Measurement of the photon structure function F with the L3 detector at ...

Physics Letters B 622 (2005) 249–264 www.elsevier.com/locate/physletb

γ

Measurement of the photon structure function F2 with the L3 detector at LEP

L3 Collaboration P. Achard , O. Adriani , M. Aguilar-Benitez y , J. Alcaraz y , G. Alemanni w , J. Allaby r , A. Aloisio ac , M.G. Alviggi ac , H. Anderhub aw , V.P. Andreev f,ah , F. Anselmo h , A. Arefiev ab , T. Azemoon c , T. Aziz i , P. Bagnaia am , A. Bajo y , G. Baksay z , L. Baksay z , S.V. Baldew b , S. Banerjee i , Sw. Banerjee d , A. Barczyk aw,au , R. Barillère r , P. Bartalini w , M. Basile h , N. Batalova at , R. Battiston ag , A. Bay w , F. Becattini q , U. Becker m , F. Behner aw , L. Bellucci q , R. Berbeco c , J. Berdugo y , P. Berges m , B. Bertucci ag , B.L. Betev aw , M. Biasini ag , M. Biglietti ac , A. Biland aw , J.J. Blaising d , S.C. Blyth ai , G.J. Bobbink b , A. Böhm a , L. Boldizsar l , B. Borgia am , S. Bottai q , D. Bourilkov aw , M. Bourquin t , S. Braccini t , J.G. Branson ao , F. Brochu d , J.D. Burger m , W.J. Burger ag , X.D. Cai m , M. Capell m , G. Cara Romeo h , G. Carlino ac , A. Cartacci q , J. Casaus y , F. Cavallari am , N. Cavallo aj , C. Cecchi ag , M. Cerrada y , M. Chamizo t , Y.H. Chang ar , M. Chemarin x , A. Chen ar , G. Chen g , G.M. Chen g , H.F. Chen v , H.S. Chen g , G. Chiefari ac , L. Cifarelli an , F. Cindolo h , I. Clare m , R. Clare al , G. Coignet d , N. Colino y , S. Costantini am , B. de la Cruz y , S. Cucciarelli ag , R. de Asmundis ac , P. Déglon t , J. Debreczeni l , A. Degré d , K. Dehmelt z , K. Deiters au , D. della Volpe ac , E. Delmeire t , P. Denes ak , F. DeNotaristefani am , A. De Salvo aw , M. Diemoz am , M. Dierckxsens b , C. Dionisi am , M. Dittmar aw , A. Doria ac , M.T. Dova j,1 , D. Duchesneau d , M. Duda a , B. Echenard t , A. Eline r , A. El Hage a , H. El Mamouni x , A. Engler ai , F.J. Eppling m , P. Extermann t , M.A. Falagan y , S. Falciano am , A. Favara af , J. Fay x , O. Fedin ah , M. Felcini aw , T. Ferguson ai , H. Fesefeldt a , E. Fiandrini ag , J.H. Field t , F. Filthaut ae , P.H. Fisher m , W. Fisher ak , I. Fisk ao , G. Forconi m , K. Freudenreich aw , C. Furetta aa , Yu. Galaktionov ab,m , S.N. Ganguli i , P. Garcia-Abia y , M. Gataullin af , S. Gentile am , S. Giagu am , Z.F. Gong v , G. Grenier x , O. Grimm aw , M.W. Gruenewald p , M. Guida an , V.K. Gupta ak , A. Gurtu i , L.J. Gutay at , D. Haas e , D. Hatzifotiadou h , T. Hebbeker a , A. Hervé r , J. Hirschfelder ai , H. Hofer aw , M. Hohlmann z , G. Holzner aw , S.R. Hou ar , B.N. Jin g , P. Jindal n , L.W. Jones c , t

q

0370-2693/$ – see front matter  2005 Published by Elsevier B.V. doi:10.1016/j.physletb.2005.07.028

