First model gave the following integral values:
21 /„ x[2v„(x, Ql) + G*(x, Q\)]dx = 1.07 and 1.08 in Q 2 = 2GeV2 and in Q 2 = 0.25GeV2 cases respectively which is in good agreement with 1. In case of the 'update + J / * ' the numbers are: J*x[2v*(x,Ql) + Gv(x,Ql)]dx = 0.933 and / 0 x[2vj/xif(x,Q2j,^)]dx = 0.357. Unfortunately because of the second number the fit does not seem to be consistent. Still here we should keep in mind that the model applied was only a toy model without the input gluon distribution in the J / $ meson and as is known gluons carry about half of the momentum of hadrons. Finally in figure 1 the fitted i 7 ^(a;,Q 2 )/a curves for various Q2 values are presented. For comparison the GRV'92 results and experimental points, divided into 'old' and 'new' groups, are also plotted. Points of the 'new' group in contrary to the 'old' ones has not been used in any parametrization before. We notice that both approaches used in our analysis give very similar results at high Q2s. They differ in its small values where 'update + J / $ ' increases at high x values. Comparing to the GRV'92 results new fits show much lower values of the F^{x, Q2) at high x. Surprisingly on the partonic level new gluon xG^{x, Q2) distributions have much higher values at the whole x and Q2 range apart from the very high Q2 area. Similarly updated up quark densities are higher or equal to the GRV'92 ones apart from the region of x > 0.9.
2.00 2.71 2.72 2.422
Nv 0.681 0.334 0.291 0.316
a 0.480 0.288 0.290 0.291
Q j/*
« j / *
Nj/y
<Xj/V
12.04
2.267
0.876
0.296
K
GRV '92 update 2 update 0.25 update + J / * update + J / *
/? 0.850 0.485 0.0056 0.238
*» 1.460 2.824 2.823 2.920 Pj/V 2.000
Table 1.
In conclusion we recall that the results presented here are preliminary and our work is still in progress. Our first results show a significant improvement in the F% fits to the data with new points added. We notice a high sensitivity of the fit to the way in which charm quark is included in the evolution. In order to further improve fits we should add gluonic input density in the J / $ structure as well as sea input in both light and heavy mesons. We can also replace the K parameter with the real summation over various meson states. At present our work focuses on implementing a new composite model for the heavy quark calculations in QCD recently presented in 5 .
22 1
0.8
I ' ' ' I ' ' ' I ' ' ' I
GRV'92 update 2 update + J/^l exp new ; exp old i—*i ' ' ' i
0.6 0.4 0.2
Q2 = 14.70 GeV2
0 0.8
. . .
i
i . . .
i . .
I ' ' ' I
0.6 0.4 2
2
Q = 0.38 GeV I
• i i I
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Q2 = 23.00 GeV* I
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Figure 1. F 2 7 (x,Q 2 )/a
References 1. F.Cornet, P.Jankowski, M.Krawczyk and A.Lorca, paper in preparation 2. M. Gluck, E. Reya and A. Vogt, Phys. Rev. D 46, 1973 (1992). 3. M. Gluck, E. Reya and I. Schienbein, Phys. Rev. D 60, 054019 (1999), Erratum-ibid.D 62, 019902 (2000) 4. M. Gluck, E. Reya and A. Vogt, Z. Phys. C 53, 651 (1992) 5. S. Kretzer, C. Shmidt and W. Tung, To appear in the proceedings of New Trends in HERA Physics 2001, Ringberg Castle, Tegernsee, Germany, 1722 Jun 2001. hep-ph/0110247
T H E S T R U C T U R E OP R E A L P H O T O N S AT H E R A
A L I C E V A L K A R O V A * , for the Hi and ZEUS Institute
collaborations
of Particle and Nuclear Physics, Faculty of Mathematics Charles University, V Holesovickdch 2, Praha 8, Czech E-mail: avalkar@mail. desy. de
and Physics Republic
of
Inclusive jet cross sections for the reaction e+p —> jet + X for Q 2 < 1 GeV 2 have been measured with the HI detector at HERA. Differential cross sections as a function of rjjet and Exjet a r e m good agreement with NLO QCD calculations using different sets of photon parton density functions as input. Dijet cross sections of jets with high ET were measured by both the ZEUS and HI experiments in photoproduction. Comparisons of ZEUS data to NLO QCD calculations show that the theory underestimates the data for low Xy , indicating possible inadequacies in the photon structure parametrisations. HI d a t a are in good agreement with the predictions of NLO QCD. The measurements were, however, made in different kinematic regions.
1
Introduction
In leading order (LO) QCD, two processes contribute to the photoproduction of jets at HERA: direct processes, in which the photon behaves as a pointlike particle and resolved processes, where the photon acts as an object with structure. The quark densities in the photon are not strongly constrained for x7 a values larger than 0.5 by e + e~ experiments 1 . The photoproduction of jets at HERA is directly sensitive to the gluon content of the photon and the data are also sensitive to the parton densities of the proton at xp values up to 0.6. Therefore one of the possible tools to investigate the structure of quasi-real photons, 7, is to measure the production of jets in -yp interactions at HERA. The production of high transverse momentum jets provides a hard scale which makes perturbative QCD calculations reliable and renders the results less sensitive to non-perturbative physics such as soft particle production and hadronisation. 2 Single inclusive jet production The measurements of differential jet cross sections as a function of the jet transverse energy, E3Tet, and pseudorapidity, rfet, were analysed by experiment Hi 2 . The jet search was performed in the laboratory frame by applying 'supported by centre for particle physics, project no. LN 00A006. x-y,(xp) are the fractions of 7(proton) momentum in hard subprocesses.
a
23
24 H1 preliminary
H1 preliminary 21<E'? 21 GeV and - 1 < r]jet < 2.5. The HERWIG 4 and PYTHIA 5 Monte Carlo generators have been used to correct the data for detector effects. The corrected differential e+p cross section da/dE^f for jet production in the kinematic region defined by Q2 < 1 GeV 2 and 95 < W < 285 GeV is shown in figure la). The data are compared with QCD calculations, for both LO and NLO 6 . Hadronisation corrections, estimated using the Monte Carlo generators, are ~ 5% and are roughly constant with Ei^1'. On the same figure the theoretical uncertainty originating from the scale dependence is also shown. Within errors, the NLO QCD calculations describe the magnitude and the shape of the energy spectrum very well. In figure lb) the differential cross section da/drf** is shown and compared with theory. The calculated cross sections using all three photon PDFs (GRVHO, GSG-HO and AFG-HO) describe the data quite satisfactorily.
25 ZEUS Preliminary 96-97
ZEUS Preliminary ^ 2000 1 1 Q. 1800 H4<E, " < 17 GeV m 1600 ^ - 1 4 0 0 .0.2 < y < 0.85 5
1200
"O 1000 800 600 400
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HLO QCD, AFO-HO
r
* r L r !
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25 < £ , " ' < 35 GeV
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250
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200
50 40
150
i r
30 100 50
i
20
...
10 . . i—.—rr. . i . 0.4 0.6
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Figure 2. a) Differential cross sections in x^ in intervals of the transverse energy of the jet with higher E3^*, E3^ . The energy scale uncertainty is shown as the band, b) Differential cross sections in cosO* for events with x^bs > 0.75, x^bs < 0.75 and both distributions, normalised to the content of the first three bins.
In order to compare the HI results with previous ZEUS measurements, the differential cross sections were analysed in the same kinematic range 7 , 8 . Within the errors, the measurements of the two experiments are in good agreement
3
Dijet differential cross sections
The analysis was presented by the ZEUS experiment in 9 . The jets were found using the kr cluster algorithm in the pseudorapidity region — 1 < rfet < 2 in the laboratory frame, with the transverse energy of the highest E? jet, E3^1 > 14 GeV and the second-highest, E3Tet2 > 11 GeV. The cross section is given in the kinematic region Q2 < 1 GeV2 and 0.2 < y < 0.85. The measured (and corrected for detector effects) differential cross section da/dx°bs b is shown in figure 2a) in four ranges of E3^ . The effect of hadronisation (not shown ''The fraction of the photon's momentum participating in the hard proces i * was defined
26
|
• H1 data • QCDNLO 3 NLO(1+8 hadr ) QCDLO
10
Q.
- • ... B
25 < £ , „ „ < 35 OeV
35 < E T „ „ < 80 QeV
0.1 < y < 0.5
0.1 < y < 0.5
H1 data, prelim. QCDNLO NLO(1+8Mr)
6 "O
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..? 1
111
•°10
: HI preliminary
10 30
40
50
60
70
~r,max
80
(GeV)
-
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Figure 3. a) Differential ep cross section for dijet production as a function of the ET of the highest ET jet, Er,max- The theoretical LO and NLO predictions use the CTEQ5M proton structure function and the GRV-HO photon structure function. NLO predictions are corrected to hadronisation (full line), and the grey band is the uncertainty of the theoretical prediction, b) Differential cross section as a function of rj of the two highest ET jets in two intervals of y and ET,max-
here) has been found to be ~ 10 - 15%. At high x°bs where the contribution from direct processes dominates, the data are reasonably well described by NLO QCD calculations. However, at lower values, x°bs < 0.75, the data are always above the NLO predictions. The angle between the dijet axis and the beam axis in the dijet CMS can be written as cosd* = tanh((r]jetl -r]jet2)/2). This variable is sensitive to the parton dynamics. For direct photon processes, where the propagator a is quark with spin 1/2, the angular dependence of the cross section is proportional to (1 - |cos0*|) _1 , for resolved processes where the gluon propagator with spin 1 dominates, to (1 - \cos0*\)~2. The measured cross section as a function of \cos6*\ is shown in figure 2b) for x°bs > 0.75 and x°bs < 0.75. In this figure the additional cuts on the invariant mass of the dijets Mj:j > 39 GeV and 0 < (r)jetl + rfet2)/2 < 1 were applied. As observed before, the data in the high x°bs region are well described by the NLO calculations and poorly in the low x°bs region. The shapes of the measured distributions are well described by the theory for both regions in x°bs (see the lowest plot of figure 2b)). Thus the parton dynamics of both
27 25<E TJ1U , X 25 GeV and ET,2 > 15 GeV. The pseudorapidity of jets is restricted to —0.5 < rjjet < 2.5. In figure 3a) the dijet cross section as a function of the ET of the highest transverse energy i?T,i = -Er.max is compared to NLO QCD calculations. The differential cross section da/drj is displayed for two different y regions and two different ET,max bins in figure 3b). An overall agreement between data and NLO QCD is observed, taking into account the uncertainties of the calculations and data points. Figure 4a) displays the relative difference of the experimental and theoretical dijet cross sections da/dx^ as a function of x 7 for two regions of ET,max- The data are compared to NLO calculations with three parametrisations of the photon structure. The predictions vary only little with photon PDF used. The lower part of the figure clearly demonstrates that the uncertainty of
28
the calorimetric energy (hatched band) together with the NLO uncertainties (shaded band) are much more important in this analysis than the difference induced by using different photon PDFs. The dijet cross section da/dcosO* is plotted in figure 4b) for x1 > 0.8 and x 7 < 0.8 (upper two plots). Although the cut on the invariant mass MJJ changes the shape of the distributions dramatically (see lower two plots in figure 4b)), the QCD calculations reproduce this behaviour nicely. 4
Conclusions
The measurement of the hadronic structure of the photon is an active field of research. The results of two experiments 2 , 8 , 9 studying the single inclusive jet production are in good agreement 2 . In dijet production, however, the conclusions of the two experiments differ. ZEUS results 9 may indicate a possible inadequacy of the two photon structure functions used. On the contrary, the HI data 10 agree well with NLO predictions using all available photon structure functions. In the two experiments, however, rather different kinematic regions were explored. In the future, cross sections in an identical phase space should be studied. References 1. R.Nisius, Phys. Rep. 332,(4-6) (2000) 165. 2. HI Collab., Measurement of single inclusive high E? jet cross sections in photoproduction at HERA, Abstract 301,Submitted to EPS 2001, July 12,2001, Budapest. 3. S.Catani et al., Nucl.Phys. B 406 (1993) 187. 4. G.Marchesini et al., Comput. Phys. Commun. 67 (1992) 465. 5. T.Sjostrand, CERN-TH-6488(1992), Comput. Phys. Commun. 82 (1994) 74. 6. S.Frixione, G.Ridolfi, Nucl.Phys. B507 (1997) 315. 7. ZEUS Collab., Inclusive jet photoproduction at HERA, Submitted to 29th ICHEP, Vancouver, Canada, 23-29 July 1998. 8. ZEUS Collab., J.Breitweg et al., Eur. Phys. J. C4 (1998) 591. 9. ZEUS Collab., The structure of the photon and the dynamics of resolved photon processes in dijet photoproduction at HERA, Submitted to the 30th ICHEP, July 27 - August 2, 2000, Osaka, Japan. 10. HI Collab., Measurement of Dijet Cross Sections in Photoproduction, Abstract 798, Submitted to EPS 2001, July 12, 2001, Budapest.
S T R U C T U R E OF V I R T U A L P H O T O N S AT H E R A K. SEDLAK * Institute
of Physics,
AS CR, Na Slovance 2, Praha 8, 182 21, Czech E-mail: ksedlakQfzu.cz O n behalf of t h e H I a n d Z E U S Collaborations
Republic
Triple differential dijet cross-sections in e^p interactions measured with the HI and ZEUS detectors at HERA are presented. The d a t a are compared to Monte Carlo simulations which differ in their assumptions about photon structure and parton evolution. Effects of the resolved processes of longitudinally polarized virtual photons at HERA are investigated for the first time.
1
Dijet Production at H E R A
The production of dijet events at HERA is dominated by processes, in which a virtual photon, radiated from the electron, interacts with a parton in the proton. In the region of photon virtuality Q2 ~^> A Q C D , hard collisions of the photons do not necessitate the introduction of the concept of the resolved photon (as for the real photon) and the process can in principle be described by the direct photon contribution alone, in which the photon interacts as a whole with partons from the proton. The analyses presented here explore the region A Q C £ ) -C Q2 5GeV Et > 6 GeV -2.5 < rf>et l 7.5 GeV £ft2>6.5GeV - 3 < rf>et L'Z < 0
Table 1. Selection criteria of the dijet samples.
electron-proton centre-of-mass energy, Ef ' and rfet1'2 are the transverse energy and pseudorapidity of the jet with the highest or second highest Et, and E~t is defined as (E{et x + Ef t 2 ) / 2 . The measured data are corrected for detector effects using a bin-to-bin method (ZEUS) or Bayesian unfolding (HI). The largest source of systematic errors arises from the main calorimeter calibration uncertainty and, in the case of HI, also from a model dependence of the detector correction. The ZEUS measurement was presented in more detail at the EPS 2001 5 .
31
3
Results and Discussion
The corrected triple-differential dijet cross-section measured by ZEUS as a function of Q2 , Et and x1 is shown in Fig. 1 (a). A prediction of HERWIG with the SaSlD parameterization of the 7^ PDF, as well as the direct contribution of HERWIG is compared to the data. Since the overall normalization of the LO Monte Carlo simulation is to some extent uncertain, the HERWIG prediction has been normalized to the highest xy bin (x 7 > 0.75) in the data. The normalization is done separately for each (Q2,Et) bin. In the region where Q2 > Et, the data are well described by the direct HERWIG component only. Resolved interactions are needed if Q2 < Et. However, even with the 7^ resolved processes included, HERWIG tends to underestimate the data in the lowest Q2 region for a:7 < 0.75. This fact is also demonstrated in Fig. 1(b) by the ratio of a(xy < 0.75)/cr(x 7 > 0.75). The slope of this distribution can be interpreted as a suppression of the virtual photon structure with increasing photon virtuality. The corrected triple-differential dijet cross-section measured at HI as a function of Q2, Et and x 7 i s shown in Fig. 2(a). The HI measurement is performed in a different phase space (see Table 1) and Monte Carlo predictions are not normalized to the data. A comparison of the Hi measurement with HERWIG leads to similar conclusions as drawn above for ZEUS. In addition, we can see that for the highest Q2 range (25 < Q 2 < 80 GeV 2 ) and x 7 < 0.75, the HERWIG direct 2 contribution almost describes the data in the lowest Et bin, but is too low 2 in the highest Et bin. This indicates an importance of the resolved processes even at high Q2 , once the hard scale, Et , is high enough. Standard HERWIG with direct and 7^ resolved contributions underestimates the data. The description is improved by adding 7^ resolved photon interactions, which is done using a slightly modified HERWIG with the correct longitudinal photon flux and a recent 7^ PDF parameterization 2 . As demonstrated in Fig. 2(a), the 7^ resolved contribution is significant, and brings HERWIG closer to the measurement. On the other hand, a simple enhancement of the PDF of the 7^ in the resolved contribution could lead to a similar prediction as the introduction of 7£. To eliminate this ambiguity, the dijet cross-section has also been studied as a function of Q2 , a;7 and y, which is shown in Fig. 2(b). HERWIG is below the data, even if the resolved 7£ is added. This may be due to the uncertainty of the overall normalization of the LO Monte Carlo prediction. In the region
32 where x^ < 0.75, the slope of the HERWIG prediction depends significantly on whether 7^ processes are included or not. The 7^ contributes significantly at low y, while it becomes very small compared to 7^ at high y. Unlike a pure enhancement of 7^ resolved processes by a constant factor, the addition of 7£ brings the y dependence of HERWIG much closer to the measurement. As motivated in Section 1, the measured cross-sections in Fig. 2 are also compared to a prediction of the CASCADE MC program based on the CCFM evolution approach. This theoretical concept does not involve any information about the virtual photon structure and involves many fewer free parameters for tuning than the usual DGLAP-like MC programs. Nevertheless, CASCADE describes the data well, except for the Q2 dependence. The Q2 behavior, however, is related to the parameterization of the unintegrated PDFs used in the program, which are not yet constrained unambiguously.
4
Conclusions
The dijet cross-sections measured as a function of Q2 , Et , x1 and Q2 , x 7 , y at HI and ZEUS have been presented. In the DGLAP evolution scheme, the importance of the 7^ resolved photon interactions is clearly demonstrated in the region where Et > Q2. Additional 7£ resolved photon contributions further improve the agreement of the HERWIG 5.9 prediction with the measurement. Exploring the CCFM approach, the MC program CASCADE 1.0 gives a qualitative description of the measured differential cross-sections; however, the Q2 dependence is not reproduced. On the other hand, the x 7 dependence in CASCADE is comparable to the sum of the direct and resolved contributions in DGLAP-like MC programs. References 1. 2. 3. 4.
J. Chyla and M. Tasevsky, Eur. Phys. J. C18 (2001), 723. J. Chyla, Phys. Lett. B488 (2000), 289. H. Jung and G.P. Salam, Eur. Phys. J. C19 (2001), 351-360. H. Jung, "Heavy Quark production at HERA in kt factorization supplemented with CCFM evolution", These proceedings. 5. ZEUS Collab., EPS 2001 conference: "The Q2 and T!?t dependence of dijet cross sections in 7*p interactions at HERA", paper no. 636.
33 O * ( 0.75) from Fig. 1(a).
34 d3atr/(dQ2 2
80>Q >25GeV
2
2
2
25 > Q > 10 GeV
dE,2dx,)
2
10 > Q > 4.4 GeV2 N-
ts»
(pbGeV*)
4.4>Q 2 >2GeV 2
(*i
A
ml A
S o » S A
Jfll
jnl
a)
d3<s„/(d&d^dy) 80>Q 2 >25GeV 2 25>Q 2 >10GeV 2 10 > Q2 > 4.4 GeV2
"•*
(pbGeV3)
4.4>Q 2 >2GeV 2
—
0.8)
0.2 -1
0
(b):
1
1
1—1..1. 1 1,1 ,
10
I
I
I
I
I -I.J.I 1,.
10
J
-
l - . i . I,. I. I
L_J
.
10.
Q 2 [GeV2] Figure 3. The evolution of F£ with Q2 at medium values of a; compared to several parametrisations.
statistical precision the data start to challenge the existing parametrisations of F2 . Given this, several theoretical as well as experimental issues have to be addressed in more detail. Examples are the suppression of F% with the virtuality squared of the target photon P2 and radiative corrections to the deep-inelastic scattering process. An update has been presented 5 of the OPAL measurement of the charm component F^ using D* mesons to identify charm quarks. The analysis is based on improved Monte Carlo models and higher statistics compared to the published result 6 . This led to an improved precision of the measurement. In a similar way to the structure function for light quarks, F^ receives contributions from the point-like and the hadron-like components of the photon structure, as explained e.g. in 1 . These two contributions are predicted 7 to have different dependences on x, with the hadron-like component dominating at very low values of x and the point-like part accounting for most of K7C
42
at x > 0.1. For x > 0.1 the OPAL measurement is described by perturbative QCD at next-to-leading order. For x < 0.1 the measurement is poorly described by the NLO prediction using the point-like component alone, and therefore the measurement suggests a non-zero hadron-like component of F ^ c . Increased statistics and a better understanding of the dynamics for x < 0.1 are needed to get a more precise measurement in this region. To increase the statistics it would be advantageous to combine the data from the four LEP experiments. 2.2
Results from proton-photon scattering
New results from HI and ZEUS have been presented concerning the structure of quasi-real photons 8 , and also of virtual photons without 9 and with 10 identified charm quarks. There is good agreement between the ZEUS and HI results on the inclusive production of jets as can be seen from Figure 4. The observed inclusive H1 preliminary
Figure 4. The inclusive jet cross-section as a function of £r,jet compared to NLO predictions.
jet cross-sections are well described by existing parton distribution functions of the photon that have been obtained from measurements of F^In contrast, there is a longstanding difference between HI and ZEUS results for di-jet final states 1,11 . The new preliminary Hi result 8 , is consistent with the predictions based on existing parametrisations of i 7 ^ and at present
43
the data are not precise enough to distinguish between different parametrisations. This has to be confronted with the earlier result from ZEUS 12 ' 8 which suggested that the parton distribution functions of the photon, obtained from fits to measurements of F^ made at e + e~ colliders, are too low for medium values of Bjorken x and at factorisation scales of several hundred GeV 2 . There are several differences between the ZEUS and Hi analyses such as the choice made for the value of as, the parton distributions used for the photon, and most notably the corrections applied to the data. The HI data are corrected for detector as well as hadronisation effects and are shown at the partonic level. In contrast, the ZEUS results are corrected only for detector effects and phase space regions are selected, where the hadronisation corrections, as implemented in Monte Carlo models, are found to be small. It remains to be seen how much of the apparent differences between the results can be explained by the different analysis methods. Important information now also comes from LEP, where the parametrisations of J ^ are found to be consistent with the measurements for factorisation scales up to 750 GeV 2 , leaving less room for changes to the parton distribution functions of the photon. It is certainly desirable to complement the measurements of i 7 ^ with the jet measurements from HERA, which extend to even larger factorisation scales, when fits for the parton distribution functions of the photon are performed. However, first it has to be seen if a consistent picture of the various HERA results can be established. The measurement of di-jet production has been extended to the investigation of the structure of virtual photons. In the recent ZEUS measurement 9 the suppression of the photon structure with the photon virtuality has been measured based on the ratio of the cross-sections for low and high values of x7. The LO predictions fail to describe this ratio when using only transverse virtual photons together with the SaSID 1 3 parametrisations of the photon structure. A similar difference has been found by HI. In addition, it has been demonstrated by HI that the inclusion of longitudinal virtual photons helps to improve on the description of the observed triple differential cross-section shown in Figure 5. But the y dependence of the cross-section is still not adequately described 9 for y < 0.3. More experimental as well as theoretical investigations are needed to better understand these findings. The structure of virtual photons has also been investigated for the charm component alone, using D* mesons to identify charm quarks. The mass of the charm quark enters as yet another scale in the process, in addition to E\ , et and Q2. By again using the ratio of the cross-sections for low and high values of x^ it is found that the suppression with Q2 is much weaker in the presence of charm than for the sample containing all flavours10. The result is
44 • HI PreUmiuarj
%$, Htnefg&ir i^i HerwlgntT
36 1.5 GeV, the differential cross sections are better represented by a power law function Ap^B. The value of the power B is compatible with 4 for both 7T° and Kg. In Figure 1, the data are compared to analytical NLO QCD predictions 13 . The agreement with the data is satisfactory in the Kg case, but it is poor for the 7T° case in the high-p t range. Similar disagreement was already found with PETRA single-tagged data 2 . The da/d\r)\ differential cross sections, are also compared to QCD calculations as shown in Figure 2a. The shape of the data,
52 and in particular the measurement at (\r)\) = 3.85, is well reproduced. Fairly good agreement is found with previous experiments as shown in Figure 2b. OPAL charged hadrons production data 4 are scaled to the 7T° kinematical range taking into account the different luminosity function, the 7j range and the fragmentation function. Omega Photon jp —* 7r° + X data 1 4 , with a mean beam energy of 80 GeV and a Feynmann variable 0.7 < XL < 0.8, are normalised to the first bin. The later exhibit the typical exponential behaviour discussed above. Acknowledgements We would like to thank B. A. Kniehl, L. Gordon and M. Fontannaz for providing us with their NLO QCD calculations and R. Engel and T. Sjostrand for useful discussions. References 1. L. E. Gordon, Phys. Rev.D 50 (1994) 6753. 2. J. Binnewies, B. A. Kniehl and G. Kramer, Phys. Rev.D 53 (1996) 6110. 3. L3 Coll., B. Adeva et al., Nucl. Instr. Meth. A 289 (1990) 35; L3 Coll., M. Acciarri et al., Nucl. Instr. Meth. A 351 (1994) 300. 4. OPAL Coll., G. Abbiendi et a l , Eur. Phys. J. C 6 (1999) 253. 5. PHOJET version 1.05c is used; R. Engel and J. Ranft, Phys. Rev.D 54 (1996) 4246. 6. PYTHIA version 5.722 and JETSET version 7.409 are used; T. Sjostrand, Comp. Phys. Comm. 82 (1994) 74. 7. L3 Coll., M. Acciarri et al., preprint hep-ex/0102025 (2001), to be published in Phys. Lett. 8. KK2f version 4.12 is used; S. Jadach, B. F. L. Ward Z. Was, Comp. Phys. Comm. 130 (2000) 260. 9. S. Jadach, B. F. L. Ward and Z. Was, Comp. Phys. Comm. 79 (1994) 503. 10. M. Skrzypek, S. Jadach, W. Placzek, and Z. Was, Comp. Phys. Comm. 94 (1996) 216. 11. F. A. Berends, P. H. Daverfeldt and R. Kleiss, Nucl. Phys.B 253 (1985) 441. 12. M. L. Perl, High Energy Hadron Physics (ed. John Wiley, New-York, 1974). 13. B. A. Kniehl, private communication. 14. Omega Photon Coll. R. J. Apsimon et al, Z. Phys. C 52 (1991) 397.
F R A G M E N T A T I O N I N D I F F R A C T I V E D E E P INELASTIC SCATTERING AT H E R A D. TRAYNOR Department of Physics, Queen Mary, University of London E-mail:
[email protected] Fragmentation measurements are presented for diffractive and non-diffractive deep inelastic ep scattering data in the Breit frame of reference. The average charged multiplicity in the current hemisphere, < n >, is shown to compare well with DIS at low /? and with e+e~ at high /3. The evolution of the peak and width of the current hemisphere fragmentation functions for charged particles is studied as a function of photon virtuality, Q, and is found to agree with results obtained in non-diffractive deep inelastic scattering.
1
Introduction
Previous studies 1 ' 2,3 ' 4 of Deep Inelastic ep Scattering (DIS) in the Breit frame of reference5 have established the universality of hadronic fragmentation properties and their energy dependence for quarks ejected from a proton and for quarks produced from the vacuum in e+e"annihilation experiments. This paper summarises results 6 that further tests concepts of this universality by examining the fragmentation properties of quarks thrown out of the pomeron in diffractive DIS (DIFF) scattering when probed with the same highly virtual boson as used in non-diffractive DIS (DIS) scattering. A particularly suitable frame of reference in which to study quark fragmentation in ep scattering is the Breit Frame. In this frame and within the naive quark-parton model (QPM) the purely space-like virtual photon has longitudinal momentum — Q and collides elastically and head-on with a quark of longitudinal momentum Q/2. The struck quark is scattered with an equal but opposite momentum while the proton remnant fragments into the opposite hemisphere. Particles emerging from the interaction are assigned to the current region (and associated with the struck quark) if they have negative longitudinal momenta. The energy scale for the current region, set by the virtual photon, is given by Q/2, and is independent of the nature (diffractive or non-diffractive) of the event. 2
F r a g m e n t a t i o n Functions
The ratio of the momentum of a given charged hadron, pf, to the energy scale (Q/2) of the current hemisphere of the Breit frame is xp = pf/(Q/2).
53
54
It has been shown : to be directly comparable to xp = ph/(E*/2) for one hemisphere of an e + e~ experiment where s/^ee — E* — Q. Using £ = In f ^- J, the fragmentation function may be defined as D±
®
=
(jr)xdn£*ckM
(!)
The Modified Leading Log Approximation (MLLA) 7 coupled together with Local Parton Hadron Duality (LPHD) predicts that in the region of the peak of the hadronic £ distribution, the shape is approximately Gaussian. The MLLA also gives a prediction for the energy behaviour of the peak position and width of this Gaussian (the first and second moments of the fragmentation function respectively) in the so-called limiting spectrum approximation; Zpeak=0.5U
+ c2VU + O(l)
Udth =
/C/3/2
)]^~-
(2)
(3)
Here U = In (Q/Aeff), where A e // is an effective scale parameter, ci and C2 are constants dependent on the number of excited flavours and colours in QCD, and 0(1) is a slowly varying function of energy containing all QCD diagrams beyond leading order. This term is assumed to be constant in this analysis. Figure 1 summarises the energy evolution of the fragmentation function. The solid (dashed) line is the simultaneous fit to the peak position and width of the MLLA parameterisation for DIS (DIFF) events. These give A e // = 0.21 ± 0.04 (0.19 ± 0.03) and 0(1) = -0.42 ± 0.12 (-0.49 ± 0.12). Both DIS and DIFF distributions and parameters are compatible with each other, and with previous DIS and e + e~ experiments thus lending further support to the concept of quark fragmentation universality. 3
Average Charged Multiplicity
The area under the fragmentation function is the averaged charged multiplicity, < n >, also known as the zeroth moment of the fragmentation function. Figure 2 compares the average charged multiplicity in the current region between DIS and DIFF data and a comparison is made with MEAR 8 MonteCarlo for DIS events and with RAPGAP 9 for DIFF events using the resolved
55 HI PRELIMINARY X2.4 2.2 2 1.8 1.6 1.4 1.2 1
5
6
7
8
Q^GeV)
4
5
6
7
8
Q9GeVj
Jl.l 1 0.9 0.8 0.7 0.6 0.5
Figure 1. The energy evolution of the (a) peak position and (b) width of the fragmentation function for both DIS and DIFF selections. The solid (dashed) line is the simultaneous fit of the MLLA parameterisation to the DIS (DIFF) data.
P model and the fit 2 parameterisation from HI 1 0 . The DIFF selection is split into high and low /3 samples and shown together with a parameterisation 11 of e + e~ results for a single hemisphere, where contributions from K° and A decays have been subtracted, to be comparable with this data. The observation of a significant shortfall of < n > for DIS data compared with that of e+e~ was explained x by LO QCD processes present in ep but not in e+e~ interactions. Such higher order QCD processes lead to a depopulation of tracks in the current region (or even an empty current region). This effect is also observed for the low /3 DIFF selection which is expected to be dominated by qqg production. The high /3 DIFF selection which is expected to be dominated by qq production, compares well with the e+e~ parameterisation. Both selections are reasonable well described by the RAPGAP Monte-Carlo. 4
Conclusions
The universality of quark fragmentation has been supported by comparing spectra for quarks originating from the pomeron with those from quarks from the proton and from quarks produced from the vacuum in e + e~ annihilation
56 HI PRELIMINARY
10,9 GeV. Charged tracks are reconstructed in the central tracking detector (CTD) and used to identify secondary vertices from the decays: Ks -> 7r+7r~ and A —r pn~. To ensure the strange particle was well reconstructed in the CTD, it was required to lie in the following kinematic region, pr(Ks, A) > 0.3 GeV and \r)(K°s,A)\ < 1.5. 2
Neutral kaon production
The differential Ks cross-section da(ep - • dijet + Ks + X)/dx^bs in three bins of leading jet transverse energy (Ej? ) is shown in figure 1. The variable x°bs is defined as the fraction of the photon momentum contributing to the production of the two highest transverse energy jets. The HERWIG 5 and PYTHIA 6 predictions agree well in shape with the measured cross-section. As the transverse energy of the jets is increased there is a clear reduction in the leading order resolved (low x°bs) contribution to the cross-section. ZEUS "MOOT
> ZEUS (prel.) 96-97
Q. .
40
Energy scale uncertainty -HERWIG
5
3000|-* •PYTHIA
D •D 20001-
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Figure 1. Differential K% cross-section da/dx^bs in the interval ^(/fg)! < 1.5 and PT{K%) > 0.3 GeV in bins of E£n, compared with predictions from HEKWIG and PYTHIA. In this and all subsequent figures, the inner error bars represent the statistical errors and the outer error bars display the statistical and systematic uncertainties added in quadrature. The shaded band is the uncertainty due to the uncertainty in the calorimeter energy scale of ±2%, which is not included in the overall systematic error.
In figure 2 the differential cross-section dcr(ep -¥ dijet + Ks + X)/dr] is shown, where again the Monte Carlo simulation is in good agreement with the measured cross-section, including the forward0 region (rj ~ 1.5). In general, "The forward (+Z) direction is defined as the proton beam direction.