250

L3 Collaboration / Physics Letters B 622 (2005) 249–264

P. de Jong b , I. Josa-Mutuberría y , M. Kaur n , M.N. Kienzle-Focacci t , J.K. Kim aq , J. Kirkby r , W. Kittel ae , A. Klimentov m,ab , A.C. König ae , M. Kopal at , V. Koutsenko m,ab , M. Kräber aw , R.W. Kraemer ai , A. Krüger av , A. Kunin m , P. Ladron de Guevara y , I. Laktineh x , G. Landi q , M. Lebeau r , A. Lebedev m , P. Lebrun x , P. Lecomte aw , P. Lecoq r , P. Le Coultre aw , J.M. Le Goff r , R. Leiste av , M. Levtchenko aa , P. Levtchenko ah , C. Li v , S. Likhoded av , C.H. Lin ar , W.T. Lin ar , F.L. Linde b , L. Lista ac , Z.A. Liu g , W. Lohmann av , E. Longo am , Y.S. Lu g , C. Luci am , L. Luminari am , W. Lustermann aw , W.G. Ma v , L. Malgeri r , A. Malinin ab , C. Maña y , J. Mans ak , J.P. Martin x , F. Marzano am , K. Mazumdar i , R.R. McNeil f , S. Mele r,ac , P. Mermod t , L. Merola ac , M. Meschini q , W.J. Metzger ae , A. Mihul k , H. Milcent r , G. Mirabelli am , J. Mnich a , G.B. Mohanty i , G.S. Muanza x , A.J.M. Muijs b , B. Musicar ao , M. Musy am , S. Nagy o , S. Natale t , M. Napolitano ac , F. Nessi-Tedaldi aw , H. Newman af , A. Nisati am , T. Novak ae , H. Nowak av , R. Ofierzynski aw , G. Organtini am , I. Pal at , C. Palomares y , P. Paolucci ac , R. Paramatti am , G. Passaleva q , S. Patricelli ac , T. Paul j , M. Pauluzzi ag , C. Paus m , F. Pauss aw , M. Pedace am , S. Pensotti aa , D. Perret-Gallix d , D. Piccolo ac , F. Pierella h , M. Pioppi ag , P.A. Piroué ak , E. Pistolesi aa , V. Plyaskin ab , M. Pohl t , V. Pojidaev q , J. Pothier r , D. Prokofiev ah , G. Rahal-Callot aw , M.A. Rahaman i , P. Raics o , N. Raja i , R. Ramelli aw , P.G. Rancoita aa , R. Ranieri q , A. Raspereza av , P. Razis ad , D. Ren aw , M. Rescigno am , S. Reucroft j , S. Riemann av , K. Riles c , B.P. Roe c , L. Romero y , A. Rosca av , C. Rosemann a , C. Rosenbleck a , S. Rosier-Lees d , S. Roth a , J.A. Rubio r , G. Ruggiero q , H. Rykaczewski aw , A. Sakharov aw , S. Saremi f , S. Sarkar am , J. Salicio r , E. Sanchez y , C. Schäfer r , V. Schegelsky ah , H. Schopper u , D.J. Schotanus ae , C. Sciacca ac , L. Servoli ag , S. Shevchenko af , N. Shivarov ap , V. Shoutko m , E. Shumilov ab , A. Shvorob af , D. Son aq , C. Souga x , P. Spillantini q , M. Steuer m , D.P. Stickland ak , B. Stoyanov ap , A. Straessner t , K. Sudhakar i , G. Sultanov ap , L.Z. Sun v , S. Sushkov a , H. Suter aw , J.D. Swain j , Z. Szillasi z,5 , X.W. Tang g , P. Tarjan o , L. Tauscher e , L. Taylor j , B. Tellili x , D. Teyssier x , C. Timmermans ae , Samuel C.C. Ting m , S.M. Ting m , S.C. Tonwar i , J. Tóth l , C. Tully ak , K.L. Tung g , J. Ulbricht aw , E. Valente am , R.T. Van de Walle ae , R. Vasquez at , V. Veszpremi z , G. Vesztergombi l , I. Vetlitsky ab , G. Viertel aw , S. Villa al , M. Vivargent d , S. Vlachos e , I. Vodopianov z , H. Vogel ai , H. Vogt av , I. Vorobiev ai,ab , A.A. Vorobyov ah , M. Wadhwa e , Q. Wang ae , X.L. Wang v , Z.M. Wang v , M. Weber r , S. Wynhoff ak , L. Xia af , Z.Z. Xu v , J. Yamamoto c , B.Z. Yang v , C.G. Yang g , H.J. Yang c , M. Yang g , S.C. Yeh as , An. Zalite ah , Yu. Zalite ah , Z.P. Zhang v , J. Zhao v , G.Y. Zhu g , R.Y. Zhu af , H.L. Zhuang g , A. Zichichi h,r,s , B. Zimmermann aw , M. Zöller a a III. Physikalisches Institut, RWTH, D-52056 Aachen, Germany 2 b National Institute for High Energy Physics, NIKHEF, and University of Amsterdam, NL-1009 DB Amsterdam, The Netherlands c University of Michigan, Ann Arbor, MI 48109, USA d Laboratoire d’Annecy-le-Vieux de Physique des Particules, LAPP, IN2P3-CNRS, BP 110, F-74941 Annecy-le-Vieux cedex, France e Institute of Physics, University of Basel, CH-4056 Basel, Switzerland

L3 Collaboration / Physics Letters B 622 (2005) 249–264 f Louisiana State University, Baton Rouge, LA 70803, USA g Institute of High Energy Physics, IHEP, 100039 Beijing, China 3 h University of Bologna and INFN Sezione di Bologna, I-40126 Bologna, Italy i Tata Institute of Fundamental Research, Mumbai (Bombay) 400 005, India j Northeastern University, Boston, MA 02115, USA k Institute of Atomic Physics and University of Bucharest, R-76900 Bucharest, Romania l Central Research Institute for Physics of the Hungarian Academy of Sciences, H-1525 Budapest 114, Hungary 4 m Massachusetts Institute of Technology, Cambridge, MA 02139, USA n Panjab University, Chandigarh 160 014, India o KLTE-ATOMKI, H-4010 Debrecen, Hungary 5 p Department of Experimental Physics, University College Dublin, Belfield, Dublin 4, Ireland q INFN, Sezione di Firenze and University of Florence, I-50125 Florence, Italy r European Laboratory for Particle Physics, CERN, CH-1211 Geneva 23, Switzerland s World Laboratory, FBLJA Project, CH-1211 Geneva 23, Switzerland t University of Geneva, CH-1211 Geneva 4, Switzerland u University of Hamburg, D-22761 Hamburg, Germany v Chinese University of Science and Technology, USTC, Hefei, Anhui 230 029, China 3 w University of Lausanne, CH-1015 Lausanne, Switzerland x Institut de Physique Nucléaire de Lyon, IN2P3-CNRS,Université Claude Bernard, F-69622 Villeurbanne, France y Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, CIEMAT, E-28040 Madrid, Spain 6 z Florida Institute of Technology, Melbourne, FL 32901, USA aa INFN, Sezione di Milano, I-20133 Milan, Italy ab Institute of Theoretical and Experimental Physics, ITEP, Moscow, Russia ac INFN, Sezione di Napoli and University of Naples, I-80125 Naples, Italy ad Department of Physics, University of Cyprus, Nicosia, Cyprus ae Radboud University and NIKHEF, NL-6525 ED Nijmegen, The Netherlands af California Institute of Technology, Pasadena, CA 91125, USA ag INFN, Sezione di Perugia and Università Degli Studi di Perugia, I-06100 Perugia, Italy ah Nuclear Physics Institute, St. Petersburg, Russia ai Carnegie Mellon University, Pittsburgh, PA 15213, USA aj INFN, Sezione di Napoli and University of Potenza, I-85100 Potenza, Italy ak Princeton University, Princeton, NJ 08544, USA al University of Californa, Riverside, CA 92521, USA am INFN, Sezione di Roma and University of Rome, “La Sapienza”, I-00185 Rome, Italy an University and INFN, Salerno, I-84100 Salerno, Italy ao University of California, San Diego, CA 92093, USA ap Bulgarian Academy of Sciences, Central Laboratory of Mechatronics and Instrumentation, BU-1113 Sofia, Bulgaria aq The Center for High Energy Physics, Kyungpook National University, 702-701 Taegu, Republic of Korea ar National Central University, Chung-Li, Taiwan, ROC as Department of Physics, National Tsing Hua University, Taiwan, ROC at Purdue University, West Lafayette, IN 47907, USA au Paul Scherrer Institut, PSI, CH-5232 Villigen, Switzerland av DESY, D-15738 Zeuthen, Germany aw Eidgenössische Technische Hochschule, ETH Zürich, CH-8093 Zürich, Switzerland

Received 15 February 2005; received in revised form 9 July 2005; accepted 13 July 2005 Available online 21 July 2005 Editor: L. Rolandi

1 Also supported by CONICET and Universidad Nacional de La Plata, CC 67, 1900 La Plata, Argentina. 2 Supported by the German Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie. 3 Supported by the National Natural Science Foundation of China. 4 Supported by the Hungarian OTKA fund under contract numbers T019181, F023259 and T037350. 5 Also supported by the Hungarian OTKA fund under contract number T026178. 6 Supported also by the Comisión Interministerial de Cienciay Tecnología.

251

252

L3 Collaboration / Physics Letters B 622 (2005) 249–264

Abstract The e+ e− → e+ e− hadrons reaction, where one of the two electrons is detected in a low polar-angle calorimeter, is analysed γ in order to measure the hadronic photon structure function F2 . The full high-energy and high-luminosity data set, collected with √ the L3 detector at centre-of-mass energies 189 GeV
s
209 GeV, corresponding to an integrated luminosity of 608 pb−1 is used. The Q2 range 11 GeV2
Q2
34 GeV2 and the x range 0.006
x
0.556 are considered. The data are compared with recent parton density functions.  2005 Published by Elsevier B.V.

1. Introduction

Photons are ideal tools for probing the structure of more complex objects such as the proton in deep-inelastic scattering experiments. At LEP, in the e+ e− → e+ e− γ ∗ γ → e+ e− hadrons reaction, two virtual photons are produced by the incoming electrons7 and their interaction yields hadrons. If the scattering angle of one of the electrons, θtag , is sufficiently large, it is observed in the low polar-angle electromagnetic BGO calorimeter [1] of the L3 detector [2], originally devised to detect low angle Bhabha scattering in order to measure the LEP luminosity. This allows to measure the four-momentum, k  , of this “tagged” electron. For “single-tagged” events the second electron is undetected, its polar angle is small and the virtual photon radiated from this electron is quasi-real. In the framework of a deep-inelastic scattering formalism the process e+ e− → e+ e− hadrons is written as the convolution of the target photon flux with the reaction e(k) + γ (p) → e(k  ) + hadrons. The photon, γ ∗ , with four-momentum q = k − k  and a large virtuality Q2 = −q 2 ∼ 2Etag Ebeam (1 − cos θtag ), is considered as a point-like probe investigating the structure of the target photon, γ , with four-momentum p and virtuality P 2 = −p 2  0. Etag is the energy of the tagged electron and Ebeam the energy of the beam. The differential cross section is written in terms of the scaling variables x = Q2 /2(p · q) = Q2 /(Q2 + Wγ2γ + P 2 ) and y = (q · p)/(k · p) = 1 − (Etag /Ebeam cos2 θtag ) as [3,4]:

7 Throughout this Letter, the term “electron” indicates both elec-

tron and positron.

dσeγ →eX (x, Q2 ) d xdQ2  γ  2πα 2
 1 + (1 − y)2 F2 x, Q2 = 4 xQ  γ − y 2 FL x, Q2 .

(1)

The variable x depends on the two-photon centre-ofmass energy, Wγ γ , equal to the effective mass of the produced hadrons. The inelasticity y is small (y < 0.3) in the kinematic region of this study and consequently γ only F2 (x, Q2 ) contributes appreciably to the cross γ section. By convention, F2 /α is measured, where α is the fine-structure constant. Using this approach, the photon structure function has been extensively studied at low-energy e+ e− colliders [5] and at LEP [5–7]. A virtual photon can interact as a point-like particle in “direct processes”; it can fluctuate into a vector meson (ρ, ω, φ) inducing soft hadronic interactions in “VDM processes” or it can interact via its partonic content of quarks or gluons in “resolved processes”. High Q2 single-tag events favour perturbative QED and QCD diagrams such as γ γ → q¯q, γ q → gq or γ g → q¯q. The two resolved processes, γ q → gq and γ g → q¯q, are described using parton density functions extracted from the photon structure functions measured in previous experiments at PEP, PETRA and TRISTAN. Reviews of the existing parameterisations may be found in Refs. [8,9]. Recently, a new parametrisation was obtained adding published LEP data [10]. This analysis uses the 608.1 pb−1 of high-energy LEP data, collected at e+ e− centre-of-mass energies √ 189 GeV
√s
209 GeV. The data are grouped in four average s values, presented in Table 1. These high-energy data√allow to extend our √ previous measurements [6] at s  91 GeV and s = 183 GeV in the small-x region down to 0.006 and in the medium-x

L3 Collaboration / Physics Letters B 622 (2005) 249–264

253

Table 1 √ The average e+ e− centre-of-mass energies,  s, and the corresponding luminosities for the four data samples together with the number of 2 2 selected events in the Q intervals 11 GeV
Q2
14 GeV2 , 14 GeV2
Q2
20 GeV2 and 20 GeV2
Q2
34 GeV2 . The numbers of expected background events from the e+ e− → e+ e− τ + τ − and e+ e− → q¯q(γ ) processes and the signal purity are also listed √  s (GeV) L (pb−1 ) Events e+ e− → e+ e− τ + τ − e+ e− → q¯q(γ ) Purity (%) Q2 = 11–14 GeV2 189 194 200 206

171.8 111.4 109.3 215.6

1884 1197 1187 2418

107.6 76.3 74.9 129.6

5.7 3.3 3.7 7.7

94 93 93 94

9.7 5.4 4.9 8.7

93 93 93 94

8.1 5.8 6.7 12.7

92 92 92 92

Q2 = 14–20 GeV2 189 194 200 206

171.8 111.4 109.3 215.6

2046 1347 1359 2886

128.6 91.2 89.5 177.4 Q2 = 20–34 GeV2

189 194 200 206

171.8 111.4 109.3 215.6

1922 1331 1287 2859

143.9 103.6 101.6 202.5

region up to 0.556 for the Q2 range 11 GeV2
Q2
34 GeV2 . The e+ e− → e+ e− hadrons cross section γ and the F2 photon structure function are studied as a function of x in the three Q2 intervals 11 GeV2
Q2
14 GeV2 , 14 GeV2
Q2
20 GeV2 and γ 20 GeV2
Q2
34 GeV2 . The Q2 evolution of F2 2 is also studied combining the values at Q  = 12.4, 16.7 and 25.5 GeV2 with our previous measurements.