60
n(K°)
T,( 0.3 GeV in bins of E3^ pared with Monte Carlo predictions from HERWIG and PYTHIA.
^ )
, com-
the Kg mesons are produced within the jets, with increased production in the forward direction at higher jet Ex3
Lambda hyperon production
Differential cross-sections da(ep -> dijet + A + X)/dx?/bs have been measured in two bins of jet transverse energy, shown in figure 3. Normalizing the HERWIG and PYTHIA predictions to the measured da{ep -)• dijet+A+X)/dx°ba cross-section, gives a good description of the shape of the data. When the overall Monte Carlo normalization is taken from the measured Ks crosssection, HERWIG significantly overestimates the measured cross-section, while PYTHIA slightly underestimates the measured cross-section. At higher jet energies, the difference persists, but overall the agreement between the measured cross-section and Monte Carlo predictions is slightly better.
4
Conclusions
Differential cross-sections are presented for Ks and A production in high transverse energy photoproduction. The Ks meson production is well described by HERWIG and PYTHIA leading order Monte Carlo generators, over a large range of jet transverse energies. Normalizing the Monte Carlo predictions to the measured A cross-section, gives a reasonable shape description. Fixing the Monte Carlo predictions to the Kg cross-section, HERWIG overestimates and PYTHIA underestimates the A cross-section.
61
ZEUS .01600 Q,
•CM600: . ZEUS (prel.) 96-97 ^-"1400 Energy scale uncertainty — HERWIG: normalised to I
.riioo
5 1 0 0 0 r—HERWIG
PlOOO
TJ 8 0 0 :
"O 800
e
o J200
6
600 400
L A production r j £
'
200 -
10<Ef 1 18GeV "0 0.10.2 0.30.40.5 0.6 0.7 0.80.9 1
0 0.10.2 0.3 0.40.5 0.6 0.7 0.80.9 1 vobs
Figure 3. Differential A cross-section da/dx°ba in 2 bins of E^n with p r (A) > 0.3 GeV and |7)(A)| < 1.5. The left and right pairs of plots show the same data points compared with HERWIG and PYTHIA, respectively.
References 1. 2. 3. 4. 5. 6.
ZEUS Collaboration, J. Breitweg et al, Eur. Phys. J. C2, 77 (1998). ZEUS Collaboration, M. Derrick et al, Zeit. f. Phys. C68, 29 (1995). HI Collaboration, C. Adloffet al, Nuc. Phys. B480, 3 (1996) HI Collaboration, S. Aid et al, Zeit. f. Phys. C76, 213 (1997) G. Corcella et al, hep-ph/0011363. T. Sjostrand et al, Computer Phys. Commun. 135, 238 (2001).
DI-JET P R O D U C T I O N IN P H O T O N - P H O T O N COLLISIONS AT V 5 e e FROM 189 TO 209 GEV THORSTEN WENGLER CERN,
EP-Division, 1211 Geneva 23, E-mail: Thorsten. Wengler@cern.
Switzerland ch
Di-jet production is studied in collisions of quasi-real photons radiated by the LEP beams at e + e ~ centre-of-mass energies y/See from 189 to 209 GeV. The data have been taken with the OPAL detector. Jets are reconstructed using a fcx-clustering algorithm. The inclusive di-jet cross-section is measured as a function of the mean transverse energy Ei£ of the two jets, and as a function of x 7 for different regions of .Ep . Furthermore the inclusive di-jet cross-section as a function of |7jjet| and lA^jetl is presented, where 7jjet is the jet pseudo-rapidity. Different regions of the a;^- Xy -space are explored to study and control the influence of a possible underlying event. The results are compared to next-to-leading order perturbative QCD calculations and to the predictions of the leading order Monte Carlo generator PYTHIA.
1
Introduction
We have measured di-jet production in the collision of two quasi-real photons at v^ee fr°m 189 to 209 GeV with a total integrated luminosity of 593 p b _ 1 collected with the OPAL detector at LEP. The jets are reconstructed using an inclusive k± clustering algorithm 1 because of the advantages of this algorithm in comparing to theoretical calculations 2 . The two jets are used to estimate the fraction of the photon momentum participating in the hard interaction, which is a sensitive probe of the structure of the photon. The transverse energy of the jets provides a hard scale which allows such processes to be calculated in perturbative QCD. Fixed order calculations at next-to-leading order (NLO) in the strong coupling constant a s for di-jet production are available and are compared to the data, providing tests of the theory. At e + e~ colliders the photons are emitted by the beam electrons. Most of the photons carry only a small negative squared four-momentum, Q2, and can be considered quasi-real (Q2 sa 0). The electrons are hence scattered with very small polar angles and are not detected. Events where one or both scattered electrons are detected are vetoed in the present analysis, thereby defining an upper limit on Q2 for both photons of about 4.5 GeV 2 . The median Q2 resulting from this definition cannot be determined with the data since the scattered electrons are not tagged. For the kinematic range of this analysis both PHOJET 3 and PYTHIA 4 predict it to be « 10" 4 GeV 2 .
62
63 l l | l l ' l | l l l l | l l l l | I I M | I M I | l l l l | l l l
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Figure 2. The di-jet cross-section as a function of x 7 and logio(x-y) for the full x'ij-x1range for the regions of the mean transverse energy E^ of the di-jet system indicated in the figures. Also shown is the di-jet cross-section as a function of |ATjj et |, | i ? S t r | and | » j ^ d | , where xij > 0.75 and x^ < 0.75 or vice versa is required. The total of statistical and systematic uncertainties added in quadrature is shown where larger than the marker size. The inner error bars show the statistical errors.
dad ljet for 5 GeV < ££* < 7 GeV dlogio (z 7 ) d 0.75. Consequently we observe a significantly softer spectrum for the case x* < 0.75 than for the full X+-X"-space. The |rjj et | and |AT7jet| dependence of the di-jet cross-section also shown in Figure 1 is dominated by the low E^ events. In Figure 2 the four leftmost plots show the di-jet cross-section as a function of x 7 and logio(x 7 ) in the three regions of E3^ defined in Section 2 and the full x^-aC-space. The cross-section for the lowest values of E^1 shows the largest fraction of events at x 7 < 0.75 of the three ranges considered, and is therefore the most sensitive to the gluon initiated part of the cross section. The three rightmost plots of Figure 2 show the |7jjet| and |A?jj et | dependence of the di-jet cross-section for events in which only either x+ or x~ is smaller than 0.75, which in QCD calculations is dominated by the single resolved contribution. PYTHIA achieves the best description of the data when using the GRSG 6 parton densities (Figures 1 and 2). The agreement with the data is good when the full x+-x~-space is used and for x * < 0.75. PYTHIA/GRS-G underestimates the cross-sections by about 20% when only either x 7 or x~ is smaller than 0.75 (see Figure 2). A reasonable description of the data is also obtained when using the SaS-G ID 7 parton densities, with a tendency to be lower than for GRS-G. The sensitivity of the observables to the gluon content of the photon assumed in the calculations is demonstrated by comparing the prediction of PYTHIA using the already disfavoured LAC-G1 8 set of parton distributions to the data. The large gluon density in this set leads to predictions which are much larger than the measured cross-sections, especially at low values of x 7 (Figure 2). The influence of possible multiple parton interactions has been investigated and appears to have a significant effect mainly for low E3^ and x^ < 0.75, where double resolved events are expected to dominate. By measuring the cross-sections for events in which only either x+ or x~ is smaller than 0.75 we have isolated a region of phase space in which resolved photon processes dominate, and which at the same time is much less sensitive to multiple parton interactions, as demonstrated in the three rightmost plots of Figure 2. By performing the measurement also for x 7 < 0.75, observables (not shown here) are made available which are sensitive to the amount of multiple parton interactions added in the prediction, and which can be used
66
to study these effects in detail. Hadronisation corrections have been studied using PYTHIA 6.161 and HERWIG 6.1, and are found tojbe between 10% and 20% for the differential cross-sections as a functions of E^ , \r]jet\, and |A?7jet|. The cross-sections as a function of x 7 , however, turn out to be very sensitive to hadronisation effects. More detailed studies are necessary to assess the uncertainty associated with this correction, before a meaningful comparison of the NLO calculations to the measurements can be made. Here we only use the NLO predictions of the -E'T*' l^jetli and |A?7jet| distributions for the full x+-a;~-space for comparisons. The prediction of perturbative QCD in NLO 9 using the GRV-GHO 10 parton densities is in good agreement with the data, as demonstrated in Figure 1. The average of the hadronisation corrections as estimated by PYTHIA and HERWIG has been applied to the NLO prediction for these comparisons. References 1. S. Catani, Yu.L. Dokshitzer, M.H. Seymour, B.R. Webber, Nucl. Phys. B406 (1993) 187; S.D. Ellis, D.E. Soper, Phys. Rev. D48 (1993) 3160. 2. M. Wobisch, T. Wengler, hep-ph/9907280; M.H. Seymour, hep-ph/9707349; S.D. Ellis, Z. Kunszt, D.E. Soper, Phys. Rev. Lett. 69 (1992) 3615. 3. R. Engel, Z. Phys. C66 (1995) 203; R. Engel and J. Ranft, Phys. Rev. D54 (1996) 4244. 4. T. Sjostrand, Comp. Phys. Comm. 82 (1994) 74; T. Sjostrand, LUND University Report, LU-TP-95-20 (1995). 5. M. Klasen, G. Kramer, Phys. Lett. B366 (1996) 385; S. Frixione, G. Ridolfi, Nucl. Phys. B507 (1997) 315. 6. M. Gliick, E. Reya, M. Stratmann, Phys. Rev. D51 (1995) 3220. 7. G.A. Schuler, T. Sjostrand, Z. Phys. C68 (1995) 607. 8. H. Abramowicz, K. Charchula, A. Levy, Phys. Lett. B269 (1991) 458. 9. M. Klasen, T. Kleinwort, G. Kramer, Eur. Phys. J. Direct CI (1998) 1; B. Potter, Eur. Phys. J. Direct C5 (1999) 1. 10. M. Gliick, E. Reya, A. Vogt, Phys. Rev. D45 (1992) 3986; M. Gliick, E. Reya, A. Vogt, Phys. Rev. D46 (1992) 1973. 11. G. Marchesini et al., Comp. Phys. Comm. 67 (1992) 465.
A M E A S U R E M E N T OF T H E D U E T CROSS SECTION IN T W O - P H O T O N COLLISIONS AT LEP2 JIM MASIK Institute
of Physics,
ASCR,
Na Slovance 2, 18221, Praha 8, Czech E-mail:
[email protected] Republic
Preliminary results on fully-inclusive differential cross sections of dijet production for jets with ET > 5GeV in two-photon collisions as measured with the DELPHI detector at y/see between 192 and 202 GeV are presented.
1
Introduction
Interactions of photons emitted from electron and positron beams were a dominant process at LEP2. For large pr dijet production in two-photon collisions jets originate from partons produced in primary parton scattering. There are three contributions to the large ET dijet production - direct, single-resolved and double-resolved process as photons enter the interaction either with the direct coupling or with one or both photons fluctuated to the beams of partons. The study of the jet production can shed some light on the interaction of the resolved photons as it provides us with a link to the distribution of incoming partons. One can estimate which kind of interaction occurred by measuring fractions of photon energy x1'2 used in the hard subprocess. ! 2 _ 52jet=l(Eiet±Pzjet) s
"
n=i(Eh±pzh)
.. [)
where the sum runs over two leading jets in the nominator and over all reconstructed particles in the denominator. 2
E v e n t selection
The analysis was done on the data taken in 1999. Most data were collected at 196 GeV and 200 GeV (about 80 p b _ 1 each) with additional 25 p b - 1 at 192 GeV and 35 p b _ 1 at 202 GeV. All four subsamples were treated together for the purpose of this analysis. a " T h e dijet cross section differs by less than 3% between 192 GeV and 200 GeV according to MC simulation.
67
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Figure 1. Uncorrected jet profiles in A77 (upper plots) and A (lower plots). Jet profiles are defined as the total ET flow into the bin in the distance (A, A77) from the jet axis normalised to the total number of jets in the sample. The bands of |TJ| < 1 (\4>\ < 1|) are projected to <j> (77) axes respectively. Data (solid line) are plotted with PYTHIA and HERWIG (containing 0 or 20% of soft-underlying event in double-resolved process). Comparison is carried out in domains of x1'2 < 0.7 (and x 1 ' 2 > 0.8) where majority of events comes from double-resolved (direct) process.
At least 5 tracks were required in the central region of the detector. The requirements on the track quality were px > 100 MeV, track length at least 30 cm, track measurement error Ap/p < 1 and impact parameters less than 4 cm (10 cm) in R (z). Standard thresholds were applied for calorimeter clusters. Cone algorithm with cone half-angle R — 1 was used to search for jets and select events with two or more jets with ET > 4GeV in the range of pseudorapidity |?7| < 2. Events with high energy track or cluster (E > 30GeV) were rejected to constrain photon virtuality. Median Q2 for selected MC events is 3 x 10- 4 GeV 2 . Total pT in the event had to be below pT < 30GeV/c to suppress background of interactions at full i/i^T and radiative return to Z°. Missing px
69
?
DELPHI preliminary
s&
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1
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-
hw|& 6 < R
(1)
« is fulfilled, where E^^ is the transverse energy of the ith particle, 0 is the step function, which ensures that only particles in the cone with opening half-angle 5 contribute to the sum, and the cone radius R — 1. Events with more than one isolated photon are rejected. 3
Determination of the number of photons
The main background to the prompt photon signal originates from photons produced in ir° and rj decays, and from antineutrons. To separate signal photons from the backgrounds, a cluster shape analysis is performed. Two cluster shape variables are used: • The ratio / r a a x of the energy of the most energetic block of the cluster to the total cluster energy, / m a x = Emax/Ej. • The sum of the energy-weighted quadratic deviations of the lead-glass block coordinates with respect to the coordinates of the cluster, T and rp in the range \rp \ < 1 and p 7 , > 3.0 GeV. The inner error bars show the statistical uncertainty and the outer error bars the total uncertainty. The data are compared to the PYTHIA prediction scaled up by a factor 1.85.
To obtain the faction of prompt photons in the sample of candidates, the normalised two-dimensional distribution of / m a x and Cluster is parametrised as a linear superposition of signal and background contributions. A binned maximum likelihood fit yields a photon contribution of (85 ± 8 (stat))% and a 7T° contribution of (11 ± 8 (stat))%, where the uncertainties are due to the statistical uncertainties of the data.
4
Differential cross-section
The inclusive differential cross-sections dcr/dp7, and da/d|77 7 | for isolated prompt photon production are determined as functions of p^ and |?j 7 |. In Figure 1 the measured differential cross-sections are compared with the prediction of the Monte Carlo generator PYTHIA 8 , using the SAS-1D parametrisation 9 and using the original ratio of the single to double resolved contribution calculated by PYTHIA. The total cross-section predicted by PYTHIA has been scaled up by a factor of 1.85 to be consistent with the data. In both cases PYTHIA reproduces the shape of the distributions well but underestimates the differential cross-sections in magnitude. The differential cross-section do-/d|7j7| in the kinematic region studied is within errors independent of |TJ 7 |, in agreement with the Monte Carlo expectation.
74
5
Conclusion
The inclusive cross-section for the production of isolated prompt photons in anti-tagged 77 collisions has been measured using the OPAL detector at LEP. Data with an integrated luminosity of 638.6 p b _ 1 for centre-of-mass energies y/s^ from 183 GeV to 209 GeV are used. The prompt photons are selected by requiring the isolation criterion of 6 . Signal and background contribution from 7r°, JJ and fi are separated by a cluster shape analysis. In the kinematicaJ region p^ > 3.0 GeV and |TJ7| < 1, a total of 92.8 events remain after background subtraction. The total cross-section for inclusive isolated prompt photon production in the kinematic range p^ > 3.0 GeV and |/? 7 | < 1 is measured to be 7,6 GeV and —1 < ifet < 2. Charm quarks were tagged by identifying D** mesons through the K2ir decay mode using the A M method . The jet with closest distance in azimuthal angle to the D* meson was associated with the charm meson. The jet not associated with the £)*, referred to as the "untaggedcharm" jet, represents the unbiased, i.e. not influenced by the D* selection, jet candidate whose internal properties are studied. The measured (nsbj) as a function of the resolution scale, ycut, for the exclusive dijet sample is shown in Fig. la. The predicted {nsbj) is larger for gluon-initiated jets than for quark-initiated jets and the measured data are located between the two curves, showing that the dijet sample is a mixture of quark and gluon jets. PYTHIA 4 gives a good description of the data. Fig. l b shows (nsbj) as a function oiycut for the "untagged-charm" jet. The agreement between data and theory is very good and the predictions of charm-initiated jets are consistent with the measurements. The dependence of the substructure of jets with rfet has also been studied. In the exclusive dijet sample, (nsbj) increases with rfet (Fig. 2a), which is consistent with the predicted increase in the fraction of gluon-initiated jets with r\iet. In the "untagged-charm" jet sample, the results are consistent with a pure sample of quark jets for - 1 < t\>et < 1.5. For the highest rfet values,
77 ZEUS
ZEUS
•
ZEUS (prel.) 1996-97 yp duels
*
ZEUS (prel.) 96-00 'untagged charm' jet
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•
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^
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PYTHIA charm PYTHIA gluon
B4" >J5GeV T < r T S2
(b) 0.2
0.6
0.8
Figure 2. (a) (nsi,j) at a fixed yCut = 0.01 as a function of rfet corrected to hadron level for the exclusive dijet sample and the "untagged-charm" jet . (b) Integrated jet shape of the measured "untagged-charm" jet and the extracted gluon jet substructure.
the data show a deviation from the prediction for quark-induced jets. Since the estimated gluon contamination to the charm-induced jet sample (mainly due to "charm excitation") has its highest contribution in the forward region, the deviation could be explained by the increase of the gluon-jet fraction in the charm-enriched sample. Since the dijet PHP sample consists of a mixture of quark and gluon jets, any measured observable O of the internal structure can be written as: Odijet = fq-Oquark+fg-Ogiuon, where / „ fg = 1 - / , are the fractions of quark and gluon jets. The measurements of the substructure of the charm-enriched sample at high transverse energies (E^f > 15 GeV) can be considered as measurements for a pure sample of quark jets (Ocharm = Oquark). Taking the fractions / , , fg from LO Monte Carlo, the substructure of gluon jets can be extracted. The fraction fq predicted for a dijet sample with EjT > 15 GeV and - 1 < rfet < 2 by PYTHIA ( / , = 0.66) and HERWIG 5(fq = 0.69) are found to be similar. Fig. 2b shows the extracted gluon jet substructure, which is consistent with the QCD predictions. 3
Jet substructure in deep inelastic scattering
Quark initiated jets are expected to be predominant in charged current (CC) and neutral current (NC) deep inelastic scattering (DIS). In Fig. 3a, (nsbj) as
78
ZEUS ZEUS
D ZEUS (prel.) 96-97 e*pNC-DIS —
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.
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1.5
E?'>8GeV
1 ^cut
0.5
L
Q 2 > 200 GoV 2
-1 125 GeV 2 ) are compared. The measurements are found to be similar and in very good agreement for resolution scales ycut > 0.01, where the charm mass effects are negligible. The charm-initiated jets are very similar to light quark jets. Fig. 3b shows the evolution of (nsbj) with E^1 for a fixed ycut = 0.01 in NC and CC processes. The value of (nsbj) decreases as Ej? increases. The agreement between both measurements indicates that the pattern of parton radiation within quark jets is to a large extent independent of the hard scattering process. In Fig. 3c {nsbj) for a fixed ycut = 0.01 as a function of rjjet in CC interactions (Q 2 > 200 GeV 2 ) is shown. Both ARIADNE (CDM) 6 and LEPTO (MEPS) 7 give a good description of the data. The substructure in DIS processes shows no dependence with rfet. In NC processes, the subjet multiplicity (Fig. 4a) as a function of E^% for a fixed ycut = 0.01 and the mean integrated jet shape (Fig. 4b) for a fixed radius of r = 0.5 have been compared to NLO QCD predictions and as has been determined. The extracted value from (nsbj) for jets with E^% > 25 GeV
79 |
ZEUS
I I I I | I I I I | I I I 1 | I I I I ] I I I1 T " p l
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125 GeV1 -1 500 GeV2 (f = (fc' - k)2 = (p' -p)2) is selected. In order for the EPA to provide correct results the virtuality of the quasireal photon needs to be the smallest virtuality in the process. This is guaranteed by requiring \u\ (u = (p' - k)2 = (k' - p)2) of the electron in Figure lb) to be larger than 10 GeV 2 , the cut value on |p 2 |. Within the kinematic limits defined above the cross-section aee is predicted by grc4f 3 to be (1.77 ± 0.02) pb, while the corresponding value from PYTHIA 4 is (1.92 ± 0.03) pb. The errors are statistical only.
82
3
Event Selection
The analysis uses 174.7±0.2 (stat.) ±0.3 (syst.) p b - 1 of data collected during 1998 with the OPAL detector at a centre of mass energy of -^/s ~ 189 GeV. An event selection 5 results in 70 events being selected in the data with 68.1 ± 1.9 events expected from the MC, 48.1 ± 1.3 of those stemming from the signal simulated with grc4f. Dividing the signal into a low mass region with the invariant mass m q q of the hadronic system between 5 GeV and 60 GeV, dominated by the 7*ee final state, and a high mass region with m q q greater than 60 GeV, dominated by the Zee final state, results in signal efficiencies of 13.2 ± 0.5% and 18.0 ± 0.6%, respectively. The higher efficiency in the Zee region is due to the fact that the Z/7* is dominantly produced at small angles. The decay products of the 7* escape often down the beam-pipe, while the decay products of the Z acquire enough transverse momentum to be detected inside the detector. Systematic studies comparing the distributions of the variables used in the event selection for Monte Carlo and data lead to an error of 9 %. The efficiencies achieved using grc4f and PYTHIA are compared resulting in a systematic error of 5 %. Altogether a total systematic error of 11 % is determined. This results in the cross-sections times branching ratio for the decay of Z/7* into hadrons, aee, to be a = (1.20 ± 0.28 ± 0.14) pb for 7*ee and a — (0.69 ± 0.18 ± 0.08) pb for Zee final states within the kinematical definition listed in Table 1. For the calculation of the cross-sections the efficiencies predicted by the grc4f generator are used. The cross-sections measured using efficiencies predicted by PYTHIA lie well within the errors. 4
Differential cross sections
From the event distributions after applying the event selection, differential cross-sections for the Mandelstam variables s, t and u and the invariant hadronic mass m q q are measured, using an unfolding method taking into account the migration of events between bins. The cross-sections 0. Also shown is the cross-section ae~, (• 125 GeV i , , , i , , , i , , , i 1, 40 60 80 20 E T [GeV]
lh 2 -2 : Q > 500 GeV
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Figure 1. ET distributions in different bins of Q2 (a-c) and integrated jet shape (d). Shown are ZEUS data, standard DISENT NLO results and results of our calculation called DISSET.
In Fig. 1 we show comparisons of ZEUS inclusive jet ET spectra in three bins of Q2 (a-c) and of the integrated jet shape for the full Q2 and ET ranges (d) with a standard DISENT NLO calculation and with our results (called DISSET). Good agreement between the data, our result and DISENT can be observed for the inclusive spectra. For the jet shapes the DISENT result, which is only LO, fails. Our result however is much closer to the data since we describe the soft region by the parton shower. The remaining difference between the data and our predictions can be accounted for by hadronisation effects as we checked using the LEPT0 event generator 8 . These results show that we correctly combine the NLO cross-section normalisation with the parton shower which describes the details of the hadronic final such as the jet shapes.
87
4
The Dijet Case
After having studied the problem of inclusive jet production we proceed to dijet production in the Breit reference frame. In principle the method described above should work also for this physically more relevant case. However it turns out that the analytical solution of equation 1 is not straight forward. The relevant equation to be solved for 5 becomes 2
0= £
l n (5) i -At + Aa- ln(l + / ( * , t, u, £)/S) + A4 • ln(l + g(s, t, u, 0/5)(2)
with analytical expressions for coefficients A,. We decided for a numerical evaluation of this equation using Newton's method which after only 4 to 5 iterations gives stable results. 5
Outlook
We implemented a method to combine NLO QCD calculations with parton shower algorithms and successfully tested it on inclusive jet data in the laboratory frame from the ZEUS collaboration. In addition, we showed that the method can also be used for the dijet case in the Breit reference frame although for calculatorical reasons numerical methods have to be used here to derive the desired value 5. In the future we want to fully implement the dijet method and compare predictions from this method with the variety of dijet data that is accesible from the HERA collaborations. Further tasks for the future are the implementation of initial state parton showers and a hadronisation model. References 1. A. Doyle et al. (eds.), Proceedings of the Workshop on Monte Carlo Generators for HERA Physics, Hamburg (1999), DESY-PROC-1999-02. 2. B. Potter, Phys. Rev. D 63, 114017 (2001). 3. B. Potter and T. Schorner, Phys. Lett. B 517, 86 (2001). 4. S. Catani and M. Seymour, Phys. Lett. B 378, 287 (1996); Nucl. Phys. B 485, 291 (1997). 5. T. Sjostrand, Comp. Phys. Comm. 82, 74 (1994). 6. M. Przybycien for the ZEUS Collaboration, Nucl. Phys. B (Proc. Suppl.) 79, 481 (1999). 7. ZEUS Collaboration, Eur. Phys. J. C 8, 367 (1999). 8. G. Ingelmann et al, Comp. Phys. Comm. 101, 108 (1997).
I N T E R F E R E N C E T E R M S A N D C O N T R I B U T I O N OF H I N T H E E L E C T R O N - P R O T O N COLLISION U. JEZUITA-D4BR0WSKA Institute of Theoretical Physics, Warsaw University 69 Hoza Street, 00-681 Warsaw, Poland E-mail:
[email protected] The importance of the interference terms and contribution due to the longitudinally polarised virtual photon in the semi-inclusive ep collision is discussed. The numerical results for the unpolarized Compton process at the Born level are shown.
1
Introduction
In cross sections for semi-inclusive or two-photon exchange processes the terms coming from the interference between the longitudinally and transversely polarised virtual photons or between two different transverse states of 7* can appear 2 . The detailed studies of various contributions for the process e + e~ -> e+e~(j,+fj,~ performed for the kinematical range of the PLUTO and LEP experiments 3 show the importance of interference terms. Here (see also *) we study the longitudinal-transverse interference terms and contributions due to the ^*L and 7^ in the unpolarised semi-inclusive electron-proton collisions. Assuming the one-photon exchange we factorise the cross-section onto the photon emission by the electron and the j"p collision in an independent on the reference frame way. For this purpose we use the propagator decomposition method and explicit forms of all polarisation vectors of the virtual photon (q2 < 0). 2
Factorisation formulae for unpolarised ep collisions
The cross section for an unpolarised IN -> IX process, for example DIS ep —• eX (Fig. 2), can be factorised onto the leptonic and hadronic vertices, da ~ WWpv Moreover the cross section can always be decomposed on the parts related to the subprocesses 7^-iV -> X and 7£iV -* X, respectively: dae^eX
= T T da^p^X
+ TL dal*p^x
.
(1)
The above factorisation and separation formula can be obtained in various ways. One of them uses the known hadronic tensor and explicit form of the scalar polarisation vector 4 . Another way is the propagator decomposition
88
89
Im
*= 0 Figure 1. The optical theorem relation for the process ep —> eX.
method 5 in which the cross section is written as follows dv"»eX
~ Lf
iSE izl w»pv . q2 q2
(2)
Afterwards one can decompose the propagator of the exchanged photon using the completeness relation. This leads directly to Eq. (2). This method is especially useful in analysing the semi-inclusive processes. In case of the semi-inclusive process, for example the Compton process (Fig. 2), one additional particle in the final state is produced. Using the
Im
t =o Figure 2. The optical theorem for the Compton process ep —> cyX.
propagator decomposition method one can factorise the corresponding cross section and obtain the following decomposition:
90 In the above formula two additional contributions related t o t h e interference between two different transverse ( T T ) or between the transverse and longitudinal (LT) polarisation states of the exchanged photon appear.
3
Numerical results for Compton process ep —• ejX
We calculate various contributions to t h e cross sections for t h e unpolarised C o m p t o n process ep -> ejX in the CMep frame, for the H E R A energy y/SeV = 300 GeV. We consider, a t the Born level, the emission of the 7 with the large transverse m o m e n t u m pr > 1 GeV, from the hadronic vertex (i.e. we consider the 7*9 —> jq subprocess o n l y ) a . 10 3 10 2 10 1 10° 10-1
"i
r
T
da d&r daL I d,TLT I
J
2
1010- 3
_L 20
0
40
60
2
2
Q 10
4
1
10 2 {10°
10-
2
10- 4 ~b~
1
1
l\
T\
-
0
[GeV ]
. — " ~
*" *"•*' \ — 1 *V> "
.... x 1
40 PT
100
™
•w ~\ ^\^
10- 7 — 10- 8
80
80
(CMep)
120 [GeV]
160
-4-2
Y
0
2
4
(CMep)
Figure 3. Contributions to da/dQ2 (at the top) and to da/(dprdY) (below) as a functions of PT with Y = 0 (on left) or Y with pr = 5 GeV (on right). For the proton we have used the CTEQ5L parton parametrization r with Nf = 4 and the hard scale equals to prT h e cross section da/dQ2, a
(Fig. 3, top) is strongly dominated by contri-
The cross section for the Bethe-Heitler process, i.e. production of the 7 from the electron line, can be neglected for the photon's rapidity range Y(CMep) < 0 6 .
91
bution due to the transversely polarised 7*, even for large values of virtuality Q2. Also the cross sections da/(dprdY) (Fig. 3, bottom), as a function of pr or rapidity Y, are very well described by the 7J cross section only . We find that in the Q2, pr and Y distributions both contributions coming from the 72, daL and dr^r, are small (below 10%) and of similar size. Moreover they have opposite signs, so they almost cancel each other in the cross section. 0.13 T 0.12 „
1
1
1
1
1
r
1
1
1
1
1
L
0.11
S
0.1
5. •s
0.09 0.08 0.07 j 0.06 -
3
-
2
-
1
0
1
2
3
4> (rod.)
Figure 4. The da/d4> in the Breit frame.
We study also the azimuthal angle distribution in Breit frame for which relatively large sensitivity to the interference term dr^r was found (Fig. 4). 4
Conclusions
Our analysis show that the cross section for the Compton process (at the Born level) is strictly dominated by 7^. The contributions due to *yL and interference terms need to be included on the same footing in a consistent analysis because their values are similar but of opposite sign. References 1. U. Jezuita-Dabrowska and M. Krawczyk, in preparation; U. Jezuita-Dabrowska and M. Krawczyk, THERA BOOK, p.351. 2. V.M. Budnev et al, Phys. Rep. 15C, 181 (1975). 3. G. Abbiendi et al, Eur. Phys. J. C 11, 409 (1999); R. Nisius, Phys. Rep. 332, 165 (2000,). 4. L.N. Hand, Phys. Rev. 129, 1834 (1963); M. Gourdin, Nuovo Cim. 21, 1094 (1961). 5. P. Kessler, Nucl. Phys. B 15, 253 (1970). 6. G. Kramer et al, Eur. Phys. J. C 5, 293 (1998). 7. H.L. Lai et al, Eur. Phys. J. C 12, 375 (2000).
QCD TESTS W I T H JETS AT H E R A T. SCHORNER (on behalf of the HI and ZEUS collaborations) CERN, Division EP, CH-1211 Geneva 23 E-mail:
[email protected] Recent jet results from the HERA collaborations HI and ZEUS are reviewed. Topics covered are soft perturbative QCD studies in photoproduction multi-jet events, multi-jet cross-section measurements in deep-inelastic scattering, determinations of the strong coupling parameter as and the gluon density and jet measurements at the highest photon virtualities Q2 accessible at HERA. In most cases NLO QCD calculations deliver a satisfactory description of the data. The determinations of as using jets at HERA have achieved a precision similar to the world average.