2. Monte Carlo models The value of the Q2 variable is accurately determined by measuring the four-momentum of the scattered electron. However, the effective mass of the final state hadrons is only partially reconstructed, as these are often produced at low polar angles where no tracking system can be installed. A Monte Carlo modelling of the final state hadrons is therefore necessary [11] to determine the x variable. Three Monte Carlo generators are used to model the process e+ e− → e+ e− hadrons: PHOJET [12], PYTHIA [13] and TWOGAM [14].8 8 We thank our colleagues from DELPHI for having made their

program available to us.

PHOJET describes hadron–hadron, photon–hadron and photon–photon collisions. It is based on the dual parton model combined with the QCD-improved parton model [15]. In order to have a continuous transition between hard and soft processes, the distribution of the transverse momentum, pt , of the soft partons is matched to the one predicted by QCD. The two-photon luminosity is calculated from the flux of transversely polarised photons; corrections for the longitudinally polarised photons are thus incorporated into an effective two-photon cross section. The transition from real-photon to virtual-photon scattering is obtained by a change of the relative weight of all partial cross sections. PYTHIA is a general purpose Monte Carlo. For two-photon interactions it incorporates leading order (LO) hard-scattering processes as well as elastic, diffractive and low pt events. The classification of the photon interactions into three different components, direct, resolved and VDM, results in six different classes of events. Events are also classified according to the hard scales involved in the process: photon virtualities and parton transverse momenta. TWOGAM generates three different processes separately: point-like photon–photon interactions, resolved processes, and non-perturbative soft processes described by the generalised vector dominance model

254

L3 Collaboration / Physics Letters B 622 (2005) 249–264

(GVDM). The structure of the program is modular and the photon flux is calculated with an exact LO formula. The cross sections of the three different processes are adjusted to fit the x-distribution of the data. The cross section of the direct process is fixed to the value expected in our kinematic range, σ = 41 pb. The QCD and the VDM cross sections are then adjusted to σ = 5 pb and σ = 28 pb, respectively. For the three Monte Carlo generators parton showering and hadronisation are described by JETSET [16]. The dominant backgrounds are evaluated with PYTHIA for e+ e− → q¯q(γ ) and DIAG36 [17] for e+ e− → e+ e− τ + τ − . All Monte Carlo samples are generated with a luminosity at least five times greater than the experimental one. All events are passed through a full detector simulation which uses the GEANT [18] and GHEISHA [19] programs and takes into account detector efficiencies and time-dependent effects. Monte Carlo events are then reconstructed in the same way as the data.

3. Data analysis Events are mainly accepted by two independent triggers: the single-tag trigger and the central tracktrigger. The single-tag trigger requires at least 70% of the beam energy to be deposited in one of the low polar-angle calorimeters, in coincidence with at least one track in the central tracking chamber. The central track-trigger requires at least two tracks back-toback in the transverse plane within ±60◦ , each with pt > 150 MeV. The average trigger efficiency is about 97%. There is a single-tag trigger signal for about 90% of the selected events and a central track-trigger signal for about 85% of the selected events. 3.1. Event selection Events are selected by requiring a single scattered electron in the low polar-angle calorimeter and a hadronic final state. A tagged electron candidate is the highest energy cluster with a shape consistent with an

Fig. 1. Distribution of the highest energy clusters in the forward electromagnetic calorimeters for (a) the tagged electron side and (b) for the opposite side. (c) Total energy in the central calorimeters. (d) The visible mass of the hadronic final state. All distributions are presented after all other cuts are applied. The backgrounds from annihilation and two-photon leptonic events are indicated as shaded areas and added to the expectations of the PYTHIA, PHOJET and TWOGAM generators. The arrows indicate the position of the cuts.

L3 Collaboration / Physics Letters B 622 (2005) 249–264

electromagnetic shower, Etag /Ebeam > 0.7, as shown in Fig. 1(a), and a polar angle in the fiducial region 0.0325 rad
θ
0.0637 rad inside the geometrical acceptance 0.030 rad
θ
0.066 rad. To ensure that the virtuality of the target photon is small, the highestenergy cluster in the low polar-angle calorimeter opposite to the tagged electron must have an energy less than 20% of the beam energy, as shown in Fig. 1(b). At least four additional particles must be detected. A particle can be a track or a photon. A track must have pt > 100 MeV and a distance of closest approach in the transverse plane to the interaction vertex of less than 10 mm. A photon is a cluster in the electromagnetic BGO calorimeters with energy above 100 MeV, not associated with a charged track. To reduce the background from the process e+ e− → q¯q(γ ), the total energy deposited in the electromagnetic and hadronic calorimeters must be less than 40% of the center-of-mass energy, as shown in Fig. 1(c). The events with a large value of the total energy are due to the e+ e− → Zγ → q¯qγ process, where the radiative photon is misidentified as the tagged electron.

255

The mass of the hadronic final state, Wvis , is calculated from all tracks and calorimetric clusters. Additional clusters detected in the low polar-angle calorimeter are assigned the pion mass and included in the calculation of Wvis . To avoid the hadronic resonance region, Wvis is required to be greater than 4 GeV, as presented in Fig. 1(d). √ Fig. 2 shows the Q2 distribution for each s sample. Only events with 11 GeV2
Q2
34 GeV2 are studied. The number of selected events and the backgrounds from the e+ e− → e+ e− τ + τ − and e+ e− → q¯q(γ ) processes are given in Table 1. The background is dominated by the e+ e− → e+ e− τ + τ − production. The contribution from the e+ e− → τ + τ − and e+ e− → W+ W− processes is negligible. The background from beam-gas and beam-wall events is found to be negligible by inspection of the radial distribution of track intersections. The Wvis and 2 ) distributions are presented xvis = Q2 /(Q2 + Wvis in Fig. 3 for all selected data. The PYTHIA and TWOGAM model reproduce the data rather well, except at large values of Wvis . PHOJET presents a harder mass spectrum and predicts too many events

Fig. 2. Q2 distribution of the selected events for the four average

√ s ranges.

256

L3 Collaboration / Physics Letters B 622 (2005) 249–264

for xvis < 0.1 and is therefore not used in the following. The total acceptance is calculated for each data sample separately. It takes into account the trigger efficiency, the geometrical acceptance and the selection cuts. √ An example is presented in Fig. 4(a) for the data at s = 189 GeV.

4. Results 4.1. Unfolding and differential cross sections

Fig. 3. Distribution of the visible mass of the two-photon system and of the xvis for all selected events compared with Monte Carlo predictions. The backgrounds from annihilation and two-photon leptonic events are indicated as shaded areas and added to the expectations of the PYTHIA, PHOJET and TWOGAM generators.

The cross section σ/ x as a function of x for the reaction e+ e− → e+ e− hadrons is measured for three Q2 intervals: 11 GeV2
Q2
14 GeV2 , 14 GeV2
Q2
20 GeV2 and 20 GeV2
Q2
34 GeV2 . Each data set is subdivided into bins of xvis of similar statistics, as listed in Table 2. A Bayesian unfolding procedure [20] is used to relate the measured xvis to the true value of x and to correct the data for the detector acceptance and efficiency. This procedure is applied using, in turn, the PYTHIA and TWOGAM generators. The average of the cross sections obtained in the two cases is retained. The correlation between the generated value of x and xvis is similar for the two models. The one obtained with PYTHIA is shown in Fig. 4(b). The cross-sections measured for each x interval of av√ erage value x and for each value of s are given

Fig. 4. (a) The detector acceptance and selection efficiency, ε, obtained by the PYTHIA and TWOGAM generators. (b) Comparison of the √ reconstructed and generated value of x for the PYTHIA Monte Carlo at s = 189 GeV for different values of Q2 . The mean observed value and the standard deviation of xvis are plotted for events generated in a given x bin.

L3 Collaboration / Physics Letters B 622 (2005) 249–264

257

Table 2 √ Cross sections σ/ x as a function of x for the reaction e+ e− → e+ e− hadrons for the four average values of s, in three Q2 intervals. The first uncertainty is statistical, the second systematic √  s 189 GeV 194 GeV 200 GeV 206 GeV

x range

x

σ/ x (pb)

σ/ x (pb)

σ/ x (pb)

σ/ x (pb)

106.4±10.2±10.4 63.9 ± 6.3 ± 5.2 53.4 ± 5.5 ± 5.3 44.0 ± 4.0 ± 4.4 39.3 ± 3.6 ± 4.3 36.9 ± 3.4 ± 4.2 33.0 ± 2.9 ± 4.3 31.6 ± 2.8 ± 4.0 28.3 ± 2.7 ± 3.7 25.5 ± 2.6 ± 3.8

115.3±7.8±16.4 69.6 ± 4.5 ± 7.7 52.0 ± 3.6 ± 5.4 43.8 ± 2.8 ± 5.3 39.6 ± 2.8 ± 5.1 37.9 ± 2.5 ± 4.4 35.8 ± 2.4 ± 4.3 32.6 ± 2.0 ± 4.4 30.7 ± 1.9 ± 4.4 29.5 ± 1.8 ± 3.9

102.4±10.4±11.1 64.2 ± 7.1 ± 6.2 53.4 ± 5.3 ± 4.3 44.5 ± 4.2 ± 2.6 37.9 ± 3.6 ± 3.2 36.7 ± 3.3 ± 2.1 33.3 ± 3.0 ± 1.7 32.2 ± 2.8 ± 1.8 30.0 ± 2.3 ± 1.7 29.4 ± 2.8 ± 1.3 26.8 ± 2.7 ± 1.7

113.0±7.7±11.5 72.2 ± 5.2 ± 7.8 55.8 ± 3.6 ± 2.7 47.8 ± 2.9 ± 3.1 41.5 ± 2.4 ± 2.0 37.7 ± 2.3 ± 1.7 34.7 ± 2.2 ± 1.5 34.4 ± 2.0 ± 1.5 31.2 ± 1.9 ± 1.2 29.0 ± 1.9 ± 1.0 27.8 ± 1.9 ± 1.1

37.4 ± 3.6 ± 2.4 37.4 ± 3.6 ± 2.4 37.4 ± 3.6 ± 2.4 32.4 ± 3.3 ± 1.9 32.1 ± 3.0 ± 2.5 28.6 ± 2.6 ± 1.7 25.0 ± 2.2 ± 1.3 25.0 ± 2.2 ± 1.3 24.3 ± 2.2 ± 1.4 23.5 ± 2.4 ± 1.2 24.0 ± 2.3 ± 2.3

39.5 ± 2.6 ± 2.0 39.5 ± 2.6 ± 2.0 39.5 ± 2.6 ± 2.0 36.3 ± 2.6 ± 1.3 33.6 ± 2.2 ± 1.2 32.2 ± 2.0 ± 1.2 27.4 ± 1.6 ± 1.2 27.4 ± 1.6 ± 1.2 25.6 ± 1.6 ± 0.9 24.5 ± 1.7 ± 1.0 24.5 ± 1.5 ± 1.5

Q2 = 11–14 GeV2 0.006–0.023 0.023–0.040 0.040–0.060 0.060–0.090 0.090–0.120 0.120–0.160 0.160–0.205 0.205–0.260 0.260–0.330 0.330–0.400

0.013 0.031 0.050 0.075 0.10 0.14 0.18 0.23 0.29 0.36

103.6±8.5±14.5 63.4 ± 5.3 ± 4.3 52.0 ± 4.0 ± 2.9 45.0 ± 3.4 ± 2.2 40.2 ± 2.9 ± 1.8 37.9 ± 2.8 ± 2.3 34.8 ± 2.5 ± 1.3 33.3 ± 2.4 ± 1.3 29.8 ± 2.1 ± 1.7 29.9 ± 2.1 ± 1.3