1
Introduction
HERA, with its high centre-of-mass energy of approximately 300 GeV, offers an optimal setting for investigating QCD using clear jet structures in the hadronic final state. In the first years of HERA the general feasibility of jet studies was investigated by the HERA experiments ZEUS and HI and first attempts of measuring the strong coupling constant, as, were undertaken using relatively small data samples. Nowadays, with the increased luminosity of the last few years, high precision measurements can be performed. These range from tests of the QCD matrix elements up to an order of 0{a2s), analyses of QCD at very low scales and the transition between hard and soft QCD to precision determinations of the strong coupling parameter as and the parton distributions functions in the proton or the analysis of the real and virtual photon structure. In this contribution some recent developments and analyses done by the HERA collaborations are summarized. 2
N e w Results on Jets in Photoproduction
Two new preliminary HI measurements of single-inclusive and dijet crosssections are presented elsewhere in these proceedings 1 , together with other HERA photoproduction jet analyses. They show that (direct 4- resolved) NLO QCD gives a good description of photoproduction jet data but that the data are not sufficiently sensitive to the photon parton distribution functions in order to allow for a determination of the photon structure. Apart from that there is one other new preliminary result on jets in photoproduction: The HI collaboration has investigated the source of a class of
92
93
/o.5
.HI Preliminary
,
Wv
HI Rapidity Gaps Between Jets
0.1 : ... PYTHIA + (7 X 1200)
''•I // / •
—
H E R W I G + J I M M Y + BFKL HBRWIG + J I M M Y
• •• P Y T H I A
0.01 ../ 0.5
.. 1,,
1
1.5
2
2.5
3
3.5
4
4.5
5
E?* GeV Figure 1. The fraction of rapidity gap events as a function of the observable J5|, u t .
events which show at the same time a large momentum transfer, t, on the proton side of the interaction and a rapidity gap. Here, a rapidity gap is defined by the condition that the difference in pseudorapidity between the two hardest jets in the event be larger than 2 units. These events are interesting because of the combination of the applicability of perturbative QCD calculations (which are possible because of the high t) and diffractive-type of events (rapidity gap) which at HERA are usually described in terms of the non-perturbative exchange of a colourless object, the pomeron. In the case of high-t rapidity gap events one can therefore speak of the 'perturbatively calculable Regge limit of QCD'. Several models are compared to the measured data: direct and resolved QCD models without colour-singlet components, additional contributions from high-t photon exchange between the proton and the resolved photon (incorporated in PYTHIA 2 ) and BFKL-pomeron exchange (implemented in HERWIG 3 ). Fig. 1 shows the fraction of photoproduction events with a rapidity gap as function of the variable E^1 which is defined as the maximum allowed sum of the transverse energies of all final state objects between the two hardest jets which were not assigned to any of these two jets. It is clearly seen that the predictions from pure PYTHIA or HERWIG without colour-singlet
94
component cannot describe the data, even if they include models for multiple interactions or soft underlying event structures like JIMMY. PYTHIA including an unreasonable amount of high-i photon exchange (labelled 7 • 1200 in the plot) and the BFKL model on the other hand give at least over some parts of the variable ETut a description of the data. The BFKL pomeron model however, which is favoured also by other observables not shown here, suffers from large uncertainties concerning choice of scales, non-leading contributions or the gap formation probability. 3
Multi-Jet Measurements in DIS
There has lately been a large effort by the HERA collaborations to measure differential jet cross-sections in deep-inelastic scattering (DIS) over a large region of phase-space. In this project, single-inclusive, dijet and three-jet cross-sections have been determined and compared to NLO QCD calculations which in the largest part of the phase-space considered give a excellent description of the data. There are, however, some regions where, for reasons not always clear, (direct) NLO QCD fails in describing the data. In single-inclusive measurements, problems with direct NLO QCD were observed in cross-sections as functions of ET in the Breit frame in different regions of Q 2 for ET < 10 GeV and Q2 < 20 GeV 2 or for low values of XBJ < 0.001 (HI preliminary 4 ) and in cross-sections as functions of the ratio ET/Q2 in the laboratory frame for ET/Q2 between 0.5 and ~20 (ZEUS 5 ). In the case of the latter measurement, calculations and models which included resolved photon contributions could however describe the data - an effect which might also be due to the fact that the resolved part simulates NNLO contributions 6 . The discrepancy between data and NLO QCD for low values of XBJ, which had already been observed in earlier HERA measurements 7 , led to discussions about the observation of BFKL evolution in the proton which could however not be confirmed. A recent HI measurement 8 of singleinclusive cross-sections at high Q2 showed perfect agreement between data and theoretical predictions. Dijet measurements have been performed by both HI 8 and ZEUS (9 and preliminary) for a variety of observables, and in almost all cases the data were well reproduced by NLO QCD calculations, see left plots in Fig. 2. Only for the lowest values of the invariant dijet mass Mjj for Q2 < 10 GeV 2 do the predictions undershoot the HI data significantly (right plot in Fig. 2). ZEUS however points out that for low Q2 DIS (below 200 GeV 2 ) the uncertainties due to the choice of the renormalization scale are usually very large which makes definite physical statements difficult.
95 ZEUS Preliminary
*!>*. •
(a)
DATA9S+S7
X.
DISENTCTEQ4M(^»tf) -—-
,.
i- ~ s 8-
O
10
NLO CTEQ5M1 NLO®(1+« l
---'--H
-
L-t-j
Q /G
^ v .
MEPJETCTECMMdi'-tf)
>.
DISENTCTEQ4M(K ! '=ET'4)
-—
10 s
^ " v
DISENTMBRTIMfM'-Q1)
.a*
H1 data
g
2 Tt
CAL Scalo Uncarlainty
Tt
^ _ ^
10'
->--
(b)
g
[5... 10] (x 50000) [10... 20] (X5000)
j ,
¥/.A
NLO Scale Uncertainty: l / 4 ^ i ' , 4 ^ i *
[20... 35] (X500)
log^Q'fGeV)
**** \
Inclusive dijet cross section inclusive k± algorithm
10:
incl. k x algorithm 15
20
30
40 50
16QQ... 5000] 'i'ri'"'i" i I 70
100
MB / GeV
Figure 2. Dijet cross-sections. Left top: ZEUS drr/dQ 2 . Left bottom: H I da/dQ2. HI d2a/dMjjdQ2.
Right:
A measurement of three-jet cross-sections in a range 5 < Q2 < 5000 GeV2 by the HI collaboration 10 aims at a derivation of as from the ratio R3/2 = 3 (right plot in Fig. 3) proved the quality of a new NLO QCD calculation 11 for the three-
96
Vr Oio'
•
H1 data QCD: NLOd+S^,) NLO LO
r :
0 •a
. . 11 I I 11
•
i
1
iH
.lS2sa_
Phase Space
0.6
H1 d a t a / N L O (1+8 hadr )
0.2 i
T
5 5000 GeV 2 ) the exchange of the weak bosons W^ and Z° in addition to pure photon exchange
98
* O 10
«?
1
s
\
r ^
5
25
50
100
75
i 1 i
0.01
f
, . i , , , , i , , , , i , , , ,
0.02
0.03
0.04
0.05
m l 2 [GeV] 0.015
-j -1
J
0.01
1
• HI Charged Current
1$ statistical < •
0.005
I
J- full error
—HI Neutral Current
f
-
o HI NC reweighted
« i
, 20
,
,
i 40
,
,
,
i
,
,
,
i
,
60
Figure 5. Distributions of CC, NC and reweighted NC cross-sections for three observables.
sets in. This gives the opportunity to test whether, as predicted by the standard model, the partonic QCD scattering process is independent of the underlying electroweak exchange mechanism. Therefore the HI collaboration has measured dijet cross-sections in a range 640 < Q2 < 35000 GeV 2 and has compared them to NLO QCD calculations 13 , using the program DISENT 14 for the NC sample and MEPJET 1 5 for the CC sample (which contained 460 events). MEPJET incorporates the W± exchange. DISENT, on the other hand, does not contain the terms for Z° exchange, a disadvantage which is compensated for by considering only ratios of jet cross-sections to totally inclusive cross-sections in which Z° contributions should approximately cancel. The analysis showed that the two QCD programs give satisfactory descriptions of the measured distributions. A rather involved reweighting procedure was then designed to make the NC and CC jet cross-sections directly comparable. Fig. 5 shows CC and reweighted NC dijet cross-sections, the good agreement signalling that indeed the partonic QCD scattering is independent of the underlying electroweak exchange process.
99 6
Conclusion
A short review of jet physics and QCD tests at HERA (mainly in DIS) was given. It was shown that for most observables and analyses NLO QCD gives a fairly good description of the data. Nevertheless there are a few weak spots which need further progress. The problem of large scale uncertainties and of discrepancies between data and theory in low Q2 DIS is especially prominent. Possible solutions for this problem range from NNLO QCD calculations over resolved photon contributions to the failure of DGLAP and the onset of BFKL evolution. But also in photoproduction a few points need to be clarified. First, a method for a consistent extraction of the real photon structure is wanted. Second, the transition from soft, non-perturbative to hard, perturbative QCD needs further investigation. All in all HERA I has proven to be a very fruitful source of QCD tests using jets. Bearing this and the remaining questions in mind, HERA II, with its increased luminosity, promises another period of successful jet physics. References 1. 2. 3. 4.
5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
A. Valkarova, these proceedings. T. Sjostrand, Comp. Phys. Coram. 82, 74 (1994), G. Marchesini et al, Comp. Phys. Comm. 67, 465 (1992). T. Schorner, in Proceedings of the 8th International Workshop on DeepInelastic Scattering and QCD (DIS2000), ed. J.A. Gracey and T. Greenshaw (World Scientific, Singapore, 2000). ZEUS Collaboration, J. Breitweg et al, Phys. Lett. B 474, 223 (2000). S. Frixione and G. Ridolfi, Nucl. Phys. B 507, 315 (1997). G. Kramer and B. Potter, Eur. Phys. J. C 5, 665 (1998). HI Collaboration, C. Adloff et al., Nucl. Phys. B 538, 3 (1999). ZEUS Collaboration, J. Breitweg et al, Eur. Phys. J. C 6, 239 (1999). HI Collaboration, C. Adloff et al, Eur. Phys. J. C 19, 289 (2001). ZEUS Collaboration, J. Breitweg et al., Phys. Lett. B 507, 70 (2001). HI Collaboration, C. Adloff et al, Phys. Lett. B 515, 17 (2001). Z. Nagy and Z. Trocsanyi, Phys. Rev. Lett. 87, 82001 (2001). S. Bethke, J. Phys. G 26, R27 (2000). Particle Data Group, D.E. Groom et al, Eur. Phys. J. C 15, 1 (2000). HI Collaboration, C. Adloff et al, Eur. Phys. J. C 19, 429 (2001). S. Catani and M. Seymour, Phys. Lett. B 378, 287 (1996): Nucl. Phys. B 485, 291 (1997). E. Mirkes and D. Zeppenfeld, Phys. Lett. B 380, 23 (1996).
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3 Charm and Beauty Production
Session Convenors: A. Finch and S. Frixione
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H E A V Y Q U A R K P R O D U C T I O N I N 77 COLLISIONS JIRI CHYLA Center for Particle Physics, Institute of Physics, Academy of Science of the Republic, Na Slovance 2, 18221 Prague 8, Czech Republic E-mail:
[email protected] Czech
Current theoretical framework for the calculation of heavy quark production in 7 7 collisions is reviewed. The importance of including direct photon contributions up to the order a2a^ and of proper choice of renormalization and factorization scales in the evaluation of (7(77 —> QQ) is emphasized.
1
Introduction
Heavy quark production in 77 collisions has recently received increased theoretical attention 1>2'3 motivated by new experimental data on cc and bb production from LEP2 (see 4 for detailed list of references). Although the data on bb production have sizable errors and the theoretical predictions suffer from uncertainties, the excess by a factor of about three of the data over theoretical predictions represents a serious problem for perturbative QCD. Interestingly, a similar excess of data on bb production has also been observed in 7*p and pp collisions. In such a situation it appears timely to reanalyze the theoretical framework used for analyses of heavy quark production in 77 collisions, paying particular attention to the renormalization and factorization scale dependence, as these represent the main source of theoretical uncertainty. Due to the presence of the inhomogeneous splitting functions in the evolution equations for PDF of the photon, their general solutions can be split into the particular solutions of the full inhomogeneous equations and a general solutions, called hadron-like (HAD), of the corresponding homogeneous ones. A subset of the former resulting from the resummation of contributions of diagrams describing multiple parton emissions off the primary pure QED vertex 7 —> qq and vanishing at M = Mo, are called point-like (PL) solutions. Due to the arbitrariness in the choice of Mo the separation D(x, M) = DPh(x, M, M0) + DHAD(x, M, M0).
(1)
is, however, ambiguous. All complications of QCD description of hard processes involving initial photons stem from the presence of the point-like parts. The different nature of the UV renormalization of QCD quantities, generating the renormalization scale dependence of the colour coupling as(fx)
103
104
and mass factorization involved in the definition of dressed PDF provides a powerful argument for keeping the renormalization and factorization scales as independent free parameters. In 1 , 2 ' s the "next-to-leading order" QCD approximation to the total cross section (7(77 —• QQ) is defined by taking into account the first two terms in expansion of direct, as well as single and double resolved photon contributions
qq and cannot therefore be interpreted as l/as(M). If QCD is switched off by sending, for fixed M and Mo, A —• 0 a , quark and gluon distribution functions of the photon approach QED expressions qi(x,M)
-> q?ED = ^ 3 e 2 f c ( ° ) ( , ) l n ^ , G(x,M)
- G ^
= 0.
(5)
In the limit of vanishing colour coupling we thus get, as we must, the purely QED resultCT^J. Had the PDF of the photon really behaved as a/as, we would, on the other hand, get finite contributions from the lowest order single and double resolved photon contributions (3,4) even in the limit of switching QCD off, which is clearly untenable. All calculations 1 ' 2 ' 3 of heavy quark production in 77 collisions were done with fixed renormalized quark masses, i.u. define TUQ in the on-shell scheme. In this convention o ^ / in (2) can also be written in the form croc^(s/ m Q)i where c^\p) is again a function of s/rriQ only. "There is no obstacle to performing this limit, as by decreasing A we get ever closer to the asymptotic freedom point as = 0 and thus our perturbation expansions are progressively better behaved.
105
2
Direct photon contribution
For proper treatment of •> n-vi2GeV / c , | T ,iD -* T * +| < 1 .
Figure 3: pij distribution in the kinematical region | 7jD | < 1.
A comparision of the measured differential cross-section dcr/dpJp with a next-to-leading order (NLO) calculation by Frixione et al. 8 and a m o d e l 9 is shown in Fig.3. The experimental distribution is consistent with the m o d e l 9 , where a fragmentation of charm quarck near the threshold is described in detail. T h e NLO calculation with the massive charm quark m a t r i x element underestimates the experimental distribution. T h e cross section of inclusive D * + production in the considered kinematical region 2 G e V / c < p ° * + < 12 G e V / c , | ?7D*+ | < 1 is then '(e+c
e + e - D + + X ) = iV°p/(e D .-£-J3T-) = 18.0±1.8(stat.)±1.6(syst.) pb,
where N® is the observed number of D * + mesons, ED* is the reconstruction efficiency of D * + in the corresponding mode, C is the total integrated luminosity and Br is the branching ratio of D * + decay to the corresponding decay c h a i n 1 0 . T h e D * + reconstruction efficiencies £Q-+ for each D° decay mode are calculated using P Y T H I A . T h e m a i n sources of systematic uncertainties are due to the limited number of MC events (~6-8%), K/V selection procedure (~3-5%) and the branching fractions uncertainties (~2.4-4.2%). T h e systematic uncertainties are added in quadrature. To obtain the total cross-section of charm production we extrapolated the measured cross section o"^ es to the full kinematical range. For calculation of the extrapolation factor the P Y T H I A based MC was used. T h e total cross section of inclusive D * + production is corrected then by the probability of
112 charm quarks to fragment into a D* + section is
10
. T h e obtained value of the total cross
o-(e+e" -» e + e " c c ) = 783 ± 78(stat.) ± 70(syst.) ± 190(extr.) p b agrees with the NLO calculation 8 . The extrapolation procedure introduces large uncertainties to the total cross section value. 4
Conclusions
T h e inclusive production of D * + in 7 7 collisions at LEP-II energies has been measured. T h e relative fractions of contributions from direct and single resolved processes in the kinematical region 2 G e V / c < pJjT < 12 G e V / c , | rf |< 1 was measured. T h e measured differential cross section dcr/dpJp is consistent with the m o d e l 9 . T h e NLO calculation with the massive charm quark m a t r i x element underestimates the experimental distribution. T h e extrapolation of the cross section of inclusive D * + production measured in the restricted kinematical region to the total charm cross section gives the value which agrees with the NLO calculation. References 1. J.J. Sakurai and D. Schildknecht, Pkys. Lett. B 4 0 , 121 (1979); I. F. Ginzburg and V.G. Serbo, Phys. Lett. B 1 0 9 , 231 (1982). 2. S.J. Brodsky, T . Kinoshita and H. Terazawa, Phys. Rev. D 4 , 1532 (1971). 3. S.J. Brodsky, T.A. DeGrand, J . F . Gunion and J.H.Weis, Phys. Rev. Lett. 4 1 , 672 (1978); Phys. Rev. D 19, 1418 (1979). 4. P. Aarnio et al., D E L P H I Collab., Nucl. Instrum. Methods A 3 0 3 , 233 (1991). 5. P. Abreu et al, D E L P H I Collab., Nucl. Instrum. Methods A 3 7 8 , 57 (1996). 6. T . Sjostrand, Comput. Phys. Comm. 82, 74 (1994). 7. Z. Albrecht, M. Feindt and M. Moch, MACRIB. High efficiency - high purity hadron identification for DELPHI, DELPHI/99-150 (October 1999). 8. S. Frixione, M. Kramer and E. Laenen, Nucl. Phys. B 5 7 1 , 169 (2000). 9. A.V. Berezhnoy, V.V. Kiselev and A.K. Likhoded, Pkotoproduction and electroproduction of charm at high energies, hep-ph/9905555 (Jun 2000); A.K. Likhoded and A.V. Berezhnoy, private communication. 10. Review of Particle Physics Eur. Phys. J. C 15, 1 (2000).
I N C L U S I V E J/ip P R O D U C T I O N I N T W O - P H O T O N COLLISIONS AT LEP
Institute
A . A . SOKOLOV for High Energy Physics, 142284 Protvino, Russia E-mail:
[email protected] Moscow
region,
Inclusive J/ip production in photon-photon collisions has been observed by the DELPHI collaboration at LEP II beam energies. A clean signal from the reaction 77 —t J/tj) + X is seen. Number of observed events, N(J/ij> —» n+ n~) — 36 ± 7 for the integrated luminosity 617 pb , yielding a cross section of a{J/tp —* fi' M—) = 25.2 i 10.2 pb. Based on a study of the event shapes of different types of 77 processes in the PYTHIA program, we conclude that (74±22)% of the observed J/ij> events are due to the 'resolved' photons, the dominant contribution of which is evidently a single color-octet gluon within the photon.
1
Introduction
An i m p o r t a n t component of the e+e~ collisions at L E P II energies is the twophoton fusion process. It has been pointed out t h a t two-photon production of inclusive J/iji's e + + e~ —* e+ + e~ + 7X + T3 followed by 7X + 7 2 —* J/ip + X is a sensitive tool for the gluon distribution in the p h o t o n 1 . There are two i m p o r t a n t processes leading to inclusive J/tj) production. T h e first process is undoubtedly attributable to the vector-meson dominance (VMD) m o d e l 2 . T h e second process is due t o the color-octet m o d e l 3 . It proceeds through the so-called 'resolved' contribution of the photons, in which the intermdediate photons are 'resolved' into its constituent partons. T h e purpose of this paper is to study the inclusive J/ip production, in order to assess the relative importance of the production processes discussed above. 2
Experimental Procedure
T h e analysis presented here is based the d a t a taken with the D E L P H I detector 4 ' 5 during the years 1996-2000. T h e integrated luminosity used in the analysis is 617 p b - 1 . After the requirement for the T P C detector to have a good-quality operation for the selected events the hadronic two-photon events have been extracted by applying the following cut on the full sample: there is either (i) at least 1 charged track in the barrel region (40° < 6 < 140° with pt > 1 . 2 G e V / c 2 ) or (ii) at least 1 neutral track in Forward Electromagnetic Calorimeter ( F E M C ) ( 10° < 9 < 36° and 144° < 9 < 170°) with energy greater t h a n 10 G e V / c 2
113
114 or (iii) sum of number of charged tracks in barrel with pt > 1 G e V / c 2 and charged tracks in forward region (10° < 6 < 40° or 140° < B < 170°) with pt > 2 G e V / c 2 and neutrals in F E M C with E > 7 G e V / c 2 greater t h a n one or (iv) sum of number of charged tracks in barrel with pt > 0 . 5 G e V / c and charged tracks in forward with pt > 1 G e V / c and neutral tracks in F E M C with E > 5 G e V / c 2 greater t h a n four. T h e trigger efficiency for the events which passed the above requirement is bigger t h a n 98%. Finally the following cuts were applied: visible invariant mass is W v i s < 3 5 G e V / c 2 ; number of charged tracks 4 < Ncb < 30; the s u m of the transverse energy components with respect to the b e a m direction of all charged particles is £ E™ > 3 G e V / c 2 . A total of 274 510 events remain in the d a t a sample after applying all these cuts. T h e m a i n background comes from the process e+e~ —* Z°-y and a m o u n t s to ~ 1 . 2 % of the selected 7 7 events. J/ip candidates have been selected using the fi+\L~ decay channel. For the muon selection the following criteria have been imposed: track should satisfy the D E L P H I standard muon-tagging algorithm 5 or identified as muons by hadronic calorimeter 6 ; track should not come from any reconstructed secondary vertex or be identified as kaon, proton or electron by s t a n d a r d DELP H I identification packages. At least two charged particles with zero s u m m a r y charge should be identified as a muon candidates. 3
I n c l u s i v e J/tj) P r o d u c t i o n
We give in Fig. 1 the invariant mass of fJ.+fJ.~ from the D E L P H I d a t a selected as outlined in the precious section. It is seen t h a t the J/0 produced with a little background. A mass-dependent fit to the M((j.+fj.~) distribution with gaussian for the signal and polinomial for the backgrond gives the following results: J/xj> mass M = 3119 ± 8 M e V / c 2 , width T(obs) = 35 ± 7 M e V / c 2 . T h e number of observed events is N(J/ip) — 36 ± 7 from the fit. For efficiency estimation we used P Y T H I A 6.156 g e n e r a t o r 7 . T h e generated events were passed through the simulation of the D E L P H I detector 5 and t h a n processed with the same reconstruction and analysis programs as the real d a t a . There is a substantial fraction of P Y T H I A events where J/ip are produced just as a simple fusion of two photons because there is not enough phase space to produce additional particles. We checked t h a t all such events are produced when b o t h the colliding photons are direct or one photon is anomalous and the other one is DIS (we use here the P Y T H I A n o t a t i o n 7 ) . T h a t is why for the efficiency estimation we did not use the events with direct-direct or DIS-anomalous photon interactions. Among the rest of the P Y T H I A events
115
M(/i>-), GeV/c*
-
Figure 1: M ( j j + / i ) distribution from the DELPHI data.
a b o u t 9 3 % J / 0 are produced when at least one photon is a VDM photon. Fig. 2 shows the p* (.//VO distribution from the D E L P H I d a t a . DELPHI
Figure 2: p* (J/V>) distribution from the DELPHI data.
Figure 3: |y| distribution for the J/ij> from the DELPHI data.
As expected, the P Y T H I A prediction for the P2T{J/TJ>) distribution is sharply peaked near zero for the diffractive MC events, while the 'resolved' M C events are very much spread out. We fitted the experimental p^,(J/ip) distribution as a function of the two categories of MC events
dN dpi
f
dN dpi
+ < - " • ! Diffractive
Resolved
which gives / = (26.0 ± 22.0)%. T h e P Y T H I A study tells us t h a t the experimental efficiencies are very different for the two categories: e(Diffractive)=(1.79±0.07)%, e(Resolved)=(6.79±0.16)%. From this we deduce t h a t the overall experimental efficiency must be 1/e = //e(Diffractive) + (1 — / ) / e ( R e s o l v e d ) . T h e cross section of inclusive J/ip production is then a = N -(Br-C-
e ) " 1 = 25.2 ± 10.2 pb
116 where Br = (5.88 ± 0.10)% is the branching ratio for J/ip -* fJ.+n~ 8 and £ — 6 1 7 p b _ 1 is the total integrated luminosity. Finally, the rapidity distribution for the J/iji is shown in Fig. 3. T h e P Y T H I A MC events have been combined using the measured fraction / and then normalized to the observed number of events in 0 < \y\ < 2. It is seen t h a t the M C events are in fair agreement with the experimental rapidity dsitribution, although the d a t a tend to have some deficiency below \y\ — 0.4 4
Conclusions
We have studied the inclusive J/0 production from 7 7 collisions. T h e d a t a have been taken by the D E L P H I collaboration during the L E P II phase, i.e. *Js of the L E P machine ranged from 161 to 207 G e V / c 2 . A clean signal from the reaction 7 7 —+ J/ip + X is seen. T h e preliminary value for inclusive cross section is cr(J/tj) —> / i + / i ~ ) = 25.2 ± 10.2 p b . Based on a study of the event shapes of different types of 7 7 processes in the P Y T H I A program, we conclude t h a t some (74±22)% of the observed J/ip events are due to the 'resolved' photons, the d o m i n a n t contribution of which is evidently derived from a single color-octet gluon within the photon. T h e p%.(J/ip) and y distributions are presented. References 1. Physics ar LEP2, edited by G. Altarelli, T . Sjostrand a n d F . Zwirner, CERN96-01 (Vol. 1), p . 330 (Feb 1996). 2. J . J . Sakurai and D. Schildknecht, Phys. Lett. B 4 0 , 121 (1979); I. F. Ginzburg and V.G. Serbo, Phys. Lett. B 1 0 9 , 231 (1982). 3. M. Klasen et al, DESY 01-039 (April 2001); R. M. Godbole et al, LC-TH-2001-019 (February 2001); E. L. Berger and D. Jones, Phys. Rev. D 2 3 , 1521 (1981); H. J u n g , G. A. Schuler and J. Terron, Int. J. Mod. Phys. A 7, 7955 (1992); B. Naroska, Nucl. Phys. B (Proc.Suppl.) 8 2 , 187 (2000). 4. P. Aarnio et al, Nucl. Instrum. Methods A 3 0 3 , 233 (1991). 5. P. Abreu et al, Nucl. Instrum. Methods A 3 7 8 , 57 (1996). 6. J. Ridky, V. Vrba, J. Chudoba, ECTANA. User's Guide, D E L P H I / 9 9 - 1 8 1 T R A C K 96 (17 November 1999). 7. T . Sjostrand, Comput. Phys. Comm. 82, 74 (1994). 8. Review of Particle Physics, Eur. Phys. J. C 1 5 , 1 (2000).
HEAVY FLAVOUR P R O D U C T I O N IN T W O - P H O T O N INTERACTIONS V. P. A N D R E E V Dept. of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA E-mail:
[email protected] Measurements of charm and bottom quarks production in two-photon collisions at LBP are presented. The cross section of b production is in excess of the QCD prediction by a factor of three.
1
Introduction
The production of heavy quarks in two-photon collisions consists mainly of charm quarks. Because of their smaller electric charge and larger mass, the production of b-quarks is expected to be suppressed by more than two orders of magnitude relative to the production of charm quarks. The resolved photon cross section is dominated by the photon-gluon fusion diagram 7g —• cc, bb. At LEP energies, the direct and resolved processes, shown in Figure 1, are predicted to give comparable contributions Direct Singlt Resolved to the cross section 1 . Figure 1. Diagrams contributing to charm and beauty Measurements of charm production in 77 collisions at LEP. production in twophoton collisions were done at LEP by ALEPH 2 , DELPHI 3 , L3 4 - 5 and OPAL 6 collaborations. Beauty production has been measured by L3 5 for the first time in gammagamma collisions. Preliminary result on beauty production from OPAL collaboration has been presented at PHOTON2000 conference.
117
118
2
Charm Production
Charm particles in the final state were identified by the reconstruction of charged D* meson decays by ALEPH, DELPHI, L3 and OPAL. Both, charm and beauty quarks were identified by the L3 collaboration using tagging by electrons and muons from semileptonic charm and beauty decays. The total inclusive charm cross sections are plotted in Figure 2 together with previous measurements. The data are compared to the theory predictions of Ref.1. The dashed line corresponds to the direct process, NLO QCD calculation, while the solid line shows the QCD prediction for the sum of the direct and the resolved processes calculated to NLO accuracy. The prediction for open charm is calculated using a charm mass of either 1.3 GeV or 1.7 GeV and the open charm threshold energy is set to 3.8 GeV. The theory prediction for the resolved process is calculated with the GRV parton density function 7 . The renormalization and factorization scales are chosen to t _ _ , _ m„=1.3Q»V 4 be the heavy quark m =1.7G»V..,;_ ' QCD, JQ 10 mass. The direct a. process 77 —» cc is direct insufficient to den scribe the data, even 10' 10 o : f'A • L3 D'.orei. if real and virtual / A ALEPH lopt.pFBl. * ALEPH D'pfBi. gluon corrections + » DELPHI D'.prol. 0 OPALIept„prel. are included. The * OPAL D". pre!. * Ulept. T data therefore re* ALEPH D* 'a> 1 0 quire a significant X AMYIept.,it. + : * TOPATD'.if ,lept. m =4.5QeV.., gluon content in the * VENUS lept. m =5.0 Q.Y. : A TASSO ty •.:.• photon. bb O JADE D* ^J&Z #
r
0
:
\J0^ -
>t
:
b
B
a TPCttyD*
^ c ^ ^ ^
The cross sec. . , . i . . / + mc with charm quark mass value mc — 1.5GeV. The calculations have been also done using different renormalization scales separately for the direct and single-resolved contributions and different charm quark masses to estimate the theory prediction uncertainty. The measurements are in agreement with NLO QCD calculation within rather big theory prediction uncertainty. The L3 collaboration measured the cross sections a(e+e~ —> + e e ccX) and cr (77 -> ccX) in the interval ! i GeV < W, 77 < 70 Figure 4 shows the cr (77 —» ccX) as function of GeV 10 . W.11 at yfs 189 - 202 GeV with NLO QCD calculations 11 In the calculations 10° the charm mass, : * DELPHI prel. m c , is fixed to 1.2 GeV, the renor• L3 prel. • malization and • OPAL 10' factorization scales NLO QCD Massive, GRS p.d.f. are set to mc and • • • • m =1.2 GeV; m=2m (dir) / m /2(res) > : At 2m c m =1.5 GeV; n =m respectively, 1 •> Y CD the QCD param- - m =1.8GeV;M =m /2(dir)/2m (res) CD eter A5 is set -Q 10 at 227.5 MeV, and CL hi < 1.4 the GRS-HO 9 phoD_ -o ton parton density function is used. "° 1 Using this set of input parameters, \\ the NLO QCD predictions reproduce ' *"**. -1 well the energy 10 dependence and • ' • ' the normalization. 0 2 4 6 8 10 12 The calculation PT [GeV] with mc = 1.5 GeV Figure 3. The differential D* production cross section D results in about 50% compared to the NLO QCD calculations n . lower cross section values, except the first point, where it is lower by 25%. A change in the renormalization scale from m, ; to 2m c decreases the QCD prediction by c
T
c
H
T
c
fl
T
T
T
\1
\ S J -IJ-
! • • • !
1
1
•
QQ is considered. If the transverse momentum ptg of the additional gluon is of the order of that of the quarks, then in the collinear approach the full 0(a?) matrix element for 2 —> 3 has to be calculated. In fct-factorization such processes are naturally included, even if only the LO as off-shell matrix element is used, since the kt of the incoming gluon is not restricted from above, and therefore can acquire a virtuality similar to the ones in a complete fixed order calculation. In Fig. 1 the basic ideas are shown schematically . Not only does fct-factorization include (at least parts of) NLO diagrams, it also includes diagrams of the resolved photon type u , with the natural transition from real to virtual photons.
124
The 0(as) matrix element in fct-factorization includes the 0(as) matrix element of collinear factorization but in addition also higher order contributions because the incoming gluon is off-shell and the unintegrated gluon density resums parts of the virtual corrections (Fig. 2). b - jet - mi
P, •vwv
z "O 2(M)0
71"
0.03 (see Fig. 3), where the application of fct-factorization is questionable and also where the unintegrated gluon density is not at all constrained by the fit to F2. 180 1S0
•
H1 pral(M-S7)
(b)
CASCADE EPJPSI
"
140 120 100
ao 60 40
: :
P 1
20
10 12.5 15 17.5 20 22.S 25 P t 2(GeV
2
0
0.1
0.2 0.3 0.4
0.5
0.6
0.7 0.5
0.9
1
)
Figure 5. The cross section of fp —> J/ip + X as a function of the transverse momentum (a) and of of the fractional momentum z (b) of the J/rp as measured by HI 1 8 compared to the predictions of CASCADE and EPJPSI.
The cross section for 'yp —* J/ip+X as a function of the transverse momen-
126
turn of the J/tp shows a significant deviation from the leading order color singlet model prediction (as implemented in E P J P S I 19 ) in collinear factorization. In Fig. 5, the preliminary HI measurement 18 is compared to the prediction of 19 E P J P S I . In collinear factorization, the harder transverse momentum spectrum is interpreted as a signal for significant next-to-leading order corrections. Also shown in Fig. 5a is the prediction of CASCADE using the same CCFM unintegrated gluon density as before together with the fct-factorized matrix element 20 for 75* —> J/tpg. The inelastic J/tp photoproduction cross section {z < 0.9) as a function of px is nicely described by CASCADE. Especially the large transverse momentum part is explained as additional hard initial state QCD radiation. The same is also observed in full NLO calculations, and it shows again the advantage of the fct-factorization in simulating a large part of the NLO correction of the collinear approach, due to the non zero virtuality of the incoming gluon. The distribution in the fractional momentum z of the J/tp is also reasonably well described (Fig. 56). 4
Conclusion
The application of the fct-factorization approach to heavy quark production at HERA has been discussed. It is shown, that the visible bb production cross section as measured at ZEUS is nicely reproduced by CASCADE, using the CCFM evolved unintegrated gluon density obtained from a fit to F2(x,Q2). It was pointed out, that the extrapolation from the measured to the total bb cross section contains large model dependencies. The differential cross sections for inelastic J/tp photoproduction can be reasonably well described with CASCADE, both in terms of shape and normalization. The large transverse momentum tail is a direct signal for additional hard initial state QCD radiation. It is the advantage of the fct-factorization approach that important parts of NLO and even NNLO contributions are consistently included due to the off-shell gluons, which enter into the hard scattering process. Acknowledgments I want to thank the organizers M. Kienzle and M. Wadhwa for this very nice workshop. I am also grateful to S. Frixione for the invitation to this workshop and his interest in fct-factorization. Many thanks also go to S. Baranov and N. Zotov for interesting discussions and our fruitful collaboration. I am also grateful to L. Gladilin, B. Naroska and J. Whitmore for careful reading of the manuscript. All thanks for the great times with Antje.
127
References 1. 2. 3. 4. 5. 6. 7. 8.