108.2±10.8±15.4 67.0 ± 6.5 ± 8.4 55.7 ± 5.1 ± 7.8 47.7 ± 4.4 ± 6.1 40.8 ± 3.9 ± 5.3 37.4 ± 3.4 ± 5.3 33.9 ± 2.9 ± 4.7 31.9 ± 3.1 ± 4.8 29.1 ± 2.9 ± 4.0 27.5 ± 2.7 ± 4.0 Q2 = 14–20 GeV2

0.006–0.023 0.023–0.040 0.040–0.060 0.060–0.090 0.090–0.120 0.120–0.160 0.160–0.205 0.205–0.260 0.260–0.330 0.330–0.400 0.400–0.467

0.013 0.031 0.050 0.075 0.10 0.14 0.18 0.23 0.29 0.36 0.42

97.0±8.5±12.7 59.3 ± 4.9 ± 3.6 49.6 ± 4.3 ± 5.7 40.8 ± 2.9 ± 1.7 36.1 ± 2.9 ± 1.9 32.5 ± 2.2 ± 1.5 31.8 ± 2.3 ± 1.3 30.8 ± 2.1 ± 1.0 27.7 ± 2.0 ± 1.0 28.1 ± 2.1 ± 1.1 26.7 ± 2.1 ± 2.1

100.4 ± 10.2 ± 9.8 64.0 ± 6.5 ± 4.9 50.8 ± 5.2 ± 5.0 42.5 ± 3.9 ± 1.9 38.0 ± 3.6 ± 2.3 35.7 ± 3.0 ± 1.6 31.9 ± 2.7 ± 1.7 30.6 ± 2.8 ± 1.3 27.6 ± 2.3 ± 1.2 26.8 ± 2.4 ± 1.3 25.2 ± 2.5 ± 1.8 Q2 = 20–34 GeV2

0.023–0.040 0.040–0.060 0.060–0.090 0.090–0.120 0.120–0.160 0.160–0.205 0.205–0.260 0.260–0.330 0.330–0.400 0.400–0.467 0.467–0.556

0.031 0.050 0.075 0.10 0.14 0.18 0.23 0.29 0.36 0.42 0.49

48.6 ± 5.4 ± 3.6 41.9 ± 4.1 ± 4.1 35.8 ± 2.8 ± 1.7 32.8 ± 2.7 ± 2.2 29.1 ± 2.5 ± 1.7 27.7 ± 2.1 ± 1.1 25.0 ± 1.7 ± 1.0 25.0 ± 1.7 ± 1.0 24.5 ± 1.8 ± 1.2 23.6 ± 1.8 ± 1.5 22.8 ± 1.6 ± 2.5

54.3 ± 6.5 ± 3.3 36.0 ± 3.4 ± 2.4 36.0 ± 3.4 ± 2.4 32.1 ± 3.3 ± 1.4 30.6 ± 2.8 ± 2.4 28.1 ± 2.6 ± 1.1 24.2 ± 2.0 ± 1.0 24.2 ± 2.0 ± 1.0 23.3 ± 2.2 ± 1.0 22.4 ± 2.0 ± 1.1 22.4 ± 2.1 ± 2.9

in Table 2 with their statistical and systematic uncertainties. The bin-to-bin correlation√matrices obtained with PYTHIA and TWOGAM for s = 189 GeV are shown in Tables 3 and 4, respectively. √Similar matrices are obtained for the other values of s. 4.2. Systematic uncertainties The systematic uncertainties on the cross sections are estimated for each data sample, for each x bin and

for each Q2 interval. Three main sources of systematic uncertainties are considered: the selection procedure, the trigger efficiency and the Monte Carlo model. Their average effects over the full data sample are listed in Table 5. The uncertainties from the selection procedure are estimated by varying the selection cuts. The fiducial value of the polar angle in the low polar-angle calorimeter is varied from 0.0325 to 0.0360 rad and from 0.0637 to 0.060 rad. These changes result in a

258

Table 3 √ Correlation matrices obtained with the PYTHIA Monte Carlo for the data at s = 189 GeV for the three Q2 intervals Q2 = 11–14 GeV2 0.006–0.023

0.023–0.040

0.040–0.060

0.060–0.090

0.090–0.120

0.120–0.160

0.160–0.205

0.205–0.260

0.260–0.330

0.330–0.400

0.006–0.023 0.023–0.040 0.040–0.060 0.060–0.090 0.090–0.120 0.120–0.160 0.160–0.205 0.205–0.260 0.260–0.330 0.330–0.400

1.00 0.92 0.75 0.55 0.45 0.39 0.28 0.25 0.22 0.17

1.00 0.92 0.79 0.67 0.62 0.50 0.45 0.38 0.36

1.00 0.96 0.85 0.78 0.67 0.59 0.49 0.50

1.00 0.94 0.89 0.80 0.69 0.59 0.60

1.00 0.98 0.95 0.84 0.79 0.77

1.00 0.97 0.87 0.82 0.78

1.00 0.94 0.91 0.86

1.00 0.99 0.98

1.00 0.97

1.00

Q2 = 14–20 GeV2 x range

0.006–0.023

0.023–0.040

0.040–0.060

0.060–0.090

0.090–0.120

0.120–0.160

0.160–0.205

0.205–0.260

0.260–0.330

0.330–0.400

0.400–0.467

0.006–0.023 0.023–0.040 0.040–0.060 0.060–0.090 0.090–0.120 0.120–0.160 0.160–0.205 0.205–0.260 0.260–0.330 0.330–0.400 0.400–0.467

1.00 0.87 0.74 0.55 0.54 0.36 0.31 0.24 0.18 0.21 0.11

1.00 0.95 0.82 0.79 0.63 0.60 0.49 0.40 0.40 0.31

1.00 0.93 0.89 0.73 0.71 0.59 0.50 0.47 0.37

1.00 0.98 0.89 0.85 0.75 0.64 0.56 0.47

1.00 0.93 0.89 0.81 0.71 0.65 0.55

1.00 0.98 0.95 0.87 0.79 0.71

1.00 0.95 0.88 0.79 0.71

1.00 0.97 0.91 0.84

1.00 0.97 0.91

1.00 0.96

1.00

Q2 = 20–34 GeV2 x range

0.023–0.040

0.040–0.060

0.060–0.090

0.090–0.120

0.120–0.160

0.160–0.205

0.205–0.260

0.260–0.330

0.330–0.400

0.400–0.467

0.467–0.556

0.023–0.040 0.040–0.060 0.060–0.090 0.090–0.120 0.120–0.160 0.160–0.205 0.205–0.260 0.260–0.330 0.330–0.400 0.400–0.467 0.467–0.556

1.00 0.92 0.87 0.80 0.66 0.62 0.58 0.47 0.43 0.38 0.39

1.00 0.96 0.88 0.75 0.71 0.64 0.54 0.49 0.45 0.44

1.00 0.97 0.89 0.82 0.76 0.66 0.61 0.55 0.54

1.00 0.96 0.91 0.86 0.77 0.71 0.63 0.63

1.00 0.97 0.93 0.88 0.81 0.73 0.73

1.00 0.98 0.95 0.88 0.78 0.78

1.00 0.97 0.92 0.83 0.84

1.00 0.97 0.91 0.91

1.00 0.98 0.98

1.00 0.99

1.00

L3 Collaboration / Physics Letters B 622 (2005) 249–264

x range

Table 4 √ Correlation matrices obtained with the TWOGAM Monte Carlo for the data at s = 189 GeV for the three Q2 intervals Q2 = 11–14 GeV2 0.006–0.023

0.023–0.040

0.040–0.060

0.060–0.090

0.090–0.120

0.120–0.160

0.160–0.205

0.205–0.260

0.260–0.330

0.330–0.400

0.006–0.023 0.023–0.040 0.040–0.060 0.060–0.090 0.090–0.120 0.120–0.160 0.160–0.205 0.205–0.260 0.260–0.330 0.330–0.400

1.00 0.91 0.79 0.63 0.52 0.46 0.36 0.27 0.24 0.19

1.00 0.96 0.86 0.74 0.66 0.57 0.45 0.42 0.36

1.00 0.95 0.86 0.78 0.69 0.56 0.52 0.45

1.00 0.95 0.90 0.82 0.69 0.65 0.58

1.00 0.98 0.92 0.80 0.73 0.64

1.00 0.97 0.88 0.83 0.74

1.00 0.97 0.93 0.86

1.00 0.98 0.93

1.00 0.98

1.00

Q2 = 14–20 GeV2 x range

0.006–0.023

0.023–0.040

0.040–0.060

0.060–0.090

0.090–0.120

0.120–0.160

0.160–0.205

0.205–0.260

0.260–0.330

0.330–0.400

0.400–0.467

0.006–0.023 0.023–0.040 0.040–0.060 0.060–0.090 0.090–0.120 0.120–0.160 0.160–0.205 0.205–0.260 0.260–0.330 0.330–0.400 0.400–0.467

1.00 0.90 0.76 0.62 0.50 0.43 0.36 0.29 0.23 0.17 0.16

1.00 0.95 0.86 0.74 0.66 0.56 0.45 0.38 0.32 0.28

1.00 0.96 0.87 0.78 0.68 0.57 0.49 0.43 0.38

1.00 0.96 0.90 0.81 0.70 0.60 0.56 0.48

1.00 0.97 0.90 0.78 0.68 0.63 0.55

1.00 0.96 0.87 0.77 0.73 0.64

1.00 0.96 0.90 0.85 0.77

1.00 0.97 0.95 0.88

1.00 0.98 0.95

1.00 0.98

1.00

Q2 = 20–34 GeV2 0.023–0.040

0.040–0.060

0.060–0.090

0.090–0.120

0.120–0.160

0.160–0.205

0.205–0.260

0.260–0.330

0.330–0.400

0.400–0.467

0.467–0.556

0.023–0.040 0.040–0.060 0.060–0.090 0.090–0.120 0.120–0.160 0.160–0.205 0.205–0.260 0.260–0.330 0.330–0.400 0.400–0.467 0.467–0.556

1.00 0.92 0.85 0.73 0.62 0.52 0.45 0.35 0.34 0.25 0.25

1.00 0.95 0.87 0.77 0.66 0.61 0.50 0.45 0.37 0.36

1.00 0.96 0.88 0.78 0.71 0.59 0.54 0.46 0.44

1.00 0.96 0.88 0.81 0.69 0.62 0.56 0.52

1.00 0.96 0.91 0.79 0.69 0.66 0.61

1.00 0.98 0.90 0.78 0.78 0.72

1.00 0.96 0.85 0.87 0.81

1.00 0.93 0.96 0.90

1.00 0.98 0.97

1.00 0.98

1.00

259

x range

L3 Collaboration / Physics Letters B 622 (2005) 249–264

x range

260

L3 Collaboration / Physics Letters B 622 (2005) 249–264

Table 5 Systematic uncertainties on the measured cross sections Source of systematic uncertainties

Uncertainty in %

Tagging calorimeter polar angle Tagging calorimeter energy Anti-tag energy Number of particles Total energy in the calorimeters Trigger efficiency Monte Carlo statistics Model dependence

0.9–8.0 1.6–2.5 0.4 0.2–2.6 0.2 1.5 0.2–0.5 0.7–9.9

Q2 -dependent uncertainty, as the highest and lowest values of the Q2 are affected by the fiducial cut. The cut on Etag is varied from 0.70Ebeam to 0.65Ebeam and 0.75Ebeam . The anti-tag cut is changed from 0.20Ebeam to 0.15Ebeam and 0.25Ebeam . The numbers of particles is varied from four to three and five. The cut √ on the total energy in the calorimeters relative to s is varied from 0.40 to 0.35 and 0.45. The uncertainty on the trigger efficiency, as determined from the data, is 1.5%. An additional uncertainty comes from the limited Monte Carlo statistics. The discrepancies of the results obtained with the PYTHIA and TWOGAM generators are considered as systematic uncertainties related to the Monte Carlo modelling. This difference is due to the calculated acceptance as well as to the unfolding procedure. An additional contribution to this modelling uncertainty is evaluated by repeating the analysis doubling or halving the VDM component of the TWOGAM generator and is found to be negligible. γ

4.3. Extraction of F2

γ

The photon structure function F2 /α is derived from the cross section of Eq. (1) and the target-photon flux calculated by the program GALUGA [21]9 as: γ

F2 (x, Q2 )

σmeas (e+ e− → e+ e− hadrons) = . α

σGaluga (e+ e− → e+ e− hadrons) The program calculates the theoretical value σGaluga γ γ in the given Q2 and x range setting F2 = 1 and FL 9 The program GALUGA writes the cross section in term of σ TT and σT L , these expressions have been modified by A. Finch in order γ γ to have the cross section in terms of F2 and F1 [4], we thank him

for making his program available to us.