9.
10. 11. 12.
13.
14. 15.
16. 17. 18.
19.
20.
CDF Collaboration; F. Abe et al., Phys. Rev. D 55(1997)2546. DO Collaboration; B. Abbott et al., Phys. Lett. B 487(2000)264. S. Catani, M. Ciafaloni, F. Hautmann, Nucl. Phys. B 366 (1991) 135. M. Ciafaloni, Nucl. Phys. B 296 (1988) 49. S. Catani, F. Fiorani, G. Marchesini, Phys. Lett. B 234 (1990) 339. S. Catani, F. Fiorani, G. Marchesini, Nucl. Phys. B 336 (1990) 18. G. Marchesini, Nucl. Phys. B 445 (1995) 49. S. Catani, fct-factorisation and perturbative invariants at small x, in Proceedings of the International Workshop on Deep Inelastic Scattering, DIS 96 (Rome, Italy, 15-19 April, 1996), hep-ph/9608310. S. Catani, Aspects of QCD, from the Tevatron to LHC, in Proceedings of the International Workshop Physics at TeV Colliders (Les Houches, France, 8-18 June, 1999), hep-ph/0005233. H. Jung, G. Salam, Eur. Phys. J. C 19(2001)351, hep-ph/0012143. S. Baranov, N. Zotov, Phys. Lett. B 491 (2000) 111. ZEUS Collaboration; M. Derrick et a l , Beauty photoproduction in the muon semi-leptonic decay mode at HERA, in Contributed paper J^96 to IECHEP 2001, Budapest, Hungary (2001). H. Jung, Unintegrated parton densities applied to heavy quark production in the CCFM approach, in Proceedings of the Rinberg workshop on "New trends in HERA physics", Ringberg Castle, Tegernsee, Germany. (2001), hep-ph/0109146. H. Jung, submitted to Phys. Rev. D (2001), DESY-01-136, hepph/0110034. H. Jung, The CCFM Monte Carlo generator CASCADE for lepton - proton and proton - proton collisions, Lund University, accepted by Comp. Phys. Comm., 2001, hep-ph/0109102, DESY 01-114, http://www.quark.lu.se/~hannes/cascade/. HI Collaboration; C. Adloff et al., Phys. Lett. B 467(1999)156, and erratum ibid. ZEUS Collaboration; J. Breitweg et al., Eur. Phys. J. C 18(2001)625. HI Collaboration; C. Adloff et al., Inelastic photoproduction of J/ip and ip(2s) at Hi, in Contributed paper 157aj to IECHEP 1999, Tampere, Finnland (1999). H. Jung, EPJPSI: A Monte Carlo generator for J/tp mesons in high energy 7 — p, e — p and p — p collisions, version 3.3, Lund University, 1995, h t t p : / / w w w - h l . d e s y . d e / ~ j u n g / e p j p s i . h t m l . V. Saleev, N. Zotov, Mod. Phys. Lett. A 9(1994)151.
C H A R M P R O D U C T I O N IN D E E P INELASTIC SCATTERING A N D D I F F R A C T I O N AT H E R A W. ERDMANN REPRESENTING THE HI AND ZEUS COLLABORATIONS Institute for Particle Physics, ETH-Zurich, Switzerland E-mail:
[email protected] D*^ production in deep inelastic scattering at HERA has been measured by HI and ZEUS using 19 p b _ 1 of e+p data. Total and differential cross sections are compared to QCD calculations. A first measurement of semi-leptonically decaying charm at HERA is presented. ZEUS has preliminary results on D** production in 16.7 p b - 1 of e~p data and 65.2 p b _ 1 of e+p data. Charm production in diffractive ep scattering has been observed and results are compared to models of diffractive interactions.
1
Introduction
The importance of charm production in deep inelastic scattering (DIS) is based on its sensitivity to the gluon content of the proton. Charm production can be calculated in QCD using gluon densities derived from the scaling violations of inclusive DIS. The comparison with measured charm cross sections provides an important test for perturbative QCD. Close to threshold, where the bulk of the charm at HERA is produced, the generation of massive quarks in the boson-gluon-fusion (BGF) process is the appropriate framework for QCD calculations. Well above threshold, a transition should occur to a regime where the mass can be neglected and charm should be included in the parton densities. The sensitivity to the gluon in the proton is obvious in the leading order BGF graph, where a virtual photon radiated from the incoming lepton interacts with a gluon from the proton to form a cc pair. Two calculations in this scheme will be compared to the data. The HVQDIS 1 program implements next-to-leading order (NLO) matrix elements and DGLAP evolution of the parton densities. It can calculate differential cross sections applying relevant experimental cuts. The CASCADE 2 program on the other hand is a Monte Carlo generator based on kt factorization with leading order matrix elements involving off-shell gluons and CCFM evolution of the un-integrated gluon density. The CCFM evolution includes coherence effects of the gluon emission and is expected to give a better description at very low x. Major sources of uncertainties in both calculations are the value of the
128
129 charm quark mass and the hadronization of the charm quarks into the experimentally observable mesons. The hadronization is modeled with the Peterson fragmentation function with parameter ec. Additional pt smearing of the meson relative to the quark is applied in HVQDIS. The full hadronic final state is modeled with Lund string fragmentation in CASCADE. HERA in its present configuration collides 27.5 GeV positrons (or electrons) with 920 GeV protons. However, most of the data presented here was taken before 1998 with a proton beam energy of 820 GeV. As usual, the event kinematics is described using the four-momentum transfer squared Q2 = — q2, the Bjorken scaling variable x = Q2/2p• q and the inelasticity y = p- q/p• i, where p, £ and q are the four-momentum of the proton, the incident positron and the virtual photon, respectively. The DIS regime is characterized by large momentum transfers, Q2 > 1 GeV 2 , resulting in a scattered positron inside the acceptance of the detector. 2
D*± production in DIS
HI has recently finalized the measurement of Dr± production using 18.6 p b _ 1 of data taken in 1996-19973. DIS events are selected in the kinematic range 1 GeV 2 < Q 2 < 100 GeV 2 and 0.05 D°nflow -¥ K~ir+TTsiow and its charge conjugate. A signal of 973 ± 4 0 D*^ mesons is obtained in the visible region pj(£)* ± ) > 1.5 GeV and •q{D*^) < 1.5. This translates into a visible cross section of 8.50 ±0A2(stat.)tljl(syst.)
±0.65(model)
nb.
The dependence of the calculated acceptance on model parameters of the Monte Carlo calculation, the charm quark mass and fragmentation, is quoted as a separate systematic uncertainty. NLO DGLAP predictions with HVQDIS using GRV98-HO parton densities range from 5.17 nb to 7.02 nb depending on the value of the charm quark mass and the fragmentation parameter ec. This range is obtained by going from a charm quark mass mc — 1.5 GeV and soft fragmentation, ec = 0.10, to a lower mass and harder fragmentation, m c = 1.3 GeV,e c = 0.035, covering the uncertainties in these parameters. The CASCADE program yields higher predictions ranging from 8.05 nb to 10.77 nb, using an un-integrated gluon density obtained from a fit to HI inclusive DIS data.
130 i
i
i
"l
r
C3 CASCADE
r
H1
H1
t
X
'Q
1
•Lr-
-L'..n,1v!
S I CASCADE ^ HVQDIS
-5
-4.4
-3.8
-3.2
-1.5
-2.6 -2 iog(x)
-0.9
-0.3
0.3
0.9
1.5 1D.
Figure 1. Differential D*^ cross section from HI vs x, Q 2 and t). The data are shown as points with error bars. The inner error bar is statistical only. Two QCD calculations are shown as shaded bands. The size of the bands represents the uncertainties due to m c and fragmentation.
The previously published ZEUS result 4 , measured in a similar kinematic region, 1 < Q2 < 600 GeV 2 ,0.02 < y < 0.7, and visible range, is ovi8 = 8.31 ± 0.31(stat.)toio(syst.)
nb.
The HI measurement is in good agreement with this value. The shapes of the differential distributions of x and Q2 are well described by both calculations (fig.l). The largest discrepancy between data and the NLO DGLAP calculation is observed in the region of positive pseudorapidities, T)(D*±), where CASCADE gives a better description of the data. Double differential cross sections show that the forward excess over the NLO DGLAP calculation occurs at lowest pt(D*±) and at all values of Q2. It has been verified that the difference between CASCADE and HVQDIS cannot be ascribed to the different treatment of hadronization. Preliminary results are available from ZEUS using 16.7 p b _ 1 of e~p data taken during the 1998-1999 running and 65.2 p b - 1 of e+p data taken 19992000. The higher beam energy is expected to increase the charm cross section by 5%. In the kinematic range 1 < Q2 < 1000 GeV 2 and 0.02 < y < 0.8, the preliminary visible cross sections results are 5 •
S3 0.7
1
i-
0.6
5? •X3
—v 0.45 -Ci £ 0.4
d)
.ZEUS 96/97 prel. semileptonic e"
•S" 0.35
0.5
r 0.4 r 0.3 n
•g
0.3 0.25
HVQDIS
0.2
0.2 0.1 0
1
(GeV)
o.a L
_
-2 10
200
i 7 -
,
m,= 1 . 3 / 1 . 5 / 1 . 7 GeV
0.15 0.1
P, (GeV)
T)
Figure 2. Kinematic properties of events in the semi-leptonic sample. The top row shows distributions of the hadronic energy, Q2 and Bjorken x, the bottom row shows transverse momentum and pseudorapidity of the electrons. Non-charm background is subtracted. The bands show the result of NLO calculations obtained with GRV94-HO parton densities and charm quark masses between 1.3 and 1.7 GeV.
for both e±p interactions, the differential cross sections in x and Q2 fall into the band of the NLO-DGLAP predictions obtained with different parton densities and values of mc. The ratio e~p over e+p cross section is largest at high values of a;, in the forward direction and for Q2 > 20 GeV 2 . 3
Semi-leptonic charm decays in DIS
Measurements of charm production at HERA have so far used fully reconstructed mesons. While this allows clean charm tags, it suffers from the small branching fractions. Due to the large branching fraction of semi-leptonic decays, leptons are an attractive signature for heavy quark production. For the first time at HERA, ZEUS has measured charm production using identified decay electrons. The advantage of the larger branching ratio is to some extent diminished by the strict cuts required to select a clean electron sample. Electrons are selected based on their energy deposition in the electromagnetic calorimeter and the specific energy loss measured in the central tracker.
132
Reconstructed 7 conversions are rejected. The kinematic properties of the selected events are shown in figure 2 after subtraction of residual contributions from hadrons and electrons from unreconstructed 7 conversion, Dalitz decays and bottom decays. The remaining distributions agree within errors with NLO DGLAP calculations. 4
D*^ p r o d u c t i o n in diffraction
Through its sensitivity to gluons, charm production can contribute to the understanding of diffraction. About 10% of the ep events occurring at HERA are diffractive, with no color flowing between the proton and the virtual photon. The signature is a large rapidity gap between the (quasi-) elastically scattered proton, and the recoiling hadronic system seen in the detector. In the resolved Pomeron model, diffractive events are interpreted as the scattering of the virtual photon on a colorless particle with partonic structure, the Pomeron (IP), emitted by the proton. This model successfully describes inclusive diffractive scattering where the quark densities of the Pomeron have been extracted. Charm production, like diffractive dijet data, probes the gluon content of the resolved Pomeron, which is almost unconstrained by inclusive diffractive DIS. Other models of diffractive interactions involve the perturbative exchange of a pair of gluons or color neutralization by soft interactions. HI has measured D*^ production in diffractive DIS using 19.1 p b - 1 collected in 1996-1997 8 . Diffractive events are selected by requiring no hadronic activity between r)max = 3.3 and the end of the detector acceptance at 77 = 7.5. A D*± signal of 46 ± 10 events is found in the kinematic range 2 < Q2 < 100 GeV 2 ,0.05 < y < 0.7 and the visible region PtiD**) > 2 GeV, |r/(D* ± )| < 1.5. This translates into a cross section of a(ep ->• e(D*X')Y)
= 246 ± 54(stat.) ± 56(syst.) pb.
The predictions of the resolved Pomeron model lie a factor 1.5-2 above this value for parton densities that are compatible with the diffractive inclusive and dijet data. The model overshoots the data at low values of XIP, where XIP is the momentum fraction of the proton carried by the Pomeron. An earlier measurement 9 by the ZEUS collaboration finds a preliminary cross section a(ep -> e(D*X')Y)
= 281 ± 41(stat.)t77l(syst.)
pb
in the region 4 < Q 2 < 400 GeV 2 ,0.02 < y < 0.7,1.5 < PtCD**) < 8 GeV, W D ^ ) ! < 1.5, xjp < 0.016 and j3 < 0.8. Because of the differences in the kinematic region, the experimental results cannot be compared directly.
133 However, when compared to the resolved Pomeron model using the same Pomeron structure input, the data to theory ratios agree within errors. Both experiments find that 6% of the total D*± production in the given regions of Q 2 ,?/,^!}**) and r)(Dt:k) is diffractive. 5
Conclusions
-D** production in DIS at HERA has been measured with improved precision in a large kinematic range. The experimental results of HI and ZEUS are consistent and are reasonably well described by the NLO DGLAP calculation. HI observes a deviation from this calculation in the forward region at very low transverse momenta. The CASCADE program using the CCFM evolution is in good agreement with the HI data. Preliminary results of a first measurement using electrons to tag semi-leptonic decays of charm from ZEUS are consistent with the D*± results. Preliminary D*± results from the much larger 1999/2000 dataset were obtained by ZEUS and are in agreement with the NLO-DGLAP expectation. However, the cross section in deep inelastic e~p scattering shows an unexpected small excess over the e+p cross section. Charm production in diffractive scattering can provide additional insight into the nature of the diffractive exchange. It is found to account for 6% of the total charm production in DIS. The measured cross sections are lower than those predicted by the resolved Pomeron model. The data analyzed so far are limited in statistics and cannot discriminate between different models of diffraction. References 1. B.W. Harris and J. Smith, Nucl. Phys. B452, 1009 (1995). 2. H. Jung and G.P. Salam, Eur. Phys. J. C19, 351 (2001). 3. C. Adloff et al. [HI Collaboration], hep-ex/0108039, submitted to Phys. Lett. B. 4. J. Breitweg et al. [ZEUS Collaboration], Eur. Phys. J. C12, 35 (2000). 5. J. Breitweg et al. [ZEUS Collaboration], Contributed paper, EPS2001, Budapest, Hungary, abstract 493 6. J. Breitweg et al. [ZEUS Collaboration], Contributed paper, ICHEP2000, Osaka, Japan, July 2000 abstract 853. 7. C. Adloff et al. [HI Collaboration], Eur. Phys. J. C20, 29-49 (2001). 8. C. Adloff et al. [HI Collaboration], Phys. Lett. B520, 191 (2001). 9. J. Breitweg et al. [ZEUS Collaboration], Contributed paper, ICHEP2000, Osaka, Japan, July 2000 abstract 874.
B o t t o m production at H E R A Monica TURCATO Dipartimento di Fisica dell'Universita and INFN, via Marzolo 8, Padova, Italy E-mail:
[email protected] (on behalf of the HI and ZEUS Collaborations) The production of bottom quarks, tagged by their semi-leptonic decay, has been studied in ep collisions at HERA with the ZEUS and HI detectors. Results are reported from both experiments on the total and differential bottom cross-sections.
1
Introduction
The study of heavy quark production in positron-proton scattering provides an important testing ground for QCD, and helps in understanding the structure, of the proton and photon. At the ep collider HERA with a centre of mass energy y/s = 300 GeV, heavy quarks are produced predominantly in collisions between a photon, emitted by an incoming positron, and a proton. The main contribution to the cross section comes from the exchange of an almost real photon (photoproduction, PHP), i.e. when the four-momentum squared, Q 2 , of the exchanged photon is Q2 ~ 0. If Q2 » 1 GeV2 (deep inelastic scattering, DIS) the cross-section is lower, but still measurable at HERA. Two types of leading order (LO) processes can contribute to heavy quark production: in direct photon processes, the photon acts as a pointlike particle, coupling directly to a parton from the proton, while in resolved processes it fluctuates into a state of quarks and gluons, with one of these partons taking part in the hard interaction. Resolved photon processes, which include also flavour excitation processes where a heavy quark is extracted directly from the photon or from the proton, are expected to be more important for PHP than for DIS. Here, the results obtained from ZEUS and HI analyses on bottom production, based on events tagged by its semi-leptonic decay into muons or electrons, are reported, in both the DIS and PHP regimes, as total and differential cross sections. The results obtained are compared to Monte Carlo simulations implementing LO matrix elements and to NLO QCD calculations. The Monte Carlo models used in the analyses are P Y T H I A J and HERWIG 2 , which implement both direct and resolved photon processes, A R O M A 3 , which has no resolved photon component, and C A S C A D E 4 , which contains only the direct photon component but implements the CCFM 5 gluon evolution in the proton.
134
135
2
H I P H P analyses
The HI collaboration has performed two measurements of bottom production in PHP, the first is published 6 using 1996 data {C = 6.6 p b _ 1 ) , while the latter is preliminary 7 , and uses 1997 data (C — 14.7 p b _ 1 ) when the vertex detector was fully commissioned. The two analyses are very similar in their methods, the main difference is the discrimination between signal and background. In the first, use was made of pT£x, the transverse momentum of the muon relative to the axis of the closest jet. In the second analysis, the impact parameter variable, 6, was also used: since a b particle has a longer mean life, the S distribution is expected to show a tail for positive values, coming from bottom events. A more detailed description of the first measurement of open bottom production by HI can be found elsewhere 6 , while here the second one is reported in detail. The selection of the data was made by requiring the presence in the event of at least two jets with ET > 5 GeV, reconstructed with the fc^-algorithm 8 and at least one muon with pj, > 2 GeV and 35° < #M < 130°, associated with one of the jets by the jet algorithm. The data sample was limited to the region Q2 < 1 GeV2 (photoproduction regime) with an inelasticity 0.1 < y < 0.8. For each muon candidate, the impact parameter 8 in the plane transverse to the beam axis and the p^ variable were calculated. Both p™1 and 5 (fig.l) distributions were plotted for the data and a likelihood fit 9 to the spectra was performed. The fits used the shapes of the distributions of b and c events from the AROMA Monte Carlo simulation, and those of fake muon events from a tagged photoproduction event sample fulfilling the same selection criteria as the signal sample, except that no muon identification was required. The results for the fractions fc obtained from the 6 distribution were fb = (26 ± 5)%, fc = (24 ± 12)% and ffake = (50 ± 5)%, while from the p ^ ' fit the fraction of bottom in the data was estimated to be fb = (27 ± 3%) (in this latter case the background from light quarks was kept fixed since charm and light quarks events could not be distinguished by the fit). Results from the two fits were in good agreement and were therefore combined in a likelihood fit to the two-dimensional distribution of these variables. The values found were then fb = (27 ±3%), fc = (27 ± 7 ) % and ffake = (46 ± 7 ) % , and were used to extract the visible cross section in the kinematic region defined by Q 2 < 1 GeV 2 , 0.1 < y < 0.8, p£ > 2 GeV and 35° < 6"1 < 130° (the same as for the previous analysis 6 ): avis(ep -*• bbX ->• nX') = 160 ± 16(stat.) ± 29(syst.) pb.
(1)
136
p,™i [ GeV ]
8 [ cm ]
Figure 1: p ^ ' (left) and impact parameter (right) distributions and their decomposition from the likelihood fit. In the p " 1 distribution, the normalisation for the fake muon contribution is fixed.
This value is in very good agreement with the published one: bbX -+ iiX') = 176 ± I6(stat.)±2£(syst.)
pb.
(2)
The two results are then combined to obtain: avia(ep ^ bbX ^/j,X')
= 170 ± 25 pb.
(3)
The prediction from the AROMA Monte Carlo is 38 pb, while CASCADE gives a value of 67 pb. NLO calculations by Prixione et al. 10 give a value of (54±9) pb, more than a factor 3 below the measured value. 3
H I DIS analysis
A similar analysis was carried out by the HI Collaboration 11 in the DIS regime. The kinematic region was denned by 2 < Q 2 < 100 GeV 2 , 0.05 < y < 0.7, and the same cuts on the muon as in the previous analysis. The fraction of bottom in the data was extracted by a combined fit on (5,^), as in the PHP regime, and found to be /& = (43 ± 8)%. The corresponding visible cross section is: °vis{ep -> bX -> fiX) = 39 ± 8(stat.) ± 10(syst.) pb.
(4)
The result obtained is again well above the theoretical expectations, since NLO calculations by HVQDIS 12 predict (11 ± 2 ) pb, AROMA 9 pb and CASCADE 15 pb.
137
4
Z E U S p™1 analysis, electron channel
The ZEUS Collaboration has published 13 the results of an analysis on bottom photoproduction with events tagged by its semi-leptonic decay into electrons, using C = 38.5 p b - 1 of data collected in 1996-97. The events were selected by requiring the presence of at least two jets with E^n^2' > 7(6) GeV and ^jeti(2) < 2.4; reconstructed with the for-algorithm 8 , at least one electron with pf > 1.6 GeV and | rf" |< 1.1, and 0.2 < y < 0.8. Other cuts were imposed in order to limit the data sample to Q2 < 1 GeV 2 . The bottom cross section was extracted by fitting the p ^ 1 distribution of the data to the sum of contributions from bottom and charm. The fraction of bottom found was /;, = (14.7 ± 3.8)%, in good agreement with the predictions by HERWIG (16%) and P Y T H I A (19%). By using that value of ft, the cross section for bottom production in the restricted region previously defined is calculated to be: ab^e~ (e+p -+ e+ dijet e~ X) = 24.9 ± 6 . 4 ^ j pb. LO Monte Carlo predictions are 8 pb
(HERWIG)
and 18 pb
(5)
(PYTHIA
and
CAS-
CADE).
This cross section was then extrapolated to the parton level in a restricted range of the transverse momentum and pseudorapidity of the quark using H E R in WIG and P Y T H I A Monte Carlo models. The value found for p^ > p™ = 5 GeV, | rib |< 2, Q 2 < 1 GeV 2 and 0.2 < y < 0.8 was: aext(ep -> e+bX) = 1.6 ± OA(stat.)±°035(syst.)t°0\{ext.)
nb,
(6)
where the central value was calculated by using HERWIG to extrapolate and the value obtained with P Y T H I A was included in the extrapolation systematic uncertainty. The CASCADE prediction for this cross section is 0.88 nb, while NLO calculations by Frixione et al. 10 give a value of (0.64+g Jo) n b ; both predictions are below the experimental value. 5
Z E U S py 1 analysis, m u o n channel
The ZEUS Collaboration has also presented some preliminary results 14 on bottom photoproduction obtained with events tagged by its semi-leptonic decay into muons. Events were required to have at least two jets reconstructed by the fey-algorithm with one of them containing a muon, associated with it by the jet algorithm. The kinematic region was defined to be Q 2 < 1 GeV 2 , 0.2 < y < 0.8, ^ T e t l ( 2 ) > 7(6) GeV, r^et1^ < 2.5, p» > 3 GeV and —1.75 < rj1* < 2.3. The difference between this analysis and the previous
138 ZEUS •
ZEUS •
ZEUS prel.) 9 6 - 9 7
0.2• D°7r+ ->• (K~ir+)n+(+c.c.) and D° -> K~ir+ (+c.c). It is assumed that the D* ± and D° are produced with equal probabilities and only in fragmentation and D° is produced either directly (f(c) -> D° 4- X) or via D* decays. This leads to: v
(atot(D0)/ £>°7r+)
v
'
where BR is the branching ratio and crtot is the measured cross section. In this paper, the analysis 1 is based on D** and D° events with an almost real photon (virtuality, Q2 sa 3.10 - 4 GeV 2 ) in a photon-proton center of mass energy, W, in the range 130 < W < 295 GeV. Using the AM = M(D*) a
D * ± ( 2 0 1 0 ) is referred to as D* for the rest of this paper.
140
141
M(D°) tag the sample is then further divided into D° mesons arising from and not from D* mesons. After this division there were 1180 ± 3 9 events with a D° meson from a D* and 5223 ± 185 inclusive D° meson events and the resulting value for P„ in the full phase space is: P„ = 0.546 ±0M5(stat)t°0f2l(syst). This is in good agreement with the values of 0.57 ± 0.05 and 0.595 ± 0.045 2 measured in e + e _ annihilations. 3
Charm with Jets
In order to understand charm production further, the inclusive jet cross section for events containing a D* meson has been measured. Here the nonperturbative effects, which are currently poorly understood, are more suppressed than in inclusive charm production. Cross sections as a function of the pseudorapidity (rf>et) for D* jet and non-D* jet samples are shown in Z E U S 1 9 9 6 + 9 7 Preliminary
l).!
<W
Figure 1. D* and non-D* jet cross sections dtr/drfjn of D* photoproduction events with the kinematic cuts: Q2 < 1 GeV2, 130 < W < 280 GeV, pi" > 3 GeV and \riD* \ < 1.5. The upper plots (a) and (b) are for E3tet > 6 GeV and the lower plots (c) and (d) are for Ei" > 8 GeV. The inner error bars represent the statistical errors, and the outer bars the quadratic sum of statistical and systematic uncertainties. The solid and dotted curves are NLO predictions using renormalisation and factorisation scales set to /IR = mj_;/*F = 2m.x with charm mass mc = 1.5 GeV and (IR = 0.5m±, mc = 1.2 GeV respectively.
Fig. 1. The D* jet is denned to be that jet nearest to the D* in T) — <j> (AR = y/{(f>jet — 4>D*)2 + (Tjjet — VD*)2 < 0.6) space. The remaining jets in the
142
event are called non-D* jets. In Fig. 1, the NLO ("massive charm" scheme 3 ) calculations underestimate both jet cross sections by approximately a factor of two. Even with an extreme set of parameters, NLO fails to describe both the shape and the absolute cross section. The differences in shape and normalization for both D* and non-D* jet cross sections cannot be accounted for by the hadronisation corrections. 4
Charm with Dijets
Given the discrepancies between data and the NLO prediction, it is of interest to probe the kinematics of charm production in more detail, by measuring the dijet cross section. The variable (x°BS) related to the momentum fraction of the parton from the photon, is denned as the fraction of the photon's energy participating in the production of the two highest transverse energy jets: jetl,2 &T PBS _ ^jetiq^T
x.7
,^
~ 2yEe where yEe is the initial photon energy. The measured differential cross section, da/dx°BS is compared with HERWIG MC (normalised to the data) and predictions from NLO massive charm calculation 3 in Fig. 2. There is a substantial tail at low x°BS, which requires a LO-resolved component to describe the data. The predictions from NLO, where charm is not treated as an active flavour in the photon structure function, significantly underestimates the data at low x°Bs. Using an extreme set of parameters in the calculation yields a larger cross section at low x°BS, but is still below the data. Further studies were made to probe more directly the production mechanism. This was done by considering the differential distribution 4 dN/d\ cos 9* |, where 6* is the angle between the jet-jet axis and the beam direction in the dijet rest frame. This distribution is sensitive to the parton dynamics of the underlying subprocesses. The distribution was considered for direct-enriched (x°BS > 0.75) and resolved-enriched (x°BS < 0.75) samples. Additional cuts (as shown in Fig. 3) on the dijet invariant mass, Mjj, and the average pseudorapidity of the jets, |»j|, were checked to ensure an unbiased phase space region. The measured differential distributions dN/d\cos9*\ for both x°BS < 0.75 and They are significantly different, which XOBS > o 75 gj-g s h o w n m pjg 3 reflects the different spins of the quark and gluon propagator. This is well reproduced by the PYTHIA prediction. The steep rise towards high | cos0*| values of the resolved dijet charm events, consistent with gluon exchange, provides strong evidence that the bulk of the resolved contribution is due to charm excitation in the photon, rather than to the more conventional resolved process gg -> cc.
143 ZEUS 1996+97
ZEUS
Figure 2. (left) The differential cross section da/dx®BS for dijets with on associated D* meson withpf* > 3 GeV, \nD* \ < 1.5, 130 < W < 280 GeV, | ^ ' e ' | < 2.4, E%n > 7 GeV and £^f' 2 > 6 GeV. The experimental data (dots) are compared to (a) HERWIG MC and (b) a parton level NLO calculation with the parameters shown in the plot. Figure 3. (right) The differential distributions dN/d\cos6* | of the data (dots) with p £ * > 3 GeV, \nD'\ < 1-5, 130 <W < 280 GeV, \rfet\ < 2.4, Eign>2 > 5 GeV, Mjj > 18 GeV, \rj\ < 1.2 and of PYTHIA MC simulations (lines). Results are given separately for direct photon (open dots/dashed lines) and for resolved photon (black dots/full histogram) events. All the distributions are normalised to the resolved data distribution in the lowest 4 bins.
5
Conclusions
Heavy-flavoured jets provide an important tool for understanding the heavy quark production mechanism. Measurement of Pv confirms the universality of the charm fragmentation. However inadequacies in current NLO calculations in describing heavy-flavour jet production are clearly evident. The | cos 9* | distribution for dijet events with a D* shows a clear signature of gluon propagator for events with x°BS < 0.75, suggesting strong evidence of charm in the photon. References 1. ZEUS Coll., Study of Inclusive Lfi Photoproduction at HERA. Paper 501, EPS HEP01, Budapest, Hungary, July 12-18, 2001. 2. OPAL Coll., K.Ackerstaff et al, Eur. Phys. J. C 5, 1 (1998); ALEPH Coll., R.Barate et al, Eur. Phys. J. C 16, 597 (2000). 3. S.Prixione et al, Phys. Lett. B 384, 633 (1995); S.Frixione et al, Nucl. Phys. B 454, 3 (1995). 4. ZEUS Coll., Dijet Angular Distributions in D* Photoproduction at HERA. Paper 499, EPS HEP01, Budapest, Hungary, July 12-18, 2001.
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4 Total Cross-Sections and Diffraction
Session Convenors: G. Pancheri and M. Wadhwa
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S T U D Y OF E+E-
A N N I H I L A T I O N I N T O H A D R O N S AT VEPP-2M
R.R. AKHMETSHINA, E.V. ANASHKINA, V.SH. BANZAROVA, L.M. BARKOV A , N.S. BASHTOVOY A , A.E. BONDAR A , D.V. BONDAREV A , A.V. BRAGIN A , D.V. CHERNYAK A , S. DHAWAN D , S.I. EIDELMAN A ' B , G.V. F E D O T O V I C H A B , N.I. GABYSHEV A , D.A. GORBACHEV^ 4 ' 3 , A.A. GREBENUK- 4 , D.N. GRIGORIEV A ' B , V.W. HUGHES D , F.V. IGNATOV A , B , S.V. KARPOV 4 , V.F. KAZANINE A , B.I. KHAZIN A ' B , LA. K O O P A ' B , P.P. KROKOVNY A , L.M. KURDADZE A , A.S. KUZMIN A ' B , LB. LOGASHENKO A ' c , P.A. LUKIN A , A.P. LYSENKO A , K.YU. MIKHAILOV A , J.P. MILLER C , A.I. MILSTEIN A ' B , I.N. NESTERENKO A , V.S. OKHAPKIN" 4 , A.S. P O P O V 4 , T.A. PURLATZ A , B.L. ROBERTS 0 , N.I. R O O T 4 , A.A. RUBAN^1, N.M. RYSKULOV A , YU.M. SHATUNOV A , B.A. SHWARTZ A ' B , A.L. SIBIDANOV A , V.A. SIDOROV 4 , A.N. SKRINSKY A , V.P. SMAKHTLN A , I.G. SNOPKOV A , E.P. SOLODOV A ' s , RYU. STEPANOV A , A.I. SUKHANOV A , J.A. THOMPSON^, YU.Y. YUDIN A , S.G. ZVEREV A A
Budker Institute of Nuclear Physics, Novosibirsk, 630090, Russia Novosibirsk State University, Novosibirsk, 630090, Russia c
Boston
D
E
University, Boston, MA 02215, USA
Yale University, New Haven, CT 06511, USA
University of Pittsburgh, Pittsburgh, PA 15260, USA
Precise knowledge of R(s) = hadrons) / a ( e + e _ —> /x+/i~") is important in a variety of problems in particle physics. While at high energies R(s) can be calculated within the framework of QCD, at low energies it has to be measured in experiment. In 1992-2000 the data with integrated luminosity of 70 p b - 1 were collected in the energy range 0.36 < v'* < 1.4 GeV with the CMD-2 and SND detectors at the VEPP-2M collider in Novosibirsk. The status of the R(s) measurements by these groups will be presented.
1
Experiment and detectors
Measurements of the total cross section of e+e~ annihilation into hadrons at low energies are of great interest for different purposes. The precise knowledge of this value is necessary for calculation of hadronic vacuum polarization contribution to anomalous magnetic moment of the muon (g — 2)M and running value of the fine structure constant a ( M | ) x .
147
148
:i lt\ T
^ v
i5*
; f 71 717E f t + - 0 C . ; 7C 71 7C 7C -?...JC\c.JE\i
: f K+K"
:
i .
, ,
/ I
.. . in
1400
,MeV
Figure 1. Overview of hadronic cross-sections for major hadronic processes at the V E P P 2M energies.
The experiments on VEPP-2M electron-positron collider2 with CMD-2 detector started in 1992. The SND detector start to collect statistics at 1995. The high luminosity of the accelerator (up to 3 • 10 30 cm~2s~1 at
^
O 10 3-
(b)
™ a) > LU
10
l u
2
10 -
'*&. 50
100 Wvis[GeV]
10
-
50
Sk\ w$MM
100 150 W v i , [GeV]
Figure 2. The hadronic visible mass, Wvls, as measured by OPAL 2 and L 3 3
The systematic uncertainties are evaluated for each W11 bin. The most important contribution comes from the Monte Carlo program used to model the process, in the following this error will be considered only when comparing the data with theoretical models. To extract the total cross section of two real photons, the luminosity function £ 7 7 8 is calculated and the hadronic two-photon process is extrapolated to Q2 = 0. A further uncertainty of ~ 5% must be added to the systematic error due to different possible choices of the form factors. In Figure 3 (left) the L3 and OPAL results are compared using only experimental statistics and systematic errors. The agreement is very good in contrast to the dispersion of previous results 9 , obtained at low energy colliders. 3
Discussion
The total cross sections for hadron-hadron interactions show a characteristic steep decrease in the region of low centre-of-mass energy, followed by a slow rise at high energies. A Regge parametrisation of the form11 crtot =Ase
+ Bs-71
(1) accounts for the energy behavior of all hadronic and photoproduction total cross sections, the powers of s being universal 12 (e = 0.093 ± 0.002 and r\ — 0.358 ± 0.015). The coefficients A and B are process and Q2 dependent. If photons behave predominantly like hadrons, this expression may also be valid for the two-photon total hadronic cross section, with s = W2.
155
800
-,600 -
800
- L3 fit OPAL fit
9
C
400
•L3 *OPAL a Pluto
200
200-
• L3 • OPAL
ATPC-2Y
oMD-1
10
50
Wn[GeV]10
100 Ww[GeV]
150
Figure 3. (left) T h e total hadronic cross-section for real photons as measured at L E P 2 ' 3 and at previous colliders 9 . The prediction of Reference 10 is superimposed to the data, (right) The Regge fits,with e free, as given by OPAL 2 and L3 3 , are superimposed to the data.
L3 Fixed e L3 Fixed e L3 Free e OPAL Free e
W11 interval (GeV) 5-65 5-185 5-185 10-110
£
0.093 0.093 0.225 ±0.021 0.101 ±0.022
X2/d.o.f. 5.3/3 55/6 12/5 68/3
CL 0.15
io- 9 0.04
Table 1. Results of the Regge fits fixing or not the parameter e. The parameter 77 is fixed to the universal value, the coefficients A, B are free parameters. OPAL uses only statistical errors, while L3 uses the full experimental uncertainty drawn in Figure 3.
Several Regge fits were performed on the data, some of them are reported in Table 1. The ones where £ is a free parameter are presented in Figure 3 (right). The exponent r\ is always fixed to the universal value, since the low mass range is too small to be sensitive to this parameter. For low Win values both L3 and OPAL data are well described by the universal parameters, whereas, using the whole W 7 7 range, the fit with fixed exponents does not represent the er77 energy dependence. By leaving e free, the fitted value is more than a factor two higher than the universal value. This conclusion is independent of the Monte Carlo model used to correct the data.
156 L3 183-202 GeV 800
800-
L3
i>
S 600-
600
400
200
0
^^c—
400
Minijet
— B. BadeleketalP.Desgrotardetal. - - C . Bourrely et al.
50
100
W w [GeV]
200
15C
50
100
15C
W w [GeV]
Figure 4. Predictions of some model 5 , 1 3 ' 1 5 compared to the L3 data. The measurements include experimental errors, statistical and systematic (full error bars), and uncertainties due to Monte Carlo corrections (dotted error bars). The band in the minijet model 1 5 (right) corresponds to different choices of the model parameters, consistent with photoproduction data.
Several models can be compared to the cross-section measurements, some example 5,13 are given in Figure 4(left). Their predictions for the twophoton total cross section are typically derived from measurements of protonproton and photoproduction total cross sections via the factorization relation: e+e~ + hadrons has been studied for the first time at LEP2 energies with both scattered e + and e~ detected at very low Q 2 , measured by the DELPHI VSAT. A reasonable agreement between data and full simulation is demonstrated and the total 77 hadronic cross-section is estimated for the 77 center of mass energy up to 100 GeV.
1
The VSAT Detector and Background Processes
The Very Small Angle Tagger (VSAT) detector covers an azimuthal angle between 3 and 10 mrad, resulting in a Q2 region from 0.02 to 0.8 GeV at LEP II energies. This is an attractive region for 77-studies as the error of interpolating the total cross-section to zero Q2 is small and at the same time the cross-section is large enough to detect both outgoing leptons from with reasonable statistics. The VSAT detector *• 2 consists of four modules placed on each side of the beam-pipe ±7.7 meters from the interaction point. The energy resolution of the VSAT detector is about 4.5% at 100 GeV, resulting in a precise measurement of the invariant mass of the 77-system in double tag 77-events. About 510 pb~l of data collected from 1998, 1999 and 2000 were used in this study, with about 320 expected double tag 77-events after cuts on the hadronic system (W > 3 GeV and at least 3 charged tracks). Unfortunately, there are two huge background processes that disturb the data collected. The VSAT detector has however also a very precise measurement of the position of the incoming particles in x and y (about 200 /im), which allows for signal and background separation. One obvious background is a bhabha event in coincidence with a no-tag 77-event. These events are however very symmetric and can be totally rejected without any significant loss of the 77-signal (less than 1.5%). More troublesome is the off-energy background electrons, which can either be in coincidence with a single tag or a no-tag 77-event. To get reasonable purity in the final data heavy cuts are imposed in the y-energy phase space (Fig. 1) of the VSAT detector. A purity above 75% in the resulting double tag sample could then be obtained with less than 40% of signal loss (Fig. 2).
158
159
Figure 1: The off-energy background come from two different locations, which result in a complicated structure in the VSAT yposition and energy phase space.
Figure 2: The impact of the off-energy background cuts on the off-energy background and the 77-Monte Carlo sample (single tag).
After the cuts 263 double tag events were seen with an expected background of 66 events. This is presented in Table 1 along with the expected purities for each year, the same numbers are also shown for the single tag sample. In total about 200 double tag and 26000 single tag 77-events are thus expected after the cuts. Year 1998 1999 2000 Tot
Lum. 138 220 152 510
D-tag 78 111 74 263
Table 1: The luminosity (pb
2
1
77 56 83 58 197
Purity 0.72 0.75 0.79 0.75
77-loss 0.43 0.32 0.37 0.36
Single Tag 8650 13273 8487 30410
Purity 0.84 0.86 0.88 0.86
) , number of double and single tag events in VSAT after cuts.
The T W O G A M Monte Carlo
In this analysis the TWOGAM 3 generator was used, which implements three different models: a soft interaction term described by the generalized Vector meson Dominance Model (VDM), a perturbative term described by the Quark Parton Model (QPM) with direct quark exchange, and a term for the hard scattering of the partonic constituents of the photon, the so-called Resolved Photon Contribution (QCD-RPC). The Gordon-Storrow parameterization with a pmin _ 2.05 ± 0.020 GeV/c cut-off value was used to separate the RPC from the non-perturbative contribution. This parameter was adjusted by comparing MC and data for different distributions. The invariant mass of the hadronic system is shown for both the
160
different MC-components and the data in Fig. taking the ratio between data and MC, and the flat distribution were taken. From Fig. 4 it is 2.05 for p^in is to prefer, rather than the value
Figure 3: The invariant mass distribution of the different model contributions and data.
3. The p™'n was adjusted by value that produced the most clear that the value of about of 1.88 previously used 4 .
Figure 4: The ratio between data and and MC for different values of pj™".
The TWOGAM MC was generated both with and without radiative corrections, with no major difference in Fig. 4. The double tag data do however show better agreement between data and MC with radiative correction than without and was therefore used in this analysis. Agreement within errors between data and MC was found, both in the VSAT double and single tag sample. The TWOGAM generator could therefore be used to extrapolated VSAT data to the total cross-section. The relative contributions of the different components as a function of Q2 and W can be seen in Fig. 5 and Fig. 6.
Figure 5: The relative contributions of the different components in TWOGAM as a function of Q 2 .
Figure 6: The relative contributions of the different components in T W O G A M generator as a function of W.
161 The VSAT+STIC (The STIC detector has 0-coverage between 2-10 degrees, with a Q2 mainly between 10 and 120 GeV2) double tag data was also probed for the first time. About 220 events were found after cuts on the VSAT data, with an expected background of about 20 events. Reasonable agreement with TWOGAM MC were also found for this data sample. 3
Results
The VSAT data were divided in bins with equal statistics to calculate the total cross-section with the TWOGAM generator with similar errors. The luminosity function was calculated and the data was extrapolated to Q2 = 0 with the GVDM model. The total cross-section as a function of Q2 and W can be found in Fig. 7 and Fig. 8. From Fig. 8 it is clear that the VSAT double tag data extrapolated with TWOGAM show better agreement with L3 and OPAL data unfolded with PYTHIA than with PHOJET.
Figure 7: The total cross-section of VSAT (at low Q2) and VSAT+STIC double tag data as a function of Q2.
Figure 8: The total cross-section of VSAT double tag data as a function of W (0.02 < Qmax < °- 8 GeV2).
References 1. 2. 3. 4.
S. Almehed et al. NIM A305(1991)320 P. Abren et al. (DELPHI Col), Phys Lett, B342(1995) 402. S. Nova, A. Olgheaski and T. Todorov. DELPHI Note 90-35 (1990). N. Zimin, Proc. PHOTON 97, Egmond aan Zee, eds. A. Buijs and F. Erne, World Scientific, Singapore, (1997) 74.
IMPACT FACTORS OF VIRTUAL P H O T O N S AT NLO
V. S. FADIN Budker
Institute
for Nuclear
Physics and Novosibirsk Novosibirsk, Russia E-mail:
[email protected] State
University,
630090
For a consistent description of small x processes in the BFKL approach one needs to know impact factors of colliding particles with the same accuracy as the kernel of the BFKL equation. The kernel is known now in the next-to-leading order (NLO), so that the problem of determination of the impact factors in the NLO became urgent. The results obtained up to now for the impact factors of highly virtual photons are briefly reviewed.
In the BFKL approach 1 the total cross section for the process A + B —> A' + B' at large center of mass energy -y/i is written as .
[B+i°° cLo f d2qA Js-ioo
f d2qB ( s \
2TTI J 2%qX J 2irqg
u
_
\s0J
(1) where the vector sign is used for momentum components transverse to the plane of the initial momenta (PA,PB), «O is a certain energy scale, the impact factor 7. is that it can be calculated "from the first principles" in perturbative QCD. Knowledge of the NLO $ 7 . is important not only when the BFKL dynamics is completely developed, but also in the case when only a few first terms in the BFKL series do contribute (that probably is the case at modern energies). In this case the NLO $ 7 » determines a size of radiative corrections to the non-decreasing with s contributions to the total cross sections. The impact factor $ 7 « is expressed in terms of the photon-Reggeon interaction amplitudes. In the leading order (LO) this expression is quite simple:
$(%-) r[q)
l =
v
f — \r{0)cD
yfN^lj^J
\2do -
(2)
2-K I V H - W WW
W
where the number of colours Nc = 3 for QCD, r L ^
162
^ is the amplitude of
163
the qq production in the ~f*R collision, evaluated in the Born approximation, M2 is the squared mass of the produced pair, dpqq- is its phase space element. The sum {a} is over all discrete quantum numbers of the produced pair. In the LO the Reggeized gluon interacting with J*(PA) acts as the ordinary gluon with polarization vector ps/s, s = 2PAPB- In this order T^.R ^ may be written as r
? f i - ^ = (20 f are the matrix elements of the colour generator, x± are the fractions of the longitudinal momenta and k± are the transverse momenta of q/q, x+ + X- = 1, k+ + fc_ = q, \I/ 7 . ( i , k) means the qq component of the photon wave function, 7 V
'
(27r)f V
2
k*+x(l-x)Q*
where eq is the electric charge of the quark, e7» is the polarization vector of the photon and — Q2 is the photon virtuality. Therefore the impact factor can be presented as $W(^ = j f
1
d
B
|c?r||^e^*r(x
>
^|
a
^^-3|i-e-«n
a
,
(5)
that makes possible the colour dipole picture of the high energy 7* interaction. The NLO is not so simple. Firstly, 3>7. is expressed in terms of T^,R_^f in more complicated way4 and depends on the energy scale SQ in (1). For So = q 2 we have: 1
„
f dM2f
M?7.
{/}
( 2 ^ - 1 J q2{q, - q)2
">
W
q2{q, - q)2 '
(6)
where the sum {/} is over all discrete quantum numbers of the contributing states, which are now qq and qqg; SA —* 00 is the cut off, which becomes necessary since the integral over M2qg is divergent (of course, the dependence on «A vanishes due to the cancellation between the first and the second terms); D = 4 + 2e is the space-time dimension taken different from 4 to regularize the infrared divergences at intermediate steps. The second term in (6) is the substraction of the contribution of the gluon emission outside the fragmentation region of 7*, which was taken into account already in the LO.
164
Secondly, in the NLO the Reggeon differs essentially from the gluon, so that, from the first sight, in order to find T^.R ^ in the NLO one needs to calculate the radiative corrections not only to the amplitude of the process 7* qqq as well. It is possible, however5,6, to escape this calculation introducing the Reggeongluon-gluon vertex 19
7 » i A )
L
ab
+p%(2k2 + hT
-
-9fi"P2-(k2-k1)
-
rfph
+ k2)v
2(fci+fc 2 ) : j W ( | P 2 - ( * l - * 2 ) | - f l f l ) ) Pi • (fci -
(7)
k2)
where T c are the colour generators in the adjoint representation, k\,2 are the gluon momenta, a, b and fi, v are their colour and vector indices, with (3Q —> 0, and adding the universal (process independent) contribution A
r
c
2
c
= LjW(-q )rM 4>((30),
-g 2 r 2 (e) w (t) = (-t)-T(2e)'
72N,
(1)
r(i-e) (4^)2+e '
(8) where w^'(t) is the one-loop gluon trajectory and
4>{z)=]nz-±Ml)-
i,{\-t)}-iP{e)
+ i>{2e), i>{x)
r;(x) T{x)-
(9)
The calculation of the VL.R^ , in the NLO is rather lengthy and tedious. It was performed by two group of authors 7,8 . The results were presented in different forms. In 8 the answer is given in terms of elementary functions and dilogarithms. In 7 some integrals are left in order to have a possibility to use usual Feynman parametrization and to change orders of integrations over all Feynman parameters at subsequent calculation of the impact factor. In both forms the results are too complicated to be presented here. The singular part of the correction was found earlier5:
(Tr R—fqq)sing
-2 + - [ln(xix2q
2
)
r(0)c L
- £ G •;{•"*-8)
(10)
-y*R-qq-
It generates the singular contribution to $ 7 », which can be presented as
_M! f
d^)(q)
(N? - 1)
1
I,
I
- I \VL[xxx2q
-2N
) -
3
-
I..J4. X\X2q
(11)
165
and which is cancelled with the singularity of the contribution of the real emission5, that is the impact factor is infrared safe. The amplitude r^. f l 5 entering into the sum in (6) must be known only in the Born approximation. It was calculated recently 9 ' 10 , so that in order to complete the calculation of $y-{q) one needs to perform the integration in (6) over the transverse momenta of the produced particles and over their fractions of the photon momentum. The problem is very complicated, so that all possible simplifications are desirable. One of them is related with the analytical properties of QCD scattering amplitudes. The first term in (6) can be presented as the integral from the 7* .ft forward scattering amplitude over the s-channel cut, which can be transformed into the integrals over the u-channel cut and over the large circle. Considerable simplifications of the calculations can be reached performing such transformation for contributions of some diagrams to the 7*.ft forward scattering amplitude 10 . Acknowledgments I am thankful to D.Yu. Ivanov, M.I. Kotsky and A.D. Martin, my collaborators in work on the impact factors. The work is supported in part by INTAS and in part by the Russian Fund of Basic Researches. References 1. V.S. Fadin, E.A. Kuraev and L.N. Lipatov, Phys. Lett. B 60, 50 (1975); E.A. Kuraev, L.N. Lipatov and V.S. Fadin, Z. Eksp. Teor. Fiz. 7 1 , 840 (1976); 72, 377 (1977); Ya.Ya. Balitski and L.N. Lipatov, Sov. J. Nucl. Phys. 28, 822 (1978). 2. V.S. Fadin and L.N. Lipatov, Phys. Lett. B 429, 127 (1998). 3. M. Ciafaloni and G. Camici, Phys. Lett. B 430, 349 (1998). 4. V.S. Fadin and R. Fiore, Phys. Lett. B 440, 359 (1998). 5. V.S Fadin and A.D. Martin, Phys. Rev. D 60, 114008 (1999). 6. V.S. Fadin and R. Fiore, to be published in Phys. Rev. D 64 (2001); hep-ph/0107010. 7. V.S. Fadin, D.Yu. Ivanov and M.I. Kotsky, in: New Trends in High Energy Physics, ed. L.L. Jenkovsky (Kiev, 2000, pp.190-194); hepph/0007119; to be published in Yad. Fiz., hep-ph/0106099. 8. J. Bartels, S. Gieseke and C.F. Qiao, Phys. Rev. D 63, 056014 (2001) , hep-ph/0009102. 9. J. Bartels, S. Gieseke and A. Kyrielreis, hep-ph/0107152. 10. V.S. Fadin, D.Yu. Ivanov and M.I. Kotsky, in preparation.
M E A S U R E M E N T OF T H E H A D R O N I C CROSS SECTION OF D O U B L E TAGGED 77 E V E N T S AT A L E P H G. PRANGE Fachbereich
Physik, Universitat Siegen, 57068 Siegen, E-mail:
[email protected] Germany
The interaction of virtual photons has been investigated using double tagged 7*7*events with hadronic final states, taken by the ALEPH experiment at e + e - centerof-mass energies s/see = 189 — 208 GeV. The measured cross section is compared to the PYTHIA and the PHOT02 Monte Carlo Model, a NLO QCD calculation and BFKL calculations. The NLO QCD prediction is largely consistent with the data. The LO-BFKL predictions are ruled out by the data while NLO-BFKL calculations are in resonable agreement with the measurement.
1
Introduction
Interactions of two photons can be studied at e+e~ colliders by investigating the reaction e + e~ —> e+e~/yy —> e+e~X where X denotes a hadronic final state. This analysis focuses on the interactions of virtual photons by selecting only double tagged events, i.e. events where both scattered electrons" are detected. Differential cross sections for this process have been measured as a function of all important observables of the final state. 2
Theoretical framework
The kinematics of electron induced 7*7* interactions is sketched in figure 1, the terms in brackets representing the 4-momenta of the particles.
Figure 1. Kinematics of 7*7* interactions at a e + e - collider.
"Electrons and positrons are generally referred to as electrons.
166
167
The kinematics can be described by the dimensionless Bjorken variables of deep inelastic scattering: Qi
n
E
'i
2^A
,,\
The hadronic invariant mass W 7 7 used in these definitions is obtained from the energies and the momenta of the final state hadrons. The virtualities of the photons Q2 = -q2 = -{pi -p'i)2 > 0 are given as: Ql = 2EbeamE'i(l
- cos(0;))
(2)
for 6i S> meiectron/^i- The squared e + e~ center-of-mass energy is given by See = (Pi
+P2)2-
According to equation 2 it is possible to select interactions of virtual photons by requiring that the scattered electrons are measured at large angles. The accessible range of virtualities and therefore the phase space depends on the region where electrons can be detected. For the comparison of the data with a BFKL calculations we define the following quantity: Y = l n f ^ - J , with see/s0 = seeyiy2/y/QlQl « W^/y/QlQl, where the approximation requires W2^ » Q2. The the two-photon cross section cr 7 . 7 . can be extracted from the measured e + e~ cross section by using the Two-Photon-Luminosity function £ T T 3
Event selection
The event selection is performed in three stages: detection of scattered electrons, verification of the presence of a hadronic system, and background reduction. 1. Detection of scattered electrons: The luminosity detectors SICAL and LCAL are used to detect scattered electrons. Thus the polar angular range is restricted to di G [35-55] mrad (SICAL) and 0j 6 [60 -155] mrad (LCAL). The energy threshold is set to E\ > 0.3.Ebeam- The energy of the detected scattered electrons (tagged electrons) is also referred to as Et&g = E't, the polar angles as 8tas = 6i. 2. Verification of the hadronic system: To ensure that the final state is a hadronic system and not a lepton pair, at least three charged particles are required. The visible mass of the hadronic system W 7 7 has to be larger than 3 GeV.
168
3. Background reduction: The total visible energy Etot — E[ + E'2 + ©hadrons should be larger than 70% of the nominal center-of-mass energy. A cut on the angle between the scattered leptons $ < 179.5° is imposed to reject remaining Bhabha events. With these cuts 891 events were selected in the data with 206.1 expected background events. The three main sources of background are: Double tagged leptonic decaying 77 events, superpositions of single tagged 77 events and off-momentum electrons from beam-gas interactions and annihilation events (e+e" ->• qq). Because of the limited statistics in the data a simple bin-by-bin method is applied to correct for detector inefficiencies. The correction factors are calculated from the Monte-Carlo simulations. The total cross sections of the Monte-Carlo generators are normalised to the measurement. 4
Results
The differential cross section as a function of the mass of the hadronic system W 7 7 and as a function of Y are shown in figure 2. The measured spectrum is
Figure 2. Differential cross sections as a function of W^ and Y.
well described by the Monte-Carlo simulations PYTHIA and PHOT02. The NLO-QCD calculation [1] predicts a slightly too low total cross section but the shapes of the spectra are in good agreement with the measurement. Finally the data are compared to a BFKL predictions. Since these calculation assume that both photons have the same virtuality, a further cut was added to the event selection: | logQ\/Ql\ < 1.0. This ensures, that the ratio of the virtualities is close to one. The whole analysis, including systematics,
169
was redone with this new cut. The agreement between ALEPH data and the Monte-Carlo simulations is as good as in the original analysis, the statistic in data is reduces by 40%. The resulting cross section as a function of Y is compared with BFKL predictions. Leading order calculations [2] (LO-BFKL) are overshooting the data. NLO-BFKL [3] results, predicting only a slight enhancement at high values of Y with respect to the QPM model, are in resonable agreement with the measurement. 5
Conclusions
The interactions of virtual photons have been studied with data taken by the ALEPH experiment. The data sample was taken at e + e~ center-of-mass energies between 189 GeV and 208 GeV and corresponds to an integrated luminosity £ = 640 pb^ 1 . The differential cross section for e + e~ —• e + e~7*7* —> e + e _ X , where X stands for a hadronic final state, has been measured as a function of various event observables. The used phase space is defined by the electron energies Ei,2 > 0.3.Ebeam, the polar angles of the electrons 35mrad < #1,2 < 155mrad, and the mass of the hadronic system W 7 7 > 3 GeV. The PYTHIA Monte-Carlo generator describes all measured aspects of the process very well. PHOT02 simulates the phase space used in this analyses mainly according to the program written by J.A.M. Vermaseren. PHOT02 gives a very good description of nearly all the measured quantities. Only the distribution as a function of the azimuthal angle between the scattered electrons A $ can not be reproduced. The results are in good agreement with L3 and OPAL measurements [4]. The NLO QCD prediction yields a slightly low cross section. This calculation gives a very good description of the shape of the measured distributions. The LO-BFKL predictions are ruled out by the data while NLO-BFKL calculations are in resonable agreement with the measurement. References 1. M. Cacciarim, V. D. Duca, S. Frixione, Z. Trocsanyi: JHEP 02 (2001), p. 029 2. J. Bartels, C. Ewerz, R. Staritzbichler: Phys. Lett. B492 (2000), p. 56 3. V. T. Kim, L. N. Lipatov and G .B. Pivovarov: hep-ph/9911242, hepph/9911242 4. M. Przybycien (OPAL) and C. H. Lin (L3), these proceedings
DOUBLE-TAG E V E N T S IN T W O - P H O T O N COLLISIONS AT L3 E X P E R I M E N T C.H. LIN ( F O R T H E L3 C O L L A B O R A T I O N ) Department
of Physics,
National E-mail:
Central University,
[email protected] Chung-Li,
TAIWAN
Double-tag events in two-photon collisions are studied using the L3 detector at LEP with centre-of-mass energies from i/« = 189 GeV to y/s = 209 GeV. The cross-sections of e + e - —* e + e — hadrons and 7*7* —> hadrons are given as a function of the photon virtualities, Q\ and Q\, of the two-photon mass, W 7 7 , and of the variable Y = l n ( W ^ / Q i Q 2 ) for an average photon virtuality (Q2) = 16 GeV 2 . The results are in agreement with NLO calculations for the QPM process in the interval 2 < Y < 5. An excess is observed in the interval 5 < Y < 7, corresponding to W 7 7 greater than 40 GeV. The P H O J E T Monte Carlo describes the data reasonably well
1
Introduction
The cross-sections of the double-tag two-photon collisions are measured by the L3 experiment, where both scattered electrons a are detected in the small angle electromagnetic calorimeters. The cross-section of e + e~ —> e + e _ hadrons is a function of Q\, Q\ and W11. The ratio of these variables defines the variable Y = ]n(W^ /QiQ2)- Taking advantage of the good energy resolution of the small angle electromagnetic calorimeters, the true value of W 7 7 is calculated from the missing mass of the two scattered electrons, Wee. This avoids an unfolding procedure, which calculates W 7 7 from the effective mass of the hadrons seen in the detector, WviS. However the Wee variable is affected by the QED radiative corrections. In the present analysis they are taken into account in the Monte Carlo generators. The double-tag two-photon interactions are dominated by QED processes and perturbative QCD processes. QED processes are described by the Quark Parton Model, QPM. Perturbative QCD processes are based on the DGLAP * evolution equation. In leading logarithm approximation, the resummed series of perturbative gluonic ladders can also be described by the BFKL equation 2 , which predicts a rise on cross-section as a power of W 7 7 , as if a "hard Pomeron" 3 was exchanged. The cross-section measurement of two virtual photons collisions is considered as a golden process to test the BFKL dynama
Electron
stands for electron or positron throughout this paper.
170
171
The data are collected at centreof-mass energies 189 GeV < y/s < 209 GeV, correspond to an integrated luminosity of 617 p b _ 1 . The value of Qj is in the range of 4 GeV2 o : 0the LO and NLO calculations - 2 0 2 4 6 0 2 4 6 8 Y of the QPM process 8 and the Figure 2. Distributions of a) Ei/E^, b) 0j, c) Ym PHOJET Monte Carlo model. and d) YeeThese calculations well repre2 sent the Q dependence of the data. For the W 7 7 and Y distributions, the QPM calculations describe the data except in the last bin, where the experimental cross-section exceeds the predictions. Such an excess is expected if the resolved photon QCD processes are required. The predictions of PHOJET represent the data reasonably well. From the measurement of the e + e~ —> e+e~hadrons cross-sections we extract the two-photon cross-section, c 7 » 7 «, by using the transverse photon luminosity function 9 , aee = LTT • cr7»7». This measurement gives an effective cross-section containing contributions from transverse (T) and longitudinal (L) photon polarisations. The hadrons processes (d,e,f).
References 1. V.N. Gribov and L.N. Lipatov, Sov. J. Nucl. Phys. 15 438 and 675 (1972); L.N. Lipatov, J. Nucl. Phys. 20 94 (1975); Yu.L. Dokshitzer, Sov. Phys. JETP 46 641 (1977); G. Altarelli and G. Parisi, Nucl. Phys. B 126, 298 (1977). 2. E.A. Kuraev, L.N. Lipatov and V.S. Fadin, Sov. Phys. JETP 45 199 (1977); Ya.Ya. Balitski and L.N. Lipatov, Sov. J. Nucl. Phys. 28 822 (1978). 3. A. Donnachie and P.V. Landshoff, Phys. Lett. B 437, 408 (1998). 4. S.J. Brodsky et al, Phys. Rev. D 56, 6957 (1997). J. Bartels et al, Phys. Lett. B 389, 742 (1996). 5. R. Engel and J. Ranft, Phys. Rev. D 54, 4244 (1996). 6. S. Nova et al, DELPHI Note 90-35 (1990) 7. F.A. Berends, P.H. Daverveldt and R. Kleiss, Comp. Phys. Comm. 40 271 (1986). 8. M. Cacciari et al., JEEP 102 29 (2001). 9. V.M. Budnev et al., Phys. Rep. C 15 181 (1975); G.A. Schuler, Comput. Phys. Commun. 108 279 (1998).
M E A S U R E M E N T OF T H E H A D R O N I C CROSS-SECTION FOR T H E SCATTERING OF TWO VIRTUAL P H O T O N S AT OPAL M. P R Z Y B Y C I E N University
of Mining
and Metallurgy,
Cracow,
Poland
The interaction of virtual photons is investigated using the reaction e + e - —> e+e~hadrons based on data taken by the OPAL experiment at e + e - centre-ofmass energies y/see =189-209 GeV, for W > 5 GeV and at an average Q 2 of 17.9 GeV 2 . The measured cross sections are compared to the predictions of the Quark Parton Model (QPM), to the leading order (LO) QCD Monte Carlo model P H O J E T , to the NLO prediction for the reaction e + e - —• e+e~qq, and to BFKL calculations. P H O J E T , NLO e + e " -> e+e~qq, QPM describe the data reasonably well, whereas the cross section predicted by a LO BFKL calculation is too large.
1
Introduction
The classical way to investigate the structure of the photon at e + e~ colliders is the measurement of the process, e(pi)e(p2) -> e ^ ^ e ^ ^ h a d r o n s , proceeding via the exchange of two photons, which can be either quasi-real, 7, or virtual 7*. The terms in brackets represent the four-vectors of the particles as shown in Fig. ??. In the analysis presented here both final state electrons are observed, which means they must be scattered at sufficiently large polar angles 6i (i = 1,2 denotes quantities which are connected with the upper/lower vertex in Fig. ??) and consequently both radiated photons, which take part in the hard scattering process, are highly virtual. For the detailed discussion of the theory of two photon interactions see e.g. 1, and the detailed description of the measurement presented in this paper can be found in 2 , where also a complete list of references to the models used, is given. In the following only main points of the analysis are presented. The kinematical variables Q2, yi and obtained from the four-vectors of the tagged electrons and the hadronic final state via: Q2i=2EhEi{\-cos6i),
yi = l-§-cos2(9i/2), V4/;
£b
'
~l -
Qi
~ Ql + Q22 + W2'
where E\> refers to the beam energy, and the electron mass has been neglected. The e + e _ centre-of-mass energy squared is given by see = (pi +P2)2 and the hadronic invariant mass squared by W2 — (gi+ffe)2. For the comparison of the data to BFKL calculations the following kinematic quantity, which is a measure of the length of the gluon ladder, is denned: Y = ln(see2/i2/2/'V Q\Q\) — \n(W2/y/QlQl) = Y, where the approximation requires W2 > Q2.
174
175
2
Event selection
The data sample used in this analysis corresponds to an integrated luminosity of 592.9 p b _ 1 accumulated by the OPAL experiment in the years 1998-2000 at e+e~ centre-of-mass energies • V /I^ = 189 - 209 GeV. Double-tagged twophoton events were selected with the following cuts: a) two electrons with energies Ei j 2 > 0.42?b and polar angles in the range 34 < #i i2 < 55 mrad, should be observed, b) there should be no additional single object with an energy above 0.25.5b, b) at least 3 tracks (iVCh) have to be found, d) the visible invariant mass, WviS > 5 GeV, e) the z position of the primary vertex is required to be below 4 cm, and the distance of the vertex from the beam axis should be below 0.5 cm. f) the z component of the total momentum vector of the event, is required to be less than 35 GeV and the total energy measured in the event should be less than 2.2E\,. g) remaining Bhabha events with random overlap of hadronic activity are tagged using the back-to-back topology of the scattered electrons, both having an energy larger than Q.7E\>. Events are rejected if the difference in radius, AR and difference in azimuthal angle, A(j> of the position of the two clusters are AR < 0.5 cm and | A — 7r| < 0.1. With these cuts 175 events are selected in the data. Among these events, we expect 18.3 background events coming from another e + e~ physics processes e+e Tr(ee)) and 24.1 background events from an overlap of off(e"1 momentum electrons with single tagged or untagged two-photon events. A PHO JET Monte Carlo sample is used to correct the data for acceptance and resolution effects. It was checked that the sum of the signal as predicted by PHO J E T and the estimated background from overlaps with off-momentum electrons and other physics processes gives a good description >X of all important kinematical variables. Radiative corrections have been studied using the BDK program. We have found that the corrections are very large (>50% for high Y) when Wv;s is calculated from final state electrons momenta, and negligible when WviS is calculated from hadronic final state. In the following, Wvis, is obFigure 1. The diagram corresponding to the process e + e — —> e~*~e_ hadrons. tained from the energies and momenta of final state hadrons, and no correction for radiative corrections is applied to the cross sections extracted from the data.
176
3
Results
The cross-section for the process e + e~ —> e + e~ hadrons has been measured in the kinematic region defined by the scattered electron energies E\^ > OAE^, the polar angles in the range 34 < #1,2 < 55 mrad with respect to the beam direction, and W > 5 GeV. From the measurement of the cross-section of e + e~ -¥ e + e~ hadrons we extract the cross-section 7*7* —> hadrons using transverse luminosity function1, LTT, calculated separately for each bin using GALUGA. The cross-sections are presented as a function of x, Q2 (Fig. 2), and W and the azimuthal correlation between the two electrons A (Fig. 3). Here Q2 refers to the maximum of Q\ and Q2., and x is the corresponding value of Xi. For the comparison with BFKL calculations we also present the cross-section as a function of Y (Fig. 4). The total measured cross-section for the process e + e~ —• e + e _ hadrons in the previously defined phase space, is 0.35 ± 0.04 (stat) t°o°oi (sys) pb. The expected cross-section from PHOJET is 0.39 ± 0.02 (stat) pb, while the prediction for QPM using massive quarks is 0.27 ± 0.02 (stat) pb and the NLO predictions for the reaction e+e~ —• e+e~qq, using massless quarks, is 0.35 pb.
Figure 2. Cross-sections for the process e + e - —> e + e - hadrons and for the process 7*7* —• hadrons as functions of x (a,b) and Q2 (c,d). Data are shown as full dots in the center of the bins with statistical (inner error bars) and statistical and systematic errors added in quadrature (outer error bars). Predictions of PHOJET1.10 are shown as solid lines, and those of QPM as dashed lines. Figure 3. As in Fig. 2 but cross-sections are shown as functions of W (a,b) and A (c,d).
177 1
i
-
'
•
•
i
'
Figure
•) OPAL - PHOJET 1.10 QPM - Kwietinski et a], • Cacciari et a). (NLO)
H-y? b
Y S. IS Kim99 Bartels99
€w
J" D
b)
12 8
I • M ^1 i s1— i
•—t
i-
.
.
J
f i
.
.
.
~±
.
i
. . .
.
i " . '
f .
.
.
i
i .'
.
.
"~
:
Cross-sections for the process e+e~ hadrons and the process
function of Y. Data are shown as full dots in the center of the bins with statistical (inner error bars) and statistical and systematic errors added in quadrature (outer error bars). Predictions of PHOJET1.10 are shown as the solid lines, that of NLO calculation of the process e+e~ —• e+e~ qq from Cacciari et al. as dotted lines and those of QPM as dashed lines. Three BFKL calculations are shown: a LO one from Bartels et al. (Bartels99), NLO from Kim et al. (Kim99) and the HO calculation from Kwiecinski et al., using the consistency constraint.
Both PHOJET1.10 and QPM describe the data equally well for the cross sections in x, Q2, W, Y. PHOJET1.10 does not describe the Acf> distribution whereas QPM reproduces the shape of the distribution. The earlier version, PHOJET1.05, describes the Acj> distribution quite well. Also the NLO calculation for the reaction e + e~ -> e + e~ qq is in accord with the data (Fig.4). The data rule out BFKL cross sections which are as large as those predicted by LO-BFKL calculations. This LO-BFKL calculation already incorporates improvements comaprad to the original results by including effects of charm quark mass, the running of as and contribution from longitudinal photon polarisation states. The NLO-BFKL calculation and calculations including dominant higher order (HO) corrections predict smaller effects in the LEP range and are found to be consistent with the measured cross sections. The limited statistics and available Y range of the data prevent establishing or ruling out the onset of BFKL dynamics in this reaction. Acknowledgements. I am very grateful to Albert de Roeck and Richard Nisius for the fruitful collaboration on the results presented in this paper. References
1. V.M. Budnev et al., Phys. Rep. 15(1975)181, R. Nisius, Phys. Rep. 332 (2000) 165. 2. OPAL Collaboration, G.Abbiendi et al., Measurement of the Hadronic Cross-Section for the Scattering of Two Virtual Photons at LEP, hep-ex/0110006, submitted to Eur. Phys. J. C.
H I G H - E N E R G Y A S Y M P T O T I C S OF P H O T O N - P H O T O N COLLISIONS IN QCD * S T A N L E Y J . B R O D S K Y ® , V I C T O R S. F A D I N + , V I C T O R T . K I M * & , LEV N. LIPATOV* AND GRIGORII B. P I V O V A R O V 5 $ SLAC, Stanford, CA 94309, USA t Budker Institute for Nuclear Physics, Novosibirsk 630090, Russia * St. Petersburg Nuclear Physics Institute, Gatchina 188300, Russia & CERN, CH-1211, Geneva 23, Switzerland § Institute for Nuclear Research, Moscow 117312, Russia
The high-energy behaviour of the total cross section for highly virtual photons, as predicted by the BFKL equation at next-to-leading order in QCD, is presented. The NLO BFKL predictions, improved by BLM optimal scale setting, are in excellent agreement with recent OPAL and L3 data at CERN LEP2.
Photon-photon collisions, particularly 7*7* processes, play a special role in QCD 1, since their analysis is much better under control than the calculation of hadronic processes which require the input of non-perturbative hadronic structure functions or wave functions. In addition, unitarization (screening) corrections due to multiple Pomeron exchange should be less important for the scattering of 7* of high virtuality than for hadronic collisions. The high-energy asymptotic behaviour of the 77 total cross section in QED can be calculated 2 by an all-orders resummation of the leading terms: a ~ ofis", tu = Tfiira? — 6 x 10~ 5 . However, the slowly rising asymptotic behaviour of the QED cross section is not apparent since large contributions come from other sources, such as the cut of the fermion-box contribution: a ~ a 2 (logs)/s 1 (which although subleading in energy dependence, dominates the rising contributions by powers of the QED coupling constant), and QCDdriven processes. The high-energy asymptotic behaviour of hard QCD processes is governed by the Balitsky-Fadin-Kuraev-Lipatov (BFKL) formalism 3 ' 4 . The highest eigenvalue, UJ, of the BFKL equation 3 is related to the intercept of the QCD BFKL Pomeron, which in turn governs the high-energy asymptotics of the cross sections: a ~ sa,p~1 = s w . The BFKL Pomeron intercept in the leading * P R E S E N T E D BY V. T. KIM
178
179
order (LO) turns out to be rather large: OLIP - 1 = LULO — 12 In 2 {as/ir) ^ 0.55 for as — 0.2 3 . The next-to-leading order (NLO) corrections to the BFKL intercept have recently been calculated 5 , but the predictions in the MS scheme have a strong renormalization scale dependence. In Ref.6 we used the Brodsky-Lepage-Mackenzie (BLM) optimal scale setting procedure 7 to eliminate the renormalization scale ambiguity. (For other approaches to the NLO BFKL predictions, see Refs.8'6 and references therein.) The BLM optimal scale setting resums the conformal-violating /3o-terms into the running coupling in all orders of perturbation theory, thus preserving the conformal properties of the theory. The NLO BFKL predictions, as improved by the BLM scale setting, yields aip — 1 = UMLO = 0.13-0.18 6 . The photon-photon cross sections with LO BFKL resummation was considered in Refs. 4>9'10. Although the NLO impact factor of the virtual photon is not known, one can use the LO impact factor of 2 ' 4 - 10 ! assuming that the main energy-dependent NLO corrections come from the NLO BFKL subprocess rather than the photon impact factors n > 1 2 . Figl compares the LO and BLM scale-fixed NLO BFKL predictions a ~ a 2 a | s w 6 - n ' 1 2 with recent LEP2 data from OPAL 13 and L3 1 4 . The spread in the curves reflect the uncertainty in the choice of the Regge scale parameter, which defines the beginning of the asymptotic regime: s0 — Q2 to 10Q 2 for LO BFKL and s 0 = Q2 to 4Q 2 for NLO BFKL, where Q 2 is the mean virtuality of the colliding photons. One can see from Fig. 1 that the agreement of the NLO BFKL predictions 11 - 12 ' 6 with the data is quite good. We also note that the NLO BFKL predictions are consistent 12 with data recently presented by ALEPH 15 . In contrast, the NLO quark-box contribution 16 underestimates the L3 data point at Y = log(s 77 /( ojp and jp —• uir°X, and on searches for the reactions 7J> —• 7r0N*, •yp —• /2(1270)X, and •yp —>• a2(1320)X, where N* denotes an excited nucleon state, are presented. The mean 7P centre-of-mass energies were (W) = 200 GeV and 215 GeV, respectively. Cross sections for the Pomeron-mediated reactions were determined in agreement with previous measurements and phenomenological expectations. In contrast, Odderon induced processes have not been observed; upper limits on cross sections are below predictions from a non-perturbative QCD model.
1
Introduction
The Pomeron 1 (IP) — the Regge-trajectory 2 that is thought to dominate the hadronic cross section at high energies — exchanges only vacuum quantum numbers and in particular it is even under crossing i.e. has C-parity of + 1 . Its hypothetical partner that is odd under crossing i.e. C = —1, called the Odderon 3 (©), has not been observed yet. This note reports on cross section measurements of the Pomeron mediated processes "yp —> cop and jp -4 o;7r0X as well as on searches for the Odderon induced reactions 7p -> TT°N*, IP -»• / 2 (1270)X and jp -> a£(1320)X in photoproduction (Q 2 w 0) at HERA, where N* denotes an / = 1/2 nucleonic state. The respective processes leading to the above final states are sketched schematically in figure 1. Only Figure 1. Generic graph ilpurely photonic final states of the mesons are lustrating 7p interactions via analysed, since together with the C-parity of the Pomeron and Odderon exincoming photon the number of final state pho- change, respectively. tons uniquely determines the C-parity of the exchanged trajectory, viz. an even number of final states photons can only be produced if odd C-parity ((D) is exchanged from the proton side, and vice versa an odd number of final state photons can only produced by a C even •SUPPORTED BY THE BUNDESMINISTERIUM FUR BILDUNG, SENSCHAFT, FORSCHUNG UND TECHNOLOGIE, GERMANY, UNDER T R A C T NUMBER 7HD27P.
182
WISCON-
183
(IP) exchange. Vector meson photoproduction can be well described in the framework of the vector meson dominance (VMD) model combined with Regge phenomenology 4 . In order to describe the Odderon induced pseudoscalar and tensor meson production of the 7r°, the j% and the a° a genuine nonperturbative QCD model is applied, namely the Stochastic Vacuum Model5'6 (SVM), in which the proton is treated as quark-diquark' system and the photon as a quark-antiquark colour dipole. Both are convoluted with appropriate wavefunctions of the initial and final states, respectively. 2
Event Selection
The analyses are based on data samples taken in the years 1996 (w, unr0, fc and a°), 1999 and 2000 (both for the exclusive ir°). The integrated luminosities are 4.5 p b _ 1 for 1996 and 30.6 p b _ 1 for the years 1999 and 2000 combined, respectively. Electrons of 27.6 GeV were brought to collision with protons of 820 GeV°. Photoproduction events were selected by demanding the scattered electron to be detected under very low angles in a small angle electron detector (ET) 33 m downstream the electron beam, resulting in a limited phase-space of Q 2 < 0.01 GeV2 and 0.3 < y < 0.7. Depending on the meson analysed the number of photons in the final state varies from two to five: 7r° -¥ 77, u -4 7r°7 -* 37, ji -> 7r°7r° -> 47, a° —>• 7r°77 —¥ 47, and W7r° —> (n0-f)ir0 —> 57, respectively. These photons are detected in the backward calorimeter(s) of the Hl-detector 7 , since the mesons are produced with only little transverse momentum but large and negative longitudinal momentum as the initial quasi-real photon is emitted nearly parallel to the incident electron with energies of ~ 8 - 20 GeV. For 1996 the analyses were restricted to the SpaCal 8 only and for the exclusive n°measurement of 1999+2000 the VLQ-calorimeter9 was included additionally. To ensure that the events selected were indeed exclusive a variant of energy-momentum conservation was utilised, viz. E := [50(49),60] GeV, where the sum runs over all photons the SpaCal, the VLQ and the electron in the ET. The number in brackets refers to the exclusive pion analysis. If E is found to be equal (within resolutions) twice the beam energy of 55 GeV the whole final state is detected. For the mesons decaying via 7T°'s and 7j's appropriate mass windows for the respective 77-masses were chosen. °For the years 1999 and 2000 the proton energy was 920 GeV.
184 For the u> it was further required that the interaction occurred elastically by imposing cuts limiting the mass of possible proton-excitations to less than 1.6 GeV, in contrast to the exclusive 7r° were it was explicitely demanded that the proton was excited into a state (N*) decaying into a leading neutron, which was detected in the forward neutron calorimeter. For the remaining analyses no constraints on the outgoing baryonic final state were imposed. 3
M o n t e Carlo Models
In order to describe the processes under study D I F F V M 1 1 and a derivative of this generator called OPIUM 126 were used. In addition to the processes based on Pomeron exchange combined with VMD as implemented in D I F F V M , OPIUM is capable to generate pseudoscalar and tensorial mesons as described in 6 . The background consisting of inclusive 7p-interactions and mesons decaying via charged pions, was studied using P Y T H I A 1 0 . 4
Results
The left part of figure 2 shows the invariant 7r°7-mass spectrum from which a cross section for elastic w-photoproduction of a(jp -> up) = (1.25 ± 0.17(stat) ± 0.22(syst) /xb) was derived. The right part of the figure shows the invariant mass of exclusive Pomeron Channel - 5y sample
Pomeron Channel - 3 Y sample
"WGeV) Figure 2. Three (left) and five (right) photon invariant mass spectra, made up of 7r°7- for the w and 0J7r° final states.
W7r°-pairs for which a cross section of a(jp -> uir°X) = (980 ± 200(stat) ± 200(syst) nb) 6
OPIUM is an acronym for Odderon, Pomeron Induced Unified Meson maker
185 was found. Figure 3 shows the invariant mass spectra of the ir0-, fi- and a%H 10 d d 8 r o n
H1 Odderon Search - 2 Y sample
Search - 4y sample
m^fGeV)
H I Odderon Search - 4y eample
m^.(QeV)
m ^ (GeV)
Figure 3. The left part shows the invariant mass of exclusive 77-pairs, the middle part shows the invariant 7r°7r°-mass and in the left the mass of 7r°rj-pairs is shown.
searches, respectively. Since the distributions observed are compatible with background alone, 95% confidence level limits were derived (with the SVM predictions in brackets): o-acc(7P ->• ir°N*) < 39nb tf(7P -»• /a-X") < 16 nb a{yp -> a°2X) < 96 nb
(200nb) (21 nb) (190 nb)
References 1. S. Nusinov, Phys. Lett. 62, 1286 (1976). 2. P. D. B. Collins, An Introduction to Regge Theory and High Energy Physics, (1977) 3. L. Lukaszuk, B. Nicolescu, Nuov. Ciem. Lett. 8, 405 (1973) 4. G. A. Schuler, T. Sjostrand, Nucl. Phys. B407, 539 (1993) 5. H. G. Dosch et al., Phys. Rev. D50, 1992 (1994) 6. E. Berger et al., Eur. Phys. J. C9, 491 (1999) E. Berger et al., Eur. Phys. J. C14, 6731 (2000) 7. I. Abt et a l , Nucl. Instrum. Methods A386, 310 and 348 (1997) 8. T. Nicholls et al., Nucl. Instrum. Methods A374, 149 (1996) 9. M. Keller et al., Nucl. Instr. Methods A409, 604 (1998) 10. T. Sjostrand, Comp. Phys. Comm. 82, 74 (1994); private communication (2001). 11. B. List and A. Mastroberardino, DIFFVM - A Monte Carlo Generator for Diffractive Processes in ep Scattering, available as: http://www.desy.de/"heramc/mclist.html. 12. W. Kornelis, private communication, Heidelberg (2000).
D I F F R A C T I V E p° P R O D U C T I O N AT H E R M E S KATERINA LIPKA ON BEHALF OF THE HERMES COLLABORATION DESY-Zeuthen, Platanenallee 6 15738 Zeuthen, Germany E-mail:
[email protected] Spin-dependent p° production has been studied at the HERMES experiment at HERA. Recent results on the cross section and the spin density matrix elements of diffractive exclusive p° production are compared to world data and theoretical predictions. The double -spin asymmetry of exclusive diffractive p° production is found to be consistent with the theoretical expectation based on the Generalized Vector Meson Dominance description of both p° production and inclusive DIS.
1
Introduction
The study of diffractive p° production in lepton-nucleon scattering is one of many objectives of the HERMES experiment. HERMES uses the longitudinally polarized electron" beam of the HERA storage ring at the DESY laboratory with an energy of 27.5 GeV and an internal target filled with polarized or unpolarized gas. The p° - meson is detected through its decay products in the channel p° —> TT+IT~. The momentum and position of the scattered electron and two produced hadrons are determined by the tracking system of the spectrometer [1] with a precision of Ap/p ~ 1%. The particle identification is performed using an electromagnetic calorimeter, preshower, transition radiation detector and Cherenkov counter, the latter replaced by a RICH in 1998. The lepton identification efficiency is 99% with the contamination by hadrons being less than 1%. Diffractive p° production in lepton-nucleon scattering is described by the fluctuation of the virtual photon that was emitted by the electron, into a qq state. The process is defined by the virtuality Q2, the energy v of the photon and the invariant mass of the photon-nucleon system W2. In a diffractive process the momentum transfer — t to the target is required to be small. Another important variable is the missing energy AE = — ^ — ^ with MM and Mx being the mass of the target nucleon and of the undetected final hadronic system, respectively. In case of exclusive production the target proton stays intact, i.e. the missing energy is close to zero. There are several models to explain exclusive diffractive p° production. In the Vector Meson Dominance model the qq state is shifted onto the mass shell forming a vector meson. In the framework of Regge-based models the process is described by Reggeon "here and further used for both electron and positron
186
187
1
iou
= 2.3GeV2 - r = 4.0GeV;
ex
W [GeV] Figure 1. The longitudinal cross section for p° production [2] versus W at different average values of Q2. The solid line represents the result of the calculation [3,4] with the dashed (dotted) curves representing the quark (two-gluon) exchange contribution within the model.
exchange at W < 5 GeV while at higher values of W the theory involves Pomeron exchange. Once a hard scale is involved the description of the nucleon structure in terms of off-forward Parton distributions (OFPDs) becomes possible. In fig. 1 the data of HERMES [2] is compared to the pQCD calculation [3,4] of the cross section of p° production from longitudinal photons in terms of OFPDs. For W below 5 GeV the rise of the longitudinal cross section is consistent with the calculation based on quark-exchange alone, at higher values of W the two-gluon exchange takes over. 2
Spin Density Matrix Elements
In exclusive diffractive p° production the angular distributions can be expressed in terms of spin density matrix elements (SDMEs) of the p° - meson: PAvA'v(^) 0C X ]
T
*v\-p%\'iT\'vX-
(1)
In Eq. (1) T\v\y are helicity amplitudes and S " A, represent the elements of the photon spin density matrix with a (running from 0 to 8) indicating the polarization state of the photon. SDMEs contain the information about the polarization properties of the p° and the parity of the object exchanged with the target. At fixed beam energy at HERMES it is impossible to separate the contributions from longitudinal and transverse photons and the longitudinal and transverse unpolarized matrix elements have to be combined. A matrix rgis introduced with the elements being linear combinations of SDMEs (p\v\>v) both being connected via the longitudinal-to-transverse cross section ratio R
188 HERMES PRELIMINARY Diffractlve p° Electroproductlon ('H)
,,,
«.
— • . _
R*r! 0 rj-i
tmr?.,
4 n.,:„
1r -
ImrJo Ifn r* t
Unpolarized Matrix Elements
Imrio
Polarized Matrix Elements
ri-. Imr)0
•I, 'in 1 . , , , 1 . . . . 1 . , . . I .', , . 1
i . . . .
i . ,
Figure 2. Elements of the p° density matrix (SDME). Vertical lines indicate the matrix elements forbidden by SCHC.
and flux ratio e. Fig. 2 shows SDMEs of the p°-meson measured at HERMES via a fit to the angular distribution function dependent on the p° production angle and two decay angles. Data obtained with an unpolarized hydrogen target was used for the analysis. The measured SDMEs show a slight violation of s-channel helicity conservation (SCHC), where the helicity of the photon is assumed to be preserved in the helicity of the p°-meson. SCHC forbids matrix elements proportional to helicity flip amplitudes. In contrast to this expectation the element rg 0 is found to be non-zero. The measured SDMEs are consistent with natural parity exchange in the t-channel, which among others implies r°o + 2ri_j = 1. 3
Double-Spin Asymmetries in p° Production
The spin dependence of the polarized photon-nucleon interaction is described by two cross section asymmetries: the asymmetry of the transverse-photon interaction with the nucleon A\ = j 1 | f 3 7^ 3 / a and the asymmetry of the transverse-longitudinal photon interference Ai = "v?—. Here <TI/2 and CT3/2 are the photon interaction cross sections with the projection of the total spin 1/2 and 3/2, and our is the interference cross section.
189 ^0.5 D.4 0.3 0.2 0.1 0 -0.1
_ KSKMES EKUTBKM FHOJHIHUIY _ u n c o r r e c t e d Coc b a c k g r o u n d
0
HERMES ESUTXR0N PRELXKnauiY ' u n c o r r e c t e d for background *
mal.m. ptMM
matured
CUD
A, B -f(A 1 *>(GVMD)
[Fru*Nud.Phys.B113]
'-* ,
0
W=0.5 0.4 0.3 0.2 0.1 0 -0.1
•
i ,
0.5
i
i ,
1
,
,
1.5
& I. 0
3.5
2.5
. H2HHBS PROTON . imtrorract«i3 f o r
s y a t e n s t i c e r r o r < 0.005
,
2
• background
HERMES PROTON
n e t . dM.
i-H-»*
1
i — 1.5
i 2
— 2.5
i
3
c
j r r o c t e d l o r background r - r r i
O phoi. pretmlMiy
i I . . . 1 . . . .i — a5 1
4
nauured A, " - 1 (A, •) (GVMD) m Nud.Phyr B113
i
15
4
Q*(GeV*)
Figure 3. The double-spin asymmetries for diffractive p° production. Left: lepton-nucleon interaction asymmetry A?, versus Q2 for exclusive diffractive and quasi-real photoproduction of p°. Right: photon-nucleon interaction asymmetry A± for exclusive diffractive p production versus x compared with the theoretical prediction [6].
The asymmetry Ax is obtained from the experimental lepton-nucleon asymmetry An = aZ~aZ
= - * - • NZ-LZ~NZ-LZ,
where N=*&
is the number
of events (mesons in case of p° production) per beam and target spin configuration, L and Pb,Pt are luminosity and polarizations of beam and target, respectively. The lepton-nucleon and photon-nucleon asymmetries are connected via the effective polarization D of the photon and a kinematic factor r): A{ = -$• — r\Ap2. The contribution of Ap2 is assumed to be given by the positivity limit y/R [5], guided by a measurement of the phase difference between amplitudes in p production from transverse and longitudinal photons. The lepton-nucleon and photon-nucleon asymmetries presented in fig.3 were measured for exclusive diffractive and quasi-real photoproduction of p° using longitudinally polarized proton and deuteron targets at HERMES. The photon-nucleon interaction asymmetry A\ is found to be consistent with a theoretical prediction [6] based on the Generalized Vector Meson Dominance (GVMD) model. In this model the exclusive p° asymmetry is related to the asymmetry AJ
in inclusive DIS,
Al
^_
A non-zero asymmetry
is connected in Ref. [6] to unnatural parity exchange in the t-channel which indicates the contribution from di-quark object exchange to p° production from transverse photons.
190 References 1. 2. 3. 4. 5. 6.
K. Ackerstaff et al, HERMES Coll. Nucl. Instr. Met. A417, 230 (1998). A. Airapetian et al, HERMES Coll. Eur. Phys. Jour. C 17, 389 (2000). M. Vanderhaeghen et al, Phys. Rev. Lett. 80, 5064 (1998). M. Vanderhaeghen et al, Phys. Rev. D 60, 094017 (1999). A. Airapetian et al, HERMES Coll. Eur. Phys. Jour. C 18, 303 (2000). H. Fraas, Nucl. Phys. B 113, 532 (1976).
D I F F R A C T I O N AT HIGH A N D LOW Q2 AT H E R A P. D. T H O M P S O N School of Physics
and Astronomy, E-mail:
University of Birmingham,
[email protected] B15 2TT,
UK.
Recent measurements of the diffractive cross section in deep-inelastic scattering (DIS) at HERA are presented. The data are used to investigate the factorisation properties of diffractive DIS and to examine its quantum chromodynamic (QCD) structure.
1
Diffractive Deep Inelastic Scattering
At low x in DIS at HERA, approximately 10% of the events are of the type ep —> eXp, where the final state proton carries in excess of 95% of the proton beam energy 1,z . The kinematics of these processes are illustrated in figure 1. A photon of virtuality Q2, coupled to the electron, undergoes a strong interaction with the proton to form a final state hadronic system X (mass Mx) separated by a large rapidity gap from the leading proton. No net quantum numbers are exchanged. A fraction x^ of the proton longitudinal momentum is transferred to the system X. The virtual photon couples to a quark carrying a fraction (3 of the exchanged momentum. The squared four-momentum transfer at the proton vertex is denoted t.
X
P
IPW
£
&
Figure 1. Illustration of the kinematic variables used to describe diffractive DIS.
Events with this 'diffractive' topology are interpreted in Regge models in terms of pomeron trajectory exchange between the proton and the virtual photon. The large photon virtualities encourage a perturbative QCD treatment of the process. However, the parton level interpretation is not obvious. In order to generate an exchange with net vacuum quantum numbers, a minimum of two partons must be exchanged in the t channel.
191
192 The differential cross section for diffractive DIS is often presented in terms of a diffractive structure function F2 (/?, Q2 ,xF,t), defined analogously to the inclusive proton structure function F2. Experimentally, diffractive events have been selected using two complementary methods; measuring the scattered proton directly in proton spectrometers (the Hi forward proton spectrometer FPS or the ZEUS leading proton spectrometer LPS) or requiring an absence of particles in the forward region (large rapidity gap method). The first method provides a clean selection of diffractive events, independent of the hadronic final state and free from proton dissociation background, and allows a direct measurement of t. However, due to the limited acceptance of the proton spectrometers the second method yields the better statistical precision. In rapidity gap analyses, where t is not directly measured, the results are presented in the form of a structure function F2 (f3,Q2,xF), corresponding to an integral of F2 over t.
2
^-dependence
H1 PRELIMINARY H1 (prel.) 99-00
* T •
ZEUS 94 ZEUS (prel.) 95 ZEUS (prel.) 97
hf«'' !l + O.l
0.2
0.3
0.4
Itl, GeV
Figure 2. Left: T h e differential cross section da/dt measured with the HI P P S in four different xp bins. Results of the fit with a function dc/dt oc ebt are shown. Right: The slope parameter b is plotted as a function of xp. Results obtained with the HI F P S and ZEUS LPS are shown.
193 Recent measurements in which the leading proton is measured in proton spectrometers have been made 3 ' 4 . A typical feature of diffractive events is an exponential fall of the differential cross section with |t|. In Fig.2, the cross section is parameterised as da/dt oc eb'*l in bins of xp, and the slope parameter b is plotted as a function of xF. The results of HI and ZEUS are consistent within the experimental uncertainties and no significant dependence o n i p is visible. 3
Factorisation Properties and Diffractive Parton Densities
The HI collaboration recently released new preliminary F2 data 5 (see figure 3) based on a factor of 5 more luminosity than previous measurements. In this section, these data are used to test the factorisation properties of diffractive DIS. In figure 3, the data are compared with the results of a fit in which the (/3, Q2) dependence is obtained by parameterising the diffractive light quark and gluon densities at Q\ = 2 GeV 2 and evolving to higher Q2 using the leading order DGLAP equations. The xp dependence is assumed to factorise from the (f3,Q2) dependence and is described by a Regge phenomehological flux factor such that
x^™
= A(/3,Qa)4-a,
(1)
where ctw(t) is the effective pomeron trajectory. The fit describes the data well and results in diffractive parton densities dominated by the gluon density, which extends to large fractional momenta. The hard scattering factorisation proof 6 makes no prediction for the (xF, t) dependence. From the QCD perspective, the diffractive parton densities could vary in both shape and normalisation with these variables. However, the success of Regge phenomenology in describing soft hadronic cross sections with a universal pomeron trajectory suggests that there may be an extended 'Regge' factorisation property whereby the xF dependence is driven by Regge asymptotics and is completely decoupled from the (/3, Q2) dependence. The dependence on (/3, Q2) then represents a structure function for the exchanged pomeron 7 . In 5 , the Regge factorisation hypothesis is tested by measuring the data at a larger number of xp values and performing a fit to equation (1) with free parameters for the effective pomeron intercept 0^(0) and A(/3,Q2) at each (/?, Q 2 ) point. The fit yields aw(0) = 1.173 ± 0.018 (stat.) ± 0.017 (syst.) t o Q35 (model), the dominant upward model dependence uncertainty arising from the unknown contribution of the cross section for Ion-
194 xlp = 0.003 H1 preliminary x=0.0003 , (3=0.1 0.05
a
« a.
X
0
S
x=0.0006 , P=0.2
X
H1 preliminary Q 1 [GeV2]
005
6.5
o 0.05
8.5
0.05
o 0.05
0
x=0.0012 , (3=0.4
0.05
0
x=0.00195, (3=0-65
0.05 . . . «t » 1
0
12
0 0.05
15
0 0.05
20
1
0 0.05
25
x=0.0027, (5=0.9
0.05
0 0.05 10
10
Q 2 [GeV2] • H1 (prel.) QCD fit (IP+IR) QCD fit (IP)
35
0 0.05
45
0 0.05
60 0.2
0.4
0.6
' H1 (prel.) — QCD fit (IP+IR) QCD fit (IP)
0.8
P
Figure 3. Left: Dependence of xp F® on Q2 for different /3 values, with fixed xp = 0.003. The data are compared with the DGLAP QCD fit described in the text. Right: Dependence of XpF^1 on /3 for different Q2 values, with fixed xp = 0.003. The data are compared with the DGLAP QCD fit described in the text.
gitudinally polarised photons. The Regge factorisation hypothesis works well within the kinematic range measured in 5 , with no significant variation of the effective a,p(0) with /? or Q2. There is thus no experimental evidence at the present level of precision for a variation of the diffractive parton densities with xF.
195 4
Comparisons with Dipole Models
The hard scattering factorisation proof for diffractive DIS does not specify the relationship between the diffractive and the inclusive parton densities. Specific models 8 ' 9 have been developed for this relationship. A popular approach is to consider the interaction in the proton rest frame, in terms of the elastic and total cross sections for the scattering on the target of qq and qqg fluctuations of the virtual photon, treated as colour dipoles. Using ideas such as the optical theorem, the same 'dipole cross section' can be used to describe total, elastic and dissociative cross sections, thus unifying the description of F2 and F® • In the "saturation" model 9 , the qq dipole cross section is obtained from a 3 parameter fit to F2 data and is then used to predict F2D, under the assumption that the diffractive cross section is driven by 2-gluon exchange. A contribution from qqg fluctuations is added in the diffractive case. Figure 4 shows a comparison of the "saturation" model with various diffractive data from ZEUS 2 ' 10 . The description is good for Q2 > 4 GeV 2 . The qqg contribution is clearly needed at large Mx. As yet, the model is not able to describe the low Q2 region. References 1. HI Collaboration, C. Adloff et al., Z. Phys. C76 (1997) 613. 2. ZEUS Collaboration, J. Breitweg et a l , Eur. Phys. J. C6 (1999) 43. 3. HI Collaboration, abstract 809, paper submitted to EPS Conference on HEP 2001, Budapest. 4. ZEUS Collaboration, abstract 566, paper submitted to EPS Conference on HEP 2001, Budapest. 5. HI Collaboration, abstract 808, paper submitted to EPS Conference on HEP 2001, Budapest. 6. J. Collins, Phys. Rev. D57 (1998) 3051, Erratum-ibid. D 61 (2000) 019902. 7. G. Ingelman and P. Schlein, Phys. Lett. B152(1985) 256. 8. W. Buchmiiller, T. Gehrmann and A. Hebecker, Nucl. Phys. B537 (1999) 477. 9. K. Golec-Biernat and M. Wiisthoff, Phys. Rev. D60 (1999) 114023. 10. ZEUS Collaboration, paper 435 submitted to International Conference on HEP 2000, Osaka.
196
ZEUS 10' «5
J*
10 9
_
Mx = 22 GeV
M, = 11 GeV
M, = 5 GeV
i o ZEUS 94
ZEUS VMDREGGE Fit
* k ZEUS (prel.) LPS 95
GBW(qq+qqg)
• n ZEUS (prel.) BPC 96-97
GBW(qqonly)
10"
, > 70> (x9.5E+06)
• (X1.7E+06)
ifl'
W-190
10J 20"
• (X2.0E+04)
(x2.0E+05)
f w = 1 6 0 "••"
W=16D
.
iflJ 10'
v- AuAup0 a second data set was collected using a low-multiplicity topology trigger which did not require a ZDC signal. In the level 0 trigger, the CTB was divided into 16 coarse pixels. For a two track topology, hits were required in opposite pixels, while pixels in the top and the bottom acted as a veto to supress cosmic rays. A fast online reconstruction - the level 3 trigger - further removed background. With this trigger, the STAR collaboration collected about 30k events in 7 hours. The p° candidates from this data set have a transverse momentum and an invariant mass distributions similar to the ones already shown in Fig. 3: a peak at low PT < 100 Mev and a peak of about 300 events around the rho mass. In contrast to the minimum bias data, the topology triggered data had almost no energy deposition in the ZDC consistent with the two gold nuclei remaining in their ground state.
206
Two-photon interactions include the purely electromagnetic process of electron-positron pair production as well as single and multiple meson production. The coupling Za (0.6 for Au) is large, hence e+e~ pair production is an important probe of quantum electrodynamics in strong fields 1. At momenta below 140 MeV, e+e~ pairs are identified by their energy loss in the TPC as shown for the minimum bias data sample in Fig. 4a. Fig. 4b shows the px spectrum for identified e+e~ pairs; a clear peak at p? < 50 MeV/c identifies the process AuAu ->• Au*Au*e+e~.
P(QeV/c)
pT{GeV/c)
Figure 4. (a) Energy loss dE/dx of tracks in the 2-track, minimum bias data; triangles indicate events where both particles are identified as electrons, (b) The PT spectrum for identified e+e~pairs.
In summary, for the first time, exlcusive p° production AuAu —> AuAup0 and p° production accompanied by nuclear breakup AuAu-¥ Au*Au*p° were observed in ultra-peripheral heavy ion collisions. The p° are produced at small perpendicular momentum, showing their coherent coupling to both nuclei. In addition, the coherent electromagnetic process AuAu —> Au*Au*e+e~ was observed. In 2001, RHIC will collide gold nuclei at y/spiN = 200 GeV, attempting to reach full design luminosity. Together with new trigger algorithms, this will allow us to collect several orders of magnitude larger statistics than presently available, thus greatly expanding the physics reach of the STAR ultra-peripheral collisions program. References 1. G. Baur, K. Hencken and D. Trautmann, J. Phys. G24, 1657 (1998); C. A. Bertulani and G. Baur, Phys. Rep. 163, 299 (1988). 2. J.J. Sakurai, Ann. Phys. 11 (1960) 1, and Phys. Rev. Lett. 22 (1969) 981, T.H. Bauer et al., Rev. Mod. Phys. 50 (1978) 261. 3. S. Klein and J. Nystrand, Phys. Rev. C60, 014903 (1999). 4. S. Klein and J. Nystrand, Phys. Rev. Lett. 84, 2330 (2000).
TOTAL CROSS-SECTIONS ROHINI M. GODBOLE Centre for Theoretical Studies, Indian Institute of Science, Bangalore, India AGNES GRAU Department of Theoretical Physics, University of Granada, Granada, Spain GIULIAPANCHERI INFN Frascati National Laboratories, Frascati, Italy We examine the energy dependence of total cross-sections for photon processes and discuss the QCD contribution to the rising behaviour.
A look at total cross-sections1 for the processes pp, pp, jp, 77 —> hadrons immediately raises a number of questions, like: what gives the energy dependence of total cross-sections? Are photon data properly normalized? Are the predictions from factorization 2 , quark counting and VMD, consistent with the complete set of data available in the same energy range? In this talk we describe work in progress towards a QCD Description of the energy dependence of total cross-sections 1,a . The issue has both a theoretical and a practical interest, since to properly evaluate the expected hadronic background at Linear Colliders, it is necessary to have a reliable model to predict total hadronic cross-sections from 77 collisions, which are responsible for the bulk of this background. Indeed, convoluting the photon spectrum with various predictions for 77 —> hadrons4, the predictions for e + e~ —• e + e~ hadrons differ by 30-j-40%. In order to reduce this uncertainty, it is necessary to drastically reduce the range of variability present in 77 collisions, where models can differ by more than a factor two in their predictions for the total cross-section. These differences are ascribable to the difficulty in determining the absolute normalization and the slope with which the total cross-section rises in photon collisions. In general the task of describing the energy behaviour of total crosssections can be broken down into three parts: i) the rise, ii) the initial decrease, iii) the normalization. The rise alone can be obtained • in the Regge-Pomeron model 6 , with atotai = Xse + Ys~n, through s £ , although it does not seem that the same power e fits protons and photons 7 : one finds e pp = 0.08, e 7 7 = 0.1 -i- 0.2. To overcome this problem, it has been suggested to add more power terms, thus increasing the number of
207
208 free parameters. • from factorization 2 , but there remain the problem of getting the protonproton cross-section from first principles • using the QCD calculable contribution from the parton-parton crosssection, whose total yield increases with energy 8 • a combination of the above In the Minijet Model, the rise is driven by the LO QCD contribution to the integrated jet cross-section r
Ojet = / JPtmin
(Per- t
f
,22 l e d2pt = Y ] / d pt pa^nsJPtmin
f
d2pt / f{xi)dxi J
f
/ f(x2)dx2 J
ffippartons
-$-z Pt
d2
which depends on the densities and very dramatically on ptmim the minimum transverse momentum cut-off. To ensure unitarity, the mini-jet cross-sections are embedded into the eikonal formulation, which gives the Eikonal Minijet Model in LO QCD (EMM) a%%} =2Jd2b[l
- e-nV>'%
a£\p) =2 J d2b[l -
e- e + e - /z + /x~ has been measured. [Fig. 1/c] The cross sections were corrected with trigger and detector inefficiencies. They are given with their statistical and systematical errors for the fiducial volume described above in table 1. To extract the two photon cross sections, (7(77 —> n+fi~), as a function of W 7 7 [Fig. 1/d] the number of observed events were corrected for the angular acceptance A which is defined as: A
_
Ngenerated{\cos{0)\) Ngenerated(\cos(e*)\)
where Ngenerated(\cos(9)\) are the number of events in the given angular range in the e+e~ center-of-mass system while Ngenerated(\cos(6*)\) is the number of events in the same angular interval in the rest frame of the two gammas. This acceptance was calculated in each W 7 7 bins. The 77 cross section was
215
calculated in each W 7 7 bin by numerically integrating the two photon luminosity function over the bin width. The values obtained at different e + e~ center-of-mass energies are in good agreement among themselves.
5
Summary, Conclusion and Acknowledgements
Based on an integrated luminosity « 596 pb'1 collected at 161 < -/s < 208 GeV the data was used to measure the cross section of muon pair production in 77 collisions. The measurements are in good agreement with the 0 ( a 4 ) order QED predicition. We wish to express our gratitude to the CERN accelerator division for the excellent performance of the LEP machines. We acknowledge with appreciation the effort of all engineers, technicians and support staff who have participated in the construction and maintenance of this experiment.
References 1. 2. 3. 4. 5.
L3 Collaboration, 0 . Adriani et al, Physics Reports 236 1 (1993). V.M. Budnev et al, Physics Reports 15 181 (1975). PYTHIA 5772, T. Sjostrand, Comp. Phys. Com. 82 74 (1994). WW generator report of the LEP2 workshop, hep-ph/9709270 GEANT 3.15 R. Brun et al. CERN DD/EE/84-1 revised, (1987)
Table 1. The number of events collected (Ncou) , the expected (a(MC)) and the measured (c(DATA)) cross-section of the process e + e ~ —• e+e~n+fj,~ with it's statistical and systematical errors at different center-of-mass energies.
< ^fs > [GeV] 161 172 183 189 198 206
Noil. ev. 189 223 1171 3932 3413 4576
a [pb], (MC) 113.0 115.4 116.9 117.7 118.9 120.5
a ± Aastat ± Aasys 101.4 ± 7 . 2 123.0 ± 7 . 8 117.7 ± 3 . 4 117.1 ± 1 . 8 118.9 ± 2 . 0 122.6 ± 1 . 8
[pb], (DATA) ±3.9 ±4.5 ±1.7 ±1.6 ±2.1 ±1.5
216
!
5 10 15 20 25 30 35 40 Invariant mass of the two photon (GeV/c1)
5 10 15 20 25 30 35 40 Momentum of the h.e. muon (fieV/c)
b.)
a.)
^160
a
J3
r r
—
M+M-)
L3 Prel,
«S140
sqrt(s)=198GeV sqrt(s)=1S9GeV sqrt(s)=1S3GeV
J 120 ©100 w e + e - p . + / ^ as a function of the center-of-mass energy, d.) The unfolded 7 7 —> A* + /i _ cross section as a function of the effective mass.
Cross Section Measurement of r Pairs in Two-Photon Collisions with the L3 detector at LEP 2 Daniel Haas*, Maneesh Wadhwa
'
University of Basle Institute for Physics Klingelbergstrasse 82 CH - 4056 Basel email:
[email protected] The production of r pairs in 77 collisions is studied with the L3 detector at LEP. Data were collected at ,/s = 189 - 208 GeV for a total integrated luminosity of 608.1 p b _ 1 . An exclusive decay channel is considered, with T^ —» e*i/ T "e and T ^ —> p^vT, with p^ —> TT^-R0. The cross section T+T~:
Two-photon physics offers a wide field of research at LEP 1 and 2. The analysis presented here measures the cross section of r pairs in two-photon collisions at energies of 189 GeV and 192 - 208 GeV. The four principal feynman diagrams for the QED process are shown in figure 1. This process has been observed and measured for the first time by L3 at 91 GeV 1 but not yet at LEP 2 energies where the cross section is expected to be large and high integrated luminosities are available. The cross section measurement of the reaction e + e~ —> e+e~r+r~ provides a test of QED to order 0(aA) over a wide range of kinematics. The four main diagrams contributing, at the lowest order, to the reaction e + e~ —> e+e~r+r~ are shown in Figure 1.
217
218
In addition, the study of the process 77 —> T+T~ at LEP can be used to measure the anomalous magnetic and electric moments of the r lepton 3 . The advantage of using this process is twofold. First of all, the anomalous magnetic moment pT and electric moment dT are defined as
^
=
e(l + F2(0))
2m T
,
'
^
=
eJ-3(0)
—2^T>
(1)
i.e. they depend of the form-factor F2 and F3 at Q2 = 0. This is directly measured in no-tag two photon processes. Second, since 77 —> T+T~ at lowest order is a pure QED process there is no contamination from other possible anomalous couplings, such as ZTT. Both couplings are related in some class of models, for instance those with a SU{2) x U{1) symmetry. Indeed, this relation has been used to extract stringent bounds on the anomalous moments from measurements of Z —• T+T~ at LEP 4 . Thus, independent measurements of the anomalous magnetic and electric moments and ZTT couplings provide a test of these class of models. The data analysed here has been taken by the L3 detector 2 at LEP from 1998 to 2000. L3 collected 172.1 p b " 1 at 189 GeV in 1998, 220.9 p b " 1 at 192 - 202 GeV in 1999, and 215.1 p b " 1 at 202 - 208 GeV in 2000 . The events were mainly triggered by the charged particle trigger of the time-expansion chamber (TEC) 5 and the newly implemented inner TEC trigger 6 , added in 1997 specially to improve acceptance. 2
Monte Carlo Simulation
For the calculation of efficiencies and for the comparison of data with QED predictions, the Vermaseren Monte Carlo 8 is used. For the cross section calculation, the DIAG36 generator 9 is used. It takes into account the full set of QED diagrams up to 0{ai) and their interference terms. For background studies mainly resonances and gg-production, the EGPC 1 0 Monte Carlo is used. The events were fully simulated in the detector, including detector and trigger inefficiencies. Data and Monte Carlo were treated with the same programs. 3
Event selection and Data Samples
The two-photon production of r-pairs is studied by considering an exclusive decay channel, with r * —> e^v^-v,, and r ^ —> p*vT, with pT —> ir^n0. This channel has the highest branching ratio and gives access to 9.02% of all produced r-pairs. The events are selected by using the following criteria:
219
• 2 good tracks of opposite charge requiring a transverse momentum greater than 0.3 GeV and less than 10 GeV, • 2 photons with an energy greater than 0.1 GeV that form a n° with 0.115 <m 7r o < 0.155 GeV, • The higher energy charged particle must be identified as an electron by a positive neural network identification", a strict cut on the shower shape in the electromagnetic calorimeter and a momentum greater than 0.6 GeV, • The least energetic charged particle is assumed to be a pion. • To reject exclusive 77 collison events, the sum of the transverse momenta of all observed particles must be greater than 0.2 GeV. After these cuts the selection efficiencies are in the order of 7.0 % with purities of about 70.0 %. The data have been corrected for trigger efficiencies. Figure 2 shows the good agreement between Monte Carlo and data after the final selection and corrections.
L3 >0)
150-
m
events/0.
Ol 0
CM
C 0
0
J-
• DATA —JAMVG EBKGD
il^n^F v y v l | 1 H—Ml''! f 1 1
00.5
m(7t7t
1.5 (GeV)
Figure 2: Final distributions after all applied cuts: The plots show the combined dataset. The left shows the Et/pt distribution of the electron, that has to peak at 1 for electromagnetic particles. The right shows the distribution of the mass m(7r+7r°) signing the decay T + —»
a
T h e neural network has been trained with SNNS 1 1 to distinguish between electrons, muons and pions by using ten input variables: momentum, dE/dx, Eg, Et/pt, no. of crystals, Ei/Eg, Eg/E25, the energy in the hadron calorimeter, the energy in a cone of 7 degrees in the hadron calorimeter, and the number of crystals for a minimum ionising particle
220
4
Results
The observed number of events are given in table 1, together with the predictions of the DIAG36 Monte Carlo generator. The effects of detector acceptance and trigger efficiencies are already included in the numbers. Good agreement is found between the data and the MC predictions.
L3 a.
^^r^"~~~^^ '102:
/
• DATA 91 GeV - DATA 189-208 GeV
+
— QED prediction
b -in
50
100
150
200
Vs (GeV) Figure 3: The cross section of e+e —• e+e — 7 7 —» e+e T+T . The data points are compared to the C ( a 4 ) QED calculations from DIAG36. The previous inclusive measurement 1 at 91 GeV is shown as well.
In order to compare the cross section with QED calculations, the data are then corrected for the detection efficiency and normalized to the integrated luminosity. The comparison is given in the range 10° < 6 < 170° and for the invariant mass W 7 7 > 3.6 GeV. The combined T branching ratio of 9.02% is then used to calculate the total cross section. The results can be seen in figure 3 and are: a = 458.6 ± 67.5(stat) ± 33.2(sys) pb at 189 GeV
(442.6 pb expected)
a = 453.7 ± 67.4(stat) ± 42.2(sys) pb at 196 GeV
(452.3 pb expected)
a = 459.4 ± 76.2(stat) ± 35.0(sys) pb at 206 GeV
(466.0 pb expected)
The measurement of the anomalous couplings of the T has been obtained by combining all three measurements into one at a mean yfs = 196 GeV,
221
sfs (GeV) 189 192 - 202 202 - 208
j£\U(pb) 172.1 220.9 215.1
Nobs 85.0 ± 9 . 2 97.0 ± 9.8 84.0 ± 9 . 2
Nbkg 24.7 31.0 28.5
N 1,1 exp 58.2 65.8 56.3
Nobs — N b k g 60.3 ± 6 . 5 66.0 ± 6 . 6 55.5 ± 9 . 2
Table 1: Centre-of-mass energies and corresponding integrated luminosities of the three data samples used for this analysis together with the number of observed events, the background contribution and expected numbers of events.
600
theoretical calculation ^r for 196 GeV ^ T
r
550 + 1a
•8. C
500
T
y
theoretical calculation for 196 GeV
\
^r /
/ S^
+^a
~r
meo.ured .
b
" : :_ -
450
=
r. , l,,,!l,,,l,,
I , , , I , , , I , , , I
,!,,,!,,
meosured a
**!.
-,,,, I , , , , I,,
.1....!....!....(..
0.3
4 d°r (10ft5e»^)
,!,,,,!,,,,!,,,, »•'
Figure 4: The comparison of the measured cross-section with theoretical calculations for: Fi in the presence of an anomalous magnetic moment (left). dT in the presence of an anomalous electric moment (right).
222
giving a = 457.2 ± 58.3 pb. In Figure 4 the comparison of the measured cross-section with the theoretical calculations 3 for Fi and dT are shown. The measured results are compatible with the Standard Model prediction. From the lcr bands, the preliminary upper limits for Fi and dT can be extracted and are: 0.062 e + e~pp. The application of QCD to exclusive two-photon reactions is based on the work of Brodsky and Lapage 1 . According to their formalism the process is factorized into a non-perturbative part and a perturbative part. To model non-perturbative effects, the introduction of diquarks has been proposed 2,3 . Recent studies 4 have extended the investigation of exclusive reactions within the quark-diquark model to two-photon reactions. The quark-diquark model works rather well for exclusive reactions in the space-like region 3 . The calculations of the integrated cross-sections for the processes 77 —> pp in the angular region |cos#*| < 0.6, 9* here is the the angle between the proton's momentum and the electron beam direction in the 77 centre-of-mass system (cms), show a good agreement with the existing data, whereas the pure quark model predicts smaller cross-sections 5 ' 6 . In this paper is presented a measurement of the cross-section for the exclusive process e + e _ —* e + e~77 —+ e + e~pp in the range 2.15 GeV < W < 3.95 GeV, using data taken with the OPAL detector at V£ = 183 GeV and 189 GeV at LEP 7 . 2
Event Selection and Cross-Section Measurements for the 77 —> pp Process
The 77 —+ pp events are selected 7 in OPAL by requiring exactly two appositely charged tracks with a minimal distance \do\ < 1cm from the beam axis. For each track the polar angle must be in the range | cos#| < 0.75, the transverse momentum p± > 400 MeV, and have a | cos#*| < 0.6. The two tracks have a "Work supported by Department of Energy contracts DE-FG03-95ER-40894 and DE-AC0376SF-00515 223
224 I EP-i-l 2 < 0-1 GeV 2 . Background from other exclusive processes is reduced by particle identification using the specific energy loss cuts, dE/dx. After all cuts 189 77 —> pp events in the range of 2.15 GeV < W pp) measurements for 2.15 GeV < W < 3.95 GeV and for |cos#*| < 0.6. Also shown in this figure are the results obtained by other experiments 8 ' 9,10 ' 11,12 ' 13 , and the quark-diquark model predictions 4 (solid line). Reasonable agreement is found between this measurement and the results obtained by the other experiments. Figure l b shows the measured 77 —> pp cross-section as a function of W together with the quarkdiquark model predictions 2 ' 4 . There is good agreement between these results and the most recent quark-diquark model 4 . Previous calculations 2 lie below the data, but within statistical and systematic uncertainties shown in the figure, the predictions can be considered in agreement with the measurement. An important consequence of the pure quark hard scattering picture (HSP), is the power law following from the dimensional counting rules 14 . For the 77 ~~y PP process the power law expects da(77 -> PP) „ m dt ~S W where n = 6. The introduction of diquarks here modify the power law of Eq. (1) by decreasing the number of constituents to be taken into account in the process studied. For the 77 —> pp process n = 4. The power law predictions of Eq. (1) are compared to the data in Figure l b for W2 = s, with three values of the exponent n: fixed values of —6, —4, and the best fit value of —5.2 ± 0.5. These three power laws give x2 probabilities of 40%, 11% and 52%, respectively, taking into account both statistical and systematic errors. More data covering a wider range of W would be required to determine the power law more precisely. Figure lc shows the differential cross-section, da(77 —» pp)/d|cos#*|, as functions of |cos0*| for 2.15 GeV < W < 2.55 GeV (low W region). This measurement is compared with the CLEO 1 2 and VENUS 1 3 results. The OPAL measurements lie here below the results obtained by CLEO and VENUS. Since the CLEO measurements were reported for W between 2.0 and 2.5 GeV, we scale the CLEO results to 2.15 GeV < W < 2.55 GeV, and we find agreement with the OPAL measurements 7 . The differential cross-section in the range of 2.55 GeV < W < 2.95 GeV (high W region) is shown in Figure Id. There' is good agreement here between the OPAL, CLEO, and VENUS measurements. The comparison of the measured differential cross-section as a function of I cos 0*| in the high W region with the calculation of4 for different distribution amplitudes, and the results of the pure quark model 5 ' 6 are shown in Figure le. The pure quark and the quark-diquark model predictions lie below
225
3.5 4 W (GeV) ^.a 16 ° CLEO I f k V v ^ J GeV s 14 ^ CLEO scaled o VENUS 2.15<W
°(yy-p~p)
o
to 00
A A N D E° PAIR P R O D U C T I O N IN T W O - P H O T O N COLLISIONS AT LEP BERTRAND ECHENARD DPNC,
on behalf of the L3 collaboration. 24 Quai Ernest-Ansermet, CH-1211 Geneve 4, E-mail:bertrand.Echenard@cern. ch
Switzerland.
Baryon pair production in two-photon collisions is studied with the L3 detector at LEP using data collected at e+e~ center of mass energies from 91 GeV to 209 GeV with an integrated luminosity of 844 p b _ 1 . The four processes 7 7 —> AA, 7 7 —> AS , 7 7 —> 2 ° A and 7 7 —> S ° E are identified. The cross section for these processes as a function of the 77 center of mass energy is measured for the first time at LEP and results are compared to quark-diquark model predictions.
1
Introduction
Using a hard scattering approach 1 , predictions have been made for the production of baryon-antibaryon pairs in two-photon interactions. Due to the failure of a three quark calculation 2 to correctly predict the cross section 77 —* PP m the few GeV region 3 , a quark-diquark model 4 has been proposed to describe baryon production for this energy regime (Fig.2a). This model includes non-perturbative effects through the use of diquarks, a qq bound state within the baryon. We present the first measurement at LEP of the cross section 77 —> (A/E°)(A/E ) with the L3 detector, indicating with this notation the four alternative processes AA, AW, E°A and E°E . The data used for this analysis correspond to a total e + e~ integrated luminosity of 844 p b " 1 . 2
Event selection
To study the reactions e+e" -> e + e-(A/E°)(A/E°), only the E° -» A7, E —> A7, A —> p7r~ and A —> p-7r+ decays are considered. Events with four tracks, a net charge of zero and two secondary vertices are selected. For each secondary vertex the proton (antiproton) is identified as the track with the largest momentum. The ionization loss measurement in the tracking chamber must be consistent with the p7r~p7r+ hypothesis. The track of the antiproton candidate must be in correspondance with a large energy deposit in the electromagnetic calorimeter produced by its annihilation. A clean signal of AA is present in the data, as shown if Fig.la), where 67 events are selected
231
232
Ol
•
i
o
Events I 10 MeV
b)
E°/Z°
20-
| 5< '
t
0.1
1 1
, .411,1.1 1.2
1.3
1.4
m(prcy) - m(p7t) + 1.115 (GeV) Figure 1. a) the bi-dimensional mass plot of m(p7r ) versus m(p7r+). A radius of 40 MeV around the nominal A/A mass defines the ( A / S ° ) ( A / E ^ ) sample, b) the ( E ° / E ) mass distribution for the selected events. E° and E candidates are selected in the mass interval 1.16 - 1.22 GeV.
inside a circle of 40 MeV around the peak of the A/A signal. The KgKg background is estimated to be less than 1%. The reconstruction of (E°/E ) is performed by combining (A/A) with photon candidates. A photon candidate is defined as a shower in the electromagnetic calorimeter with at least two crystals and an energy between 50 MeV and 150 MeV. There must be no charged track within 200 mrad around the photon direction and the cosine of the angle between the antiproton and the photon direction must be smaller than 0.8. For each photon candidate, only the combination with the effective mass nearest to the nominal E° mass is chosen. The (E°/E ) appears as a peak over a smooth background around the nominal value of 1.193 GeV in the (E°/E ) mass distribution 5 . E° and E candidates are selected in the mass interval 1.16-1.22 GeV, as shown in Figure lb). ^KK To select exclusive e + e "(A/E°)(A/E events, the total momenturn of the four charged particles in the transverse plane P ^ = E P T 2 is i
required to be less than 0.25 GeV 2 . After this cut, 33 events are selected. Until now, no distinction has been made between the different final states. The AA, (AE + E°A) and E°E channels are separated as follows. The
233
DZDA
a)
Asymptotic DA Standard DA Three quark &10
A A) corresponding to the interaction of real photons is extracted as a function of W 7 7 . The efficiencies and luminosity functions are evaluated for each W 7 7 interval and centre of mass energy. The 77 —* AA cross section measurement is compared to the one ob-
234
tained by CLEO 4 in Figure 2b). Although the results are compatible inside the large experimental errors, except for the first W 7 7 bin, the mass dependance of CLEO is steeper than the one we observe. A fit to our data of the form a oc M~ n gives a value n = 7.9 ± 3 . 1 while a similar fit to CLEO gives n = 15.2 ± 3.2. The quark-diquark model predicts n=8, a three quark model n=12. The 77 —• AA data are also compared to the predictions of recent quark-diquark model calculations 4 . The authors consider three different distribution amplitudes (DA) for the diquarks. The standard DA is obtained by transforming the harmonic oscillator wavefunction to the light cone 7 . The Dziembowski DA (DZ-DA) 7 and asymptotic DA 8 are adaptations to the diquark case of the DA proposed by Dziembowski 9 and the asymptotic three quark DA. The predictions using the standard DA reproduce well our data (CL=99%), whereas the DZ-DA and asymptotic DA models are excluded with CL=8.6 -10" 4 and CL=2 -lCT8. Acknowledgments We thank C.F.Berger and W.Schweiger for very useful discussions and for providing us their theoretical predictions. References 1. S. J. Brodsky et J. P. Lepage, Phys. Rev. D 22 (1980) 2157. 2. G. Farrar et al., Nucl. Phys. B 259 (1985) 702; Nucl. Phys. B 263 (1986) 746. 3. CLEO collaboration, M. Artuso et al, Phys. Rev. D 50 (1994) 5484. 4. C. F. Berger, B. Lechner and W. Schweiger, Fizika B 8 (1999) 371 hepph/9901338; C. F. Berger, Exclusive Two-Photon Reactions in the Few-GeV Region, Diploma Thesis, Graz University, 1997 5. Particle Data Group, D. E. Groom et al, Eur. Phys. J. C 15 (2000) 1. 6. G. A. Schuler, Improving the equivalent-photon approximation in electron-positron collisions, hep-ph/9610406, CERN-TH/96-297. 7. T. Huang, Nucl. Phys. (Proc. suppl.) B 7 (1989) 320 8. P. Kroll, M. Schurmann and W. Schweiger, Z.Phys A 338 (1991) 339. 9. Z. Dziembowski, Phys. Rev. D 37 (1998) 2030.
T H E ANALYSIS OF
TT+TT-TT0
PRODUCTION IN TWO-PHOTON PRODUCTION
Mikhail Levtchenko PNPI, High Energy Physics Dept., 188350 Gatchina, E-mail:
[email protected] Russia,
On behalf of the L3 Collaboration The reaction 77 —• Tr+Tr~iT0 has been studied with the L3 detector at LEP. The data sample corresponds to a total integrated luminosity of 682.6 p b - 1 collected at the centre-of-mass energies from 183 GeV to 209 GeV. Preliminary results of the full energy dependent partial wave analysis in the mass region 0.65 - 2.15 GeV are presented. The reaction is dominated by the a2(1320) formation. Other signals are also discussed.
1
Introduction and Motivation
Two-photon interactions provide an important tool tu study resonance formation. The two-photon width, T T 7 , is related to the flavour content of qq states and the measurement of form factors provide information about the wave function of quarks inside a meson. Smaller value of T 7 T is an indication for the presence of a glueball or hybrid components in the state. The 77 —¥ 7r+7r_7r° production has been investigated by several experiments 1 2 , using virtual photons produced in e+e~ colliders rings. In a previous publication L 3 3 has analysed data at centre-of-mass energy y/s ~ 91 GeV for an integrated luminosity L ee =140.6 pb obtaining 793 e+e~ —> e + e _ 7r + 7r~7r 0 events. In this report we present a preliminary analysis of a data sample of 22400 events, collected during the years 1997 to 2000 at LEP, for y/s = 183 209 GeV and Lee= 682.6pb . A spin-parity analysis is performed on the 1998 data on a sample of 7740 events, corresponding to Lee= 176.7 pb. 2
The 7T+7r_7r° selection and cross section
The L3 detector 5 is suitable for the study of two-photon processes since events with few tracks and low visible energy in the detector are selected by a track trigger 6 with a low threshold on the track transverse momentum, pr > 150MeV. For quasi-real photon interactions the e+e~ in the final state are mainly scattered at very small polar angles and go undetected. The e+e~ —> e + e - 7r + 7r - 7r 0 events are selected by requiring two tracks with oppo-
235
236
site charge and two isolated electromagnetic clusters forming the 7r° mass.
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Figure 3: The data of the year 1998 (dots with error bar) for 0.65 < M 7 7 < 2.15 compared to the maximum likelihood fit results (histogram) described in text. The distribution of a) the Tt+ir~n0 mass, b) the 7r+7r~ mass, c) the 7r°7r± mass, d) the angular distribution of the n^ in the 7 7 c.m.s. e) the angular distribution of the 7T° in c.m.s. of 7 7 system and f) the angular distribution of charge pion in ir+ir~ c.m.s. system .
Oio
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Figure 1. Distributions of transverse momentum squared (p 2 ) for 7T+7T 7T° events in two mass ranges. The Monte Carlo simulated with a p-pole form factor are normalized to T 7 7 = 1.0 keV for a 2 (1320) and T 7 7 • BR(7r+7r _ 7r°)= 0.29 keV for a 2 (1750).
243
background parameterized by a second order polynomial. The Monte Carlo prediction for <X2(1320) was normalized and fixed to the nominal two-photon radiative width and serves as a side-band constraint for background. The background distribution was also constrained by the above 2.0 GeV/c 2 sideband The resonance mass and width are determined by minimizing the x 2 to the Monte Carlo distributions generated at several mass positions and widths. The x 2 / n ( tf obtained in the mass region of 1.55 < m(3ir) < 2.0 GeV/c 2 is 1.3. The background fraction of the fit is 39%. The two-photon radiative width is obtained by normalizing the observed number of events to the selection efficiency. The dominant systematic uncertainties come from the estimation of background and selection efficiency. The effects were evaluated with the Monte Carlo distributions scaled for the errors in resonance mass, width and background level. The selection efficiency differs for the decay intermediate state and spin-parity. For a pure Jp = 2 + helicity 2 state with equal decay amplitude into the interference of pir and /2Tr, the parameters obtained are mass m = 1740 ± 10 ± 10 MeV/c 2 ; width T = 290 ± 30 ± 20 MeV; radiative width T 7 7 • BR^+TT-TT0) = 0.27 ± 0.02 ± 0.04 keV. The invariant mass spectra of di-pions for events in the 1750 MeV/c 2 region were examined for the decay intermediate states. The interference of pit and /27r for Jp = 2 + is expressed by the phase angle <j> and the relative amplitude a. The phase angle has an effect of shifting the di-pion mass peaks of p and f2 toward each other as 0 gets smaller. The peak positions are compatible to the nomial values at = 180°. The two interference parameters were determined by x 2 tests for the di-pion mass spectra and the Monte Carlo predictions of pure Jp = 2 + helicity 2 state. Full simulations were performed for discrete phase angles from 90 to 240 degrees and amplitude (b) a=0.9d)=140 o , >40CH
o
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• 0 .
(3)
7T
From (3) it is obvious that, in the real photon limit, the transition form factor is <x\ + Y^Bn to LO. To NLO the sum ^Bn is slightly resolved due to the running of as and evolution. In practice the analyses of Fw7 are performed with a truncation of the Gegenbauer series. The simplest analysis assumes Bn = 0 for n > 4 6 . A fit to the CLEO data 1 above Q2min = 2GeV 2 then provides £?2(1 GeV) = -0.06 ± 0.03 to NLO accuracy in the MS scheme. If one allows for B^ and BA in the analysis there is no unique result for the individual coefficients. Rather there is a strong linear correlation between both the coefficients; only extreme values of |i?2| and |i?4|, say above 1 or 2, are ruled out. A compact way of presenting the result of this fit is to quote the values of the linear combinations B2 + B4 and B2 — B4, which have approximately uncorrelated errors: B% + B\ = —0.06 ± 0.08 and B2 — B4 — 0.0 ±0.9 at a scale of 1 GeV. This illustrates that, within a leading twist NLO analysis, the CLEO data on the 7*7 —• 7r form factor approximately fixes only the sum £] Bn to be close to zero. Besides the uncertainties due to the choice of fiF, ^R and Qmin there is another important one in the analysis of the form factor data that arises from possible power corrections. While our analysis reveals that logarithmic effects suffice to describe the residual Q2 dependence of the CLEO data for Q2FW7 above 2 GeV 2 , substantial power corrections cannot be excluded since it is very difficult to distinguish a power from a logarithmic behaviour in Q2 with data in the range between 2 and 8 GeV 2 . It is to be emphasized that any estimate of power corrections is subject to a strong model dependence. Leaving this out of consideration, one may arrive at misleading results.
247 U.l
0.09
a cos IS 0.07 r ° o.o6 0
0.2
0.4
0.6
0.8
1
Figure 1. Comparison of the full result (1) for Q2Fin* (solid line) with (4) (dashed line) and the w —>• 0 limit (dash-dotted line). The form factor is evaluated at Q = 2 GeV for the distribution amplitude with Bi = 0.54, B4 = —0.40, B$ = —0.20 at a scale of 1 GeV.
Let me now turn to the case of two virtual photons. From (3) one sees that for small LO a Gegenbauer coefficient B„ is suppressed in Fn^* by a power w". Thus, for small w, one has r? ( in (A\ ^ a W\ ) cV_^ 7/ 4| li - a-» +. wT2 [[ il - -5 a-* +,y1B2 2R^l(1+ .- 5- ajA]\j | (4) The limiting behavior for u> —> 0 has already been given in 3 . Given the small numerical coefficients in front of to2, the u> independent term in Eq. (4) dominates over a rather large range of w. Even at u ~ 0.6 the OJ2 corrections amount to less than 15% if |2?2| < 0.5. Thus, for a wide range of u the 7* — 7r transition form factor is essentially independent of the pion distribution amplitude. To illustrate the quality of the small-w approximations we compare in Fig. 1 the full result (1) for Fn^> with the expression (4) for an extreme example of a distribution amplitude. The full calculation is in agreement with the CLEO data for w —^ 1. We see that, although B2 in our example is quite large and positive, both approximations are indeed very good for co < 0.6. Only for cj-values near 1 the form factor is sensitive to details of the distribution amplitude. One thus has a parameter-free prediction of QCD to leading-twist accuracy. Any observed deviation from the limiting behaviour for u> —> 0 beyond what can reasonably be ascribed to 0 ( a 2 ) terms would be an unambiguous signal for power corrections. For small ui, the limiting behaviour of the form factor has a status comparable to the famous expression of the cross section ratio R — a(e+e~ —>• hadrons)/a(e + e _ —• fi+fx~). The 7* — r] and 7* — 7/ transition form factors can be analyzed along the same lines as for the pion. The only complication is that, to order as, there is a contribution from the two-gluon Fock state, its distribution amplitude
248
mixes with the SU(3)-singlet distribution amplitude under evolution. It has been shown 7 that, in the real photon limit, the CLEO 1 and L3 8 data on the 7 — 7/') form factors are consistent with approximately equal distribution amplitudes for the n, r) and r{ and correspondingly vanishing gluon ones. For small ui one obtains in analogy to (4) 1 - as
+ 0(u;2,a2s).
(5)
where /J,ff are effective, process-dependent decay constants. Using for instance the quark-flavor mixing scheme 9 , one finds for the decay constants f*s = 0.98fir and f*? = 1.62/*. At small u and large enough Q2 the ratio of the j*-r}, T}' form factors constitutes an accurate measure of the effective decay constants. This can be used for a severe test of the r} — r\' mixing scheme. In summary: In the real photon limit the transition form factors essentially provide information on ^ Bn and these sums seem to be small. Data at large Q2 are needed in order to determine the size of power corrections. For u) < 0.6, on the other hand, the form factors are essentially independent of the distribution amplitudes. One thus has a parameter-free QCD prediction which well deserves experimental verification. Rate estimates for the running .B-factories reveal that F„-7. should be measurable for Q 2 < 4 G e V 2 (for a luminosity of 30 fb _ 1 per year). Acknowledgments It is a pleasure to thank Maria Kienzle and Maneesh Wadhwa for the wellorganized and interesting PHOTON 2001 conference. References 1. 2. 3. 4. 5. 6. 7. 8. 9.
J. Gronberg et al. [CLEO collaboration], Phys. Rev. D 57, 33 (1998). M. Diehl, P. Kroll and C. Vogt, hep-ph/0108220. F. Del Aguila and M.K. Chase, Nucl. Phys. B 193, 517 (1981). E. Braaten, Phys. Rev. D 28, 524 (1983); E.P. Kadantseva, S.V. Mikhailov and A.V. Radyushkin, Sov. Jour. Nucl. Phys. 44, 326 (1986). G.P. Lepage and S.J. Brodsky, Phys. Rev. D 22, 2157 (1980). P. Kroll and M. Raulfs, Phys. Lett. B 387, 848 (1996). T. Feldmann and P. Kroll, Eur. Phys. J. C 5, 327 (1998). M. Acciarri et al. [L3 Collaboration], Phys. Lett. B 418, 399 (1998). Th. Feldmann, P. Kroll and B. Stech, Phys. Rev. D 58, 1140006 (1998).
"GLUEBALLS": RESULTS A N D P E R S P E C T I V E S F R O M T H E LATTICE GUNNAR S. BALI Department of Physics and Astronomy, University of Glasgow, G12 8QQ, UK E-mail: [email protected] I review the present status of lattice calculations of properties of "gluon-rich" hadrons and comment on future prospects, in view of planned experiments.
1
Review of lattice results
The gluons of QCD should not only manifest themselves in deep inelastic scattering but also affect the hadron spectrum. In the sector of pseudoscalar mesons this is indeed the case: gluodynamics results in the axial anomaly which in turn implies a big mass gap between the singlet 77 and the octet of SU(3) Goldstone pions. In addition to such indirect effects, QCD in principle offers the possibility of bound states made entirely out of glue. In lattice simulations of the so-called quenched approximation (or quenched model) to QCD, i.e. QCD without sea quarks, a rich spectrum of glueballs has been established in the past decade. 1 ' 2 The scalar (J p c = 0 + + ) turns out to be lightest with a mass between 1.4 and 1.8 GeV, followed by a tensor of mass between 1.9 and 2.3 GeV and a pseudoscalar that is heavier by another 150 MeV 1,3 ' 2 ' 4 ' 5 . All but five states turn out to be heavier than 3 GeV, 1 ' 2 overlapping with charmonia states, a mass region that future experiments might shed more light onto. 6 The other striking features are the somewhat counter-intuitive spin ordering of the spectrum, e.g. 1,3,2,0 in the PC — H— sector but 0,2,3,1 in the + + sector as well as the fact that the lightest spin-exotic state is well above 4 GeV. The scalar glueball is of particular phenomenological interest. 7 While all raw lattice data agree with each other within statistical errors of about 40 MeV, rather different values are quoted in the literature: 1 ' 3 in QCD an experimental input is required to set the mass scale. However, in the quenched model ratios of light hadronic masses can easily deviate from real world experiment by as much as 10 %.8 Hence, to some degree the translation into physical units is a matter of personal preference. This uncertainty is accounted for in the mass ranges quoted above. In real QCD with sea quarks, it is not entirely obvious in how far e.g. a vector glueball that contains cc sea quarks can be distinguished from a J/ip
249
250
that contains sea gluons: no pure glueballs exist but then neither do pure quark model mesons and yet the J/«/> is distinctively different from a cf> that shares the same quantum numbers. We can interpret the former as being close to a quenched cc state and the latter as a dominantly ss state. In QCD some almost pure glueballs might exist. It might also be that some QCD states can be understood in terms of mixing between glueballs and mesons of the quenched model. In some sectors it might even happen that an interpretation in terms of mixing breaks completely down and the gluons merely result in extra states that are hard to distinguish from radial excitations. Socalled spin-exotic quantum numbers like JPC = 0 , 0 + _ , l _ + , 2 + ~ , • • • are of particular interest in the search for gluon-rich states, i.e. "glueballs" and (quark-gluon) "hybrid mesons", however, even in this sector exotic four-quark "molecules" and hybrid mesons can have very similar signatures. On the theoretical side two directions of research are being pursued: quenched and "un-quenched". The quenched model is a natural extension of the quark model and provides the language required to speak about mixing between quark model states and glueballs. In order to make the connection to phenomenology glueballs are not enough but the corresponding flavour singlet meson states have to be studied too. Lattice simulations indicate that the quenched ss isoscalar meson is about 200 MeV lighter than the scalar glueball. 9 ' 10 Another important question is that of molecules. Despite of some attempts in this direction 11 this possibility is vastly unexplored at present. The / 0 (980),a 0 (980) and the / 0 (400 - 1200) are widely believed to be KK and 7T7T resonances, 12 ' 7 however, this view which is important for the interpretation of the / 0 (1370), /o(1500) and /o(1710) 7 as mixtures between a scalar glueball and the two lightest isoscalar quark model mesons, is not completely un-debated. 13 Molecules might also be required to explain the difference between the spin-exotic 1 h mesons observed around 1.4 and 1.6 GeV in experiment but predicted around 1.9 GeV in lattice studies. The next step would be to look into mixing. In addition to the first exploratory lattice investigation 10 several models have been proposed. 14,9,15 In some references the /o(1500) receives the dominant gluonic contribution, 14 in others it is the /o(1710). 9 Finally, production and decays reveal information about the quark content of a given resonance, provided one knows what to expect from a glueball. Lattice methods are only of limited use here although an exploratory study does exist. 16,9 The second, cleanest path is to compute the spectrum of QCD as is. One can then compare with experiment and hopefully find agreement. Unfortunately, the direct approach does at present not only turn out to be prohibitively expensive computationally but it does not really tell us what we
251 1
""TT
1
I |
1
1
r
quenched *—-a—< SESAM ^ — -
1
UKQCD —*~™H
T* -
.
o
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0
0.02
*
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i
i
i
0.04
0.06
0.08
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(a/r0)2 Figure 1. The scalar "glueball" with nf = 2 vs. the lattice spacing o (r^
fa 400 MeV).
want to know either: just like in real experiment we would only be able to determine masses and, by varying the lattice volume, decay widths within a given channel but little would be revealed about the nature of the states. Mixing cannot be studied because the resonances are just out there. Fortunately, in our virtual computer experiment we can gradually reduce the quark mass, starting from the quenched approximation, and trace any changes, in particular in the neighbourhood of decay or mixing thresholds. We are still in the position that the combined "world data" on the scalar rif = 2 "glueball" fits into Fig. 1. The quenched case 4,1 is included for reference. The un-quenched results have been obtained by use of three different lattice discretisations of the Dirac action: staggered (HEMCGC 17 ), Wilson (SESAM 18 ) and clover (UKQCD 10 ' 19 ). The quarks are all heavier than m s / 3 , the scalar meson is still stable and the wave function turns out to be very close to that of the quenched glueball. 18 ' 10 Most n; = 2 points clearly lie below the quenched line, however, there is certainly a slope in the results, such that the mass in the physical a = 0 limit appears consistent with the quenched result. Within the SESAM data set there is an apparent discontinuity because different points have been obtained at different quark masses; the "glueball" becomes lighter as the quark mass is reduced. Whether this effect weakens as the continuum limit is approached is a question as open as whether anything will substantially change once the quarks have become realistically light.
252 2
Outlook
The quenched glueball spectrum is "solved" and first promising n/ = 2 results exist. Future studies of mixing in the quenched set-up are important. Flavour singlet mesons and molecules as well as standard charmonium spectroscopy has been neglected in the past for various reasons but lattice methods and computers have sufficiently matured to allow for a fast quenched relief. More challenging but ultimately necessary is an analysis of the quark mass, volume and lattice spacing dependence with rif = 2 + I sea quarks. Acknowledgments G.B. is a Heisenberg Fellow (DFG grant Ba 1564/4-1) and has received support from PPARC grant PPA/G/O/1998/00559. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
G.S. Bali, et al. [UKQCD collab.], Phys. Lett. B 309, 378 (1993). C.J. Morningstar and M.J. Peardon, Phys. Rev. D 60, 034509 (1999). J. Sexton et al. [GF11 collab.], Phys. Rev. Lett. 75, 4563 (1995). B. Lucini and M. Teper, JHEP 0106, 050 (2001). G.S. Bali, Phys. Rept. 343, 1 (2001). K. Peters in Hirschegg 2001, Structure of hadrons, ed. H. Feldmeier, J. Knoll, W. Noerenberg, J. Wambach (GSI, Darmstadt, 2001) p. 320. F.E. Close, arXiv:hep-ph/0110081; C. Amsler, these proceedings. S. Aoki et al. [CP-PACS collab.], Phys. Rev. Lett. 84, 238 (2000). W. Lee and D. Weingarten, Phys. Rev. D 61, 014015 (2000). C. McNeile and C. Michael, Phys. Rev. D 63, 114503 (2001). M. G. Alford and R. L. Jaffe, Nucl. Phys. B 578, 367 (2000). M.R. Pennington, arXiv:hep-ph/9905241. P. Minkowski and W. Ochs, arXiv:hep-ph/9905250. C. Amsler and F. E. Close, Phys. Rev. D 53, 295 (1996); F.E. Close and A. Kirk, Eur. Phys. J. C 2 1 , 531 (2001). A.V. Anisovich et al, arXiv:hep-ph/0108188; A.V. Anisovich, these proceedings; Y.A. Simonov, arXiv:hep-ph/0110033. J. Sexton et al. [GF11 collab.], Nucl. Phys. Proc. Suppl. 42, 279 (1995). K. M. Bitar et al. [HEMCGC collab.], Phys. Rev. D 44, 2090 (1991). G. S. Bali et al. [SESAM collab.], Phys. Rev. D 62, 054503 (2000) and in preparation. A. Hart and M. Teper [UKQCD collab.], arXiv:hep-lat/0108022.
MESON RESONANCES IN PROTON-ANTIPROTON ANNIHILATION C. AMSLER Physik-Institut der Universitat Zurich Winterthurerstrasse 190, CH-8035 Zurich, Switzerland E-mail: [email protected] Crystal Barrel data for proton-antiproton annihilation in flight at 900 MeV/c are presented. The channels pp —>• 37r°, 7r°7r°7j and 7r0T)T) are used to search for isoscalar 0++ and 2 + + mesons in the mass range 1500 - 2000 MeV. Both 3TT° and 7r°f)7j data sets require an isoscalar 2++ resonance decaying into 7r°7r° and Tyq with mass M - (1867±46) MeV and width T = (385±58) MeV. The analysis of ir°n°r] leads to an isovector 2++ state decaying into 7T°TJ with mass M = (1698 ± 44) MeV and width T = (265 ± 55) MeV. The 37r° and ii0nv data do not show any /o(1710). This adds supportive evidence that this meson is mainly ss.
1
Introduction
Scalar (0 + + ) mesons overpopulate the mass spectrum below 2 GeV. Table 1 shows a possible SU(3) classification of these states. The low mass scalars are interpreted as scattering resonances1. Alternatively, the ao(980) and /o(980) are often referred to as KK molecules or q2q2 states 2 ' 3 . In the literature the narrow /o(1500) and /o(1710) compete for being the ground state glueball. Recent data in pp annihilation and in central production show that both the /o(1370) and /0(1500) couple mainly to pions4'5 while /0(1710) couples mainly to kaons5. I will show that /o(1710) is dominantly ss. This then adds evidence for /o(1500) to be mainly gluonic, while /o(1370) is the uu 4- dd isoscalar meson 6 . More complicated schemes have been proposed. For a detailed discussion and for a bibliography see refs. 7 ' 8 . 7= 1 ao(980) a 0 (1450) ?
7= 0 /o(400 - 1200) (or a) /o(1370) /o(1500) /o(2020)
7= 0 /o(980)
7 = 1/2 K(900)
Nature Scattering resonances
/o(1710)
7 37r° (six entries per event) with /2(1270) (A), /o(1500) (B), /o(980) (C). Right: Dalitz plot for pp -> 7r°7r°7j (two entries per event) with /2(1270) (A), /o(980) (B), a2(1320) (C) and a0(980) (D).
The three annihilation channels were selected by applying kinematic fits requiring also three pairs of 27 invariant masses to match the 7r° or 7? masses. For measurements in flight the annihilation vertex of neutral events was not observed and had therefore to be determined by the kinematic fit. The data and results presented here are at variance with the ones reported in ref. u which assumed a vertex at the center of the detector. The feedthrough from one channel to the other was determined to be less than 0.7 %. The reaction pp -> TT°UJ with w -» 7r°7 (and a missing 7)
255
m2(m\) [GeV2]
m(T\T\) [MeV]
Figure 2: Left: Dalitz plot for pp -¥ n°r)rj (two entries per event) with ao(980) (A), a2(1320) (B), / 0 (1500)// 2 (1525) (C). Right: TJTJ mass projection showing the / 0 (1500)// 2 (1525). The long tail is due to the new /2(1870). The histogram is the final fit discussed in the text.
was the dominating background channel for TT°T)TJ and 7r07r°r/. Background contributions of 13 % to 7r°7jrj and 3 % to 7r°7r°77 were estimated from the data. The background in the 37r° channel was negligible. The symmetrised 7r07r07r° Dalitz plot is shown in fig. 1 (left). One observes the /2(1270), the /o(1500) and/or /2(1565). A faint dip in the 1500 MeV band around 1000 MeV corresponds to the /o(980) interfering destructively with the structure at 1500 MeV. Figure 1 (right) shows the Dalitz plot for 7r°7r°T?. One observes the /2(1270), the /o(980), the /2(1270), and the ao(980). The symmetrised TT°T]T} Dalitz plot and the 7777 mass projections are shown in Figure 2. One observes the ao(980), the a2(1320), the /o(1500), and/or /£(1525), and a band around 1000 MeV from the a0(980). In the region of the /o(1710), only the interference of the two oo(980) bands can be observed and no obvious signal is present (arrow D). The data sets were analysed in the helicity formalism in terms of the isobar model, in which the pp system is assumed to decay into the three-body final states through a two-body intermediate state made of a resonance and a spectator meson 12 . The K-matrix formalism described the mass dependance of resonances13. Masses and widths of resonances were given by the complex poles of the T-matrix. The following initial partial waves were included in the analysis of the present data: 1 S 0 , 3Pi, 3 P 2 + 3F2,1D2, and 3F3. The TTTT irr) and 7777 S-waves were parametrized by K-matrices with the parameters obtained at rest, where only 1So contributes14-15.
256
3
Results
The first description of 37r° included the -KIT S-wave and the /2(1270). The fit was then extended with a second pole in the rnr D-wave to test for a spin 2 meson. The fit clearly required a high-mass tensor state around 1870 MeV. The best fit was obtained by parametrising the TTTT D-wave as a K-matrix with three poles: /2(1270), /2(1565) and a broad new tensor state with mass 1877 MeV and width 318 MeV, which we call /2(1870). The first description of ir°w0T) consisted of the TTK S-wave, the /2(1270), the ao(980) and a0(1450) in the TTT] S-wave, and the a2(1320). Crystal Barrel reported in ir°rfq at 1940 MeV/c an isovector state at 1660 MeV, decaying into 7r°rj16. Hence this 02(1660) was introduced into the ( l x l ) K-matrix of the -KT) D-wave as a second pole. The fit improved significantly. The 0,2 (1660) contributes with (7 ±2) % to the data and for this 2 + + isovector state we find a mass of 1698 ± 44 MeV and a width of 265 ± 55 MeV, in excellent agreement with our result in iPt]r\ at 1940 MeV/c 16 . The first description of TT0T]T] included in thefl-77S-wave, the oo(980) and the ao(1450), and the a2(1320) in the 7rr? D-wave. Significant differences between fit and data were observed for TJT) masses around 1500 —1550 MeV and 1650 —1800 MeV. To describe the 777? peak at 1500 MeV, the tensor resonance /2(1525) was introduced. A good agreement with data could be obtained in the high mass region by adding a high mass tensor state with mass 1820 MeV and width 358 MeV. The mass and width of the latter agree with the ones found in the analysis of 7r°7r07r°. The r/r) invariant mass projection is shown in fig. 2. The data description is good and there are no significant deviations. The /o(1500) contributes with (10 ± 2) %, the .^(1525) with (15±^) %. The inclusion of the /o(1710) in the t)r\ S-wave was not successful. Hence the /o(1710) is not required to describe the 7r°r7r/ data set. Since the analyses of 7r07r07r° and 7r°?jT? require a high-mass isoscalar tensor state, the two data sets were simultaneously fitted with a common description of the resonances, e.g. the /2(1870) (for 7r07r°7j this state lies far above the phase space limit). The fitted Dalitz plots and projections for the two data sets differ only marginally from the ones obtained by the single fits. The T-matrix mass and width of the isoscalar /2(1870) are 1867 ± 46 MeV and 385 ± 58 MeV, respectively.
257 4
Discussion and conclusions
The analysis of pp -> 7r°7r°7j clearly showed that the nr) D-wave wave requires two poles, corresponding to the 02 (1320) and its radial excitation 02(1660). The L3 collaboration analysing 77 -» 7r+7r~7r° also reported a 2 + + isovector state at a mass of 1750 MeV, decaying into 7r+7r_7r° 17 . The mass of our a2(1660) is consistent with the L3 result within errors. The fits of 7r07r°7r° and 7r°rj7j including an / 0 (1710) were not satisfactory. In the best fit of pp -»• 37r° the improvement of the log-likelihood was not significant when the /o(1710) was included. When mass and width of the /o(1710) were fitted freely in the 7r07r°7r° and w°r)r) data sets, the resulting object was broad and the other resonances became unstable. The conclusion was drawn that the / 0 (1710) is not present. We derived an upper limit for the contribution of the /o(1710) to 7r07r°7r° and ir°T)r) of 2.1 % and 2.6 %, respectively, at 90 % confidence level, assuming a mass of 1715 MeV and a width of 125 MeV 1 8 . The absence of a signal for this isoscalar points to a dominant ss component, as there are no known mechanisms suppressing uu+dd scalars in pp annihilation. The absence of / o (1710) in our data is therefore compatible with an ss assignment. Recent results in central production 5 show that /o(1710) prefers to decay into KK rather than into TTTT. This also points to an ss interpretation of the /o(1710) and therefore suggests that this meson is the (mainly) ss member of the scalar nonet. New data in 77 collisions have been presented by the LEP collaborations. L3 observes three peaks below 2 GeV in the KsKs mass distribution 19 ' 20 . The lowest peak corresponds to /2(1270) and 02 (1320), interfering destructively. The amplitude analysis reveals the ^(1525) while /o(1500) is not observed. Spin 2 is preferred for the third peak around 1760 MeV. However, a large spin 0 component (as large as 50%) can be accommodated 20 . Note that the isospin is not determined in the KsKs final state. We suggest that the 2 + + state observed in 77 -> KsKs is actually 02 (1660) and that the smaller 0 + + contribution is due to /o(1710). These results in pp, 77 and central collisions strengthen the interpretation of the /o(1500) as a glueball, or as a state with a large gluonic admixture in its wave-function 6 ' 21 : since /o(1500) does not couple strongly to KK it absence in 77 -> KgKg is not surprising. However, the ALEPH collaboration, studying the reaction 77 -+ TT+TT-, observes / 2 (1270) but not / 0 (1500) 2 2 . Since /o(1500) has a large coupling to TTTT this, together with its absence in KsKs, indicates that /o(1500) is not produced in 77 processes, as expected if /o(1500) is mostly gluonic. We note that ALEPH does not observe /o(1710) either, but the data
258
are not sensitive enough for ss states. The 7r07r°7r° and ir°r)r] data sets require a high-mass tensor /2(1870) decaying to 7r°7r° or r)T). We do not confirm the narrow /2(1810) decaying into 7T7T18. What is this new state? The relative strength of the /2(1870) decaying to TjT) and 7r°7r° is 0.27 ± 0.10. This ratio is related to SU(3) mixing angles 6 . One gets two solutions for the mixing angle 10 , one being compatible with a pure uu + dd state {9 ~ 35.3°), hence a radial excitation of the / 2 (1270). Then /2(1565) and /2(1870) are both radial excitations but do notbelong to the same nonet. The other solution (6 ~ 15°) leads to a large ss component for / 2 (1870), in which case / 2 (1565), a 2 (1660) and / 2 (1870) could belong to the 2 3 P 2 nonet of radial excitations. The mass formula then predicts the kaon-like state to lie around 1800 MeV. The ambiguity between the two mixing angles could be resolved by measuring the 7777 and/or KK decay rates of the /2(1870). 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
J.A. Oiler et al., Phys. Rev. D 59 (1999) 074001 R.L. Jaffe, Phys. Rev. D 15 (1977) 267, 281 J. Weinstein, N. Isgur, Phys. Rev. D 41 (1990) 2236 A. Abele et al., Phys. Rev. D 57 (1998) 3860 D. Barberis et al., Phys. Lett. B 462 (1999) 462 C. Amsler and F. E. Close, Phys. Rev. D 53 (1996) 295 C. Amsler, Nucl. Phys. A 663 (2000) 93c C. Amsler in Rev. of Particle Physics, Eur. Phys. J. C 15 (2000) 682 C. Michael, Hadron 97 Conf., AIP Conf. Proc. 432 (1998) 657 C. Amsler et al., submitted to Eur. Phys. J. C; M. Heinzelmann, PhD thesis, Universitat Zurich, 2000 A. V. Anisovich et al., Phys. Lett. B 449 (1999) 145, 154 C. Amsler and J.C. Bizot, Comp. Phys. Commun. 30 (1983) 21 S. U. Chung et al., Ann. Physik (Leipzig) 4 (1995) 404 C. Amsler et al., Phys. Lett. B 355 (1995) 425 For a review see C. Amsler, Rev. Mod. Phys. 70 (1998) 1293 A. Abele et al., Eur. Phys. J. C 8 (1999) 67 M. Acciarri et al., Phys. Lett. B 413 (1997) 147 D. E. Groom et al., Rev. of Part. Physics, Eur. Phys. J. C 15 (2000) 1 M. Acciarri et al., Phys. Lett. B 501 (2001) 173 S. Braccini, PhD thesis, University de Geneve, 2001 F. Close and A. Kirk, Phys. Lett. B 483 (2000) 345 R. Barate et al., Phys. Lett. B 472 (2000) 189
R A D I A T I V E DECAYS OF BASIC SCALAR, V E C T O R A N D T E N S O R M E S O N S A N D T H E D E T E R M I N A T I O N OF T H E P-WAVE QQ MULTIPLET A. V. ANISOVICH Petersburg Nuclear Physics Institute, 188300 Gatchina, St.Petersburg, Russia E-mail: [email protected] We perform simultaneous calculations of the radiative decays of scalar mesons /o(980) - • 77, a 0 (980) -> 7 7 , vector meson (1020) -> 7/ 0 (980), 7a 0 (980), 771-0, 77), 77/ and tensor mesons a2(1320) -» 7 7 , /2(1270) -> 7 7 , /2(1525) -> 77 assuming all these states to be dominantly the qq ones 1. A good description of the considered radiative decays is reached by using almost the same radial wave functions for scalar and tensor mesons that supports the idea for the /o(980), ao(980) and 02(1320), /2(1270), /2(1525) to belong to the same P-wave qq multiplet.
Despite a long history of the P-wave qq multiplet 2 the problem of definition of qq scalars is still a subject of lively discussion, see e.g. 3 ' 4 ' 5 and references therein. Radiative decays of mesons may serve as a useful tool for the study of qq structure of mesons, in particular, P-wave qq component in / 0 (980) and Oo(980). In this way, it is rather important to investigate simultaneously the other mesons which belong to the P-wave qq multiplet, namely, tensor mesons a2(1320), /2(1270) and /2(1525). In the paper 1 , combined calculations of the decays oo(980) -> 77, / 0 (980) -»• 77, o2(1320) ->• 77, / 2 (1270) -> 77, and /2(1525) —> 77 are carried out assuming the qq radial wave functions in these mesons to be nearly the same. Radiative decays of the 0-meson are another source of important information on scalar mesons. We have calculated the decay processes with the production of mesons belonging to scalar and pseudoscalar sectors: 0(1020) -¥ 7/0(980),700(980) and 0(1020) -> 7710,7??,777'. These latter, of the type of V —>• 7 P , are the classical reactions, which had been used rather long ago for the determination of qq structure of vector and pseudoscalar mesons 6 . We believe that simultaneous description of the processes S -¥ 77, T -> 77, V -¥ 7 5 and V -* -yP is a necessary test for the whole calculation procedure and determination of the P-wave qq multiplet. In calculations of the decay form factors we use spectral integration over qq states together with the light-cone wave functions for the qq mesons; the method of the spectral integration for the form factor amplitudes has been developed in a set of papers 7 , 8 , 9 , 1 0 . The detailed presentation of the technique for the description of compos-
259
260 ite qq systems can be found in Refs. 8 ' 9 > 10 ; where the pion form factor was studied together with transition form factors TT° -»• 7(Q 2 )7, V ->• l(Q2)l axi 0.4 GeV/c and a polar angle —0.34 < cos#iab < +0.82. We impose a strict pt-balance requirement in the final state, IX^Ptl 2 < 0.01 GeV 2 , in order to select events induced by two quasi-real photons. Charged kaons are identified using information on Ejp from the Csl calorimeter, TOF counters, silica-aerogel counters and dE/dx in the Central Drift Chamber. Data corresponding to an integrated luminosity of 32.6 fb - 1 are used for the analysis. We show the cross section for the 77 —¥ K+K~ process derived from
263
264 Table 1. Results for the resonance parameters obtained from the W-dependence of the cross section for 7 7 -»• K+K~. r?7, (f> -> 7/7 with the KLOE detector at D A $ N E T h e K L O E C o l l a b o r a t i o n " p r e s e n t e d b y G. Lanfranchi Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, via E. Fermi 40, 00044 Frascati (Roma) E-mail: [email protected] KLOE has analysed ~ 16.6 p b _ 1 of total 30 p b " 1 collected at D A * N E by the end of 2000. The preliminary results for the branching ratios BR{<j> —* /o (980)7) = (23.7 ± 0 . 6 s t a t ) x 1 0 " 5 and BK( -» a 0 (980)7) = (5-8 ± °- 5 stat) x 1 0 ~ 5 l e a d t o a ratio BR(<j> -» / 0 (980)7)/B.R( a 0 (980)7) = 4.1 ± 0.4 s t a t with a systematic error which will not exceed 10%. The ratio BR( —» r)'-y)/BR( —> rp/) has been measured to about 10% accuracy leading to a very accurate determination of the mixing angle (pp = (40^j'g)° and to the most accurate determination of BR(4> -» n'f) to date, BR(cf> — 7/7) = (6.8 ± 0.6 ± 0.5) • 1 0 ~ 5 .
1 1.1
Detection of / -> o 0 (980)7, /o(980)7 decays Introduction
The nature and the properties of the lowest lying scalar mesons a o (980) and /o(980) l are being investigated with the KLOE detector 2 at D A $ N E 3 where these resonances can be studied in detail in radiative decays 4 . In the past several proposal have been made regarding the constitution of these scalars as complex qqqq states 5 , KK molecules 6 or ordinary qq mesons 7 . In more sophisticated pictures these states could be seeded by a compact qqqq component " T h e KLOE collaboration: A. Aloisio, F. Ambrosino, A. Antonelli, M. Antonelli, C. Bacci, G. Barbiellini, F. Bellini, G. Bencivenni, S. Bertolucci, C. Bini, C. Bloise, V. Bocci, F. Bossi, P. Branchini, S. A. Bulychjov, G. Cabibbo, R. Caloi, P. Campana, G. Capon, G. Carboni, M. Casarsa, V. Casavola, G. Cataldi, F. Ceradini, F. Cervelli, F . Cevenini, G. Chiefari, P. Ciambrone, S. Conetti, E. De Lucia, G. De Robertis, P. De Simone, G. De Zorzi, S. Dell'Agnello, A. Denig, A. Di Domenico, C. Di Donato, S. Di Falco, A. Doria, M. Dreucci, O. Erriquez, A. Farilla, G. Felici, A. Ferrari, M. L. Ferrer, G. Finocchiaro, C. Forti, A. Franceschi, P. Franzini, C. Gatti, P. Gauzzi, A. Giannasi, S. Giovannella, E. Gorini, F. Grancagnolo, E. Graziani, S. W. Han, M. Incagli, L. Ingrosso, W. Kluge, C. Kuo, V. Kulikov, F. Lacava, G. Lanfranchi, J. Lee-Franzini, D. Leone, F. Lu, M. Martemianov, M. Matsyuk, W. Mei, A. Menicucci, L. Merola, R. Messi, S. Miscetti, M. Moulson, S. Miiller, F. Murtas, M. Napolitano, A. Nedosekin, F. Nguyen, M. Palutan, L. Paoluzi, E. Pasqualucci, L. Passalacqua, A. Passeri, V. Patera, E. Petrolo, D. Picca, G. Pirozzi, L. Pontecorvo, M. Primavera, F. Ruggieri, P. Santangelo, E. Santovetti, G. Saracino, R. D. Schamberger, B. Sciascia, A. Sciubba, F . Scuri, I. Sfiligoi, J. Shan, P. Silano, T. Spadaro, E. Spiriti, G. L. Tong, L. Tortora, E. Valente, P. Valente, B. Valeriani, G. Venanzoni, S. Veneziano, A. Ventura, Y. Wu, G. Xu, G. W. Yu, P. F. Zema, Y. Zhou.
268
269
influenced by the S-wave KK8. Furthermore, significant isospin mixing effects are expected to happen due to the proximity of the K+K~ and K°K thresholds 9 . A precise measurement of BR{(j> -> / 0 (980)7) and BR( -*• 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 —> 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 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 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 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.<Wyy47r) 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)), 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.
297
298 1600201-003
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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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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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
305
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
306
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.
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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
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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
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twice that expected, assuming f(c -» Dj) « 2% 6 and 7S « 0.3 is the strangeness suppression factor in charm production. 5
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, 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-
320
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 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
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
_ „™/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„.+„.-
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 , /(*) = 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 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 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 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.
S^/GeV
250
500
750
1000 W(GeV)
•so
T
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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
„8000
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Figure 2. (a) Distribution of the product of transverse momenta squared of the scattered protons for yy (shaded histogram) and IPIP (empty histogram) collisions; (b) the same distributions smeared by the PT resolution of 15 MeV; yy and IPIP distributions are normalized as 1:1000 for pT2 < 2 GeV2.
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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Figure 4. Tagged luminosity spectrum Sw and its integral Jwo dW Syy for pAr collisions and single tagging, assuming elastic production and a 1 mm closest approach.
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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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)^
4 p. - V ] i*1a{-R *—' dxa
Fkl = ^ ± dx\
360
- ^L dxk'
1- ieAa)tl> - mij>,
(1)
(2)
361
y^-zri=i
- Jk,
3k - eip *717* Y>.
(3)
OXi
Here h — c — 1, xi = t, X2 = x, x$ = y, X4 = 2;, Ffci is the tensor of electric and magnetic fielfs, Ak is the 4-potential, 7* are Dirac matrices, if> is the Dirac spinor, m and e are mass and charge of an electron. It is shown t h a t in (1) the expression V* = d/dx^+ieAk can be considered as the translation group generator into a conformal pseudoeuclidean 4-space and ieAk appear within such approach as Tk — t h e contraction of a riemannian connectivity Tlp of this space (rfc = T f p ) . Multiplied by the reflection operators 7fc the Vifc gives the representation of a local gliding s y m m e t r y group in this space with the Dirac spinors as basic vecors of the represetation. All this gives the opportunity to interpret (1) as the metric relation for a closed connected nonorietable nonmetrized 4-manifold with a conformal pseudoeuclidean space as its universal covering space. Now we use a relation between a riemannian connection and a riemannian curvature tenor Rfk • 8
After contraction over q and / we obtain Rik - Rik,q
-
dxk
-
dx.
•
(5)
By comparison (2) and (5) we can write down the equations (1-3) using only geometrical notations 4
*7i Vi 1> ~ ^2 *7a V a ^ = ™,
(6)
a—2
4
»= 1
where R°k has the form (5). Finally, we have the following geometrical interpretation of electromagnetic field. 1. Electromagnetic field and its sources (electron-positron field) can be considered as a single closed connected nonmetrized 4-manifold.
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
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hi Right:
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).
366
Ptr>40
GeV, |r,l , | < 2 . 5 , p „ > 3 0 GeV. |7|,| 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-
375
Figure 2. Evolution of F] with Q2 in various x- regions 6 .
pi
g u r e 3 - Results for F^c
8
.
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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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
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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