γ

to the QPM value [22]. In practice the FL contribution to the cross section is smaller than 1%, due to the small value of y. The running of the fine-structure constant with Q2 is included. A GVDM form factor is used in the calculation for the target photon virtuality whose average value is of the order of 0.07 GeV2 . The low polar-angle calorimeter acceptance for the tagged and the anti-tagged electron and the Wγ γ > 4 GeV requirement are taken into account. The uncertainty on

σGaluga , as estimated by comparing the GVDM to a ρ form factor, is 2%. The contribution of radiative corrections to the cross section is evaluated by using the program RADCOR [23], which includes initial and final state radiation for the reaction e+ e− → e+ e− µ+ µ− . The corrections are mainly due to initial state radiation from the electron scattered at large angle. Final state radiation is detected together with the scattered electron due to the finite granularity of the calorimeter. Initial state radiation from the electron producing the quasi-real target photon is very small. The calculations are performed at the generator level using the Q2 from the electron variables and Wγ γ from the muon pair. The measured γ F2 /α is multiplied by the ratio, R, of the non-radiative and the total cross section, shown in Tables 6 and 7 for different values of x and Q2 . γ The F2 values, averaged over the x intervals, are first obtained for each individual data set. The results are statistically compatible and, consequently, γ a weighted average of F2 is calculated for the Q2 ranges with average values 12.4, 16.7 and 25.5 GeV2 . This procedure is applied to data unfolded separately with PYTHIA and TWOGAM and the two different values are shown in Fig. 5. Their average value is given in Table 6 and in Fig. 6 for each x interval of expected average value x. In addition to the systematic uncertainty on the cross section, presented in Table 5, two systematic uncertainties are further γ considered in the extraction of F2 . The first uncertainty, of 2%, is associated to the GALUGA calculations. The second uncertainty, also of 2%, covers the estimation of the initial-state and final-state radiative corrections. The uncertainty on initial-state radiation is assessed by changing the angular and momentum criteria which separate soft from hard photons in the Monte Carlo programs. The uncertainty on final-state radiation is estimated by varying the cone angle of the calorimeter for which final state

L3 Collaboration / Physics Letters B 622 (2005) 249–264

Table 6 γ Measured values of F2 /α and the applied radiative correction factors, R, in bins of x for the three Q2 ranges. The first uncertainty is statistic, the second systematic and the third is due to model dependence x range

x

R

0.006–0.023 0.023–0.040 0.040–0.060 0.060–0.090 0.090–0.120 0.120–0.160 0.160–0.205 0.205–0.260 0.260–0.330 0.330–0.400

0.013 0.031 0.050 0.075 0.10 0.14 0.18 0.23 0.29 0.36

0.92 0.90 0.88 0.90 0.89 0.90 0.88 0.89 0.88 0.89

0.302 ± 0.013 ± 0.026 ± 0.029 0.245 ± 0.011 ± 0.021 ± 0.010 0.257 ± 0.011 ± 0.023 ± 0.012 0.296 ± 0.012 ± 0.028 ± 0.009 0.315 ± 0.013 ± 0.032 ± 0.007 0.365 ± 0.015 ± 0.038 ± 0.008 0.399 ± 0.017 ± 0.043 ± 0.007 0.441 ± 0.018 ± 0.049 ± 0.011 0.483 ± 0.020 ± 0.054 ± 0.013 0.536 ± 0.023 ± 0.059 ± 0.025

Q2 = 14–20 GeV2 0.006–0.023 0.023–0.040 0.040–0.060 0.060–0.090 0.090–0.120 0.120–0.160 0.160–0.205 0.205–0.260 0.260–0.330 0.330–0.400 0.400–0.467

0.013 0.031 0.050 0.075 0.10 0.14 0.18 0.23 0.29 0.36 0.42

0.93 0.88 0.90 0.90 0.89 0.90 0.89 0.88 0.88 0.87 0.88

0.310 ± 0.014 ± 0.020 ± 0.028 0.258 ± 0.012 ± 0.014 ± 0.018 0.275 ± 0.012 ± 0.014 ± 0.017 0.288 ± 0.011 ± 0.014 ± 0.008 0.316 ± 0.013 ± 0.015 ± 0.014 0.337 ± 0.013 ± 0.016 ± 0.007 0.381 ± 0.015 ± 0.018 ± 0.006 0.424 ± 0.017 ± 0.019 ± 0.008 0.471 ± 0.018 ± 0.020 ± 0.009 0.510 ± 0.021 ± 0.022 ± 0.007 0.551 ± 0.024 ± 0.024 ± 0.026

Q2 = 20–34 GeV2 0.023–0.040 0.040–0.060 0.060–0.090 0.090–0.120 0.120–0.160 0.160–0.205 0.205–0.260 0.260–0.330 0.330–0.400 0.400–0.467 0.467–0.556

0.031 0.050 0.075 0.10 0.14 0.18 0.23 0.29 0.36 0.42 0.49

0.89 0.89 0.89 0.88 0.88 0.88 0.88 0.87 0.87 0.87 0.87

Table 7 γ The values of F2 /α in bins of Q2 for four x ranges together with the radiative correction factor. The first uncertainty is statistic, the second systematic and the third is due to model dependence

0.317 ± 0.017 ± 0.016 ± 0.017 0.293 ± 0.015 ± 0.014 ± 0.010 0.314 ± 0.013 ± 0.015 ± 0.012 0.338 ± 0.016 ± 0.016 ± 0.018 0.384 ± 0.017 ± 0.018 ± 0.017 0.404 ± 0.017 ± 0.018 ± 0.004 0.446 ± 0.018 ± 0.020 ± 0.009 0.488 ± 0.019 ± 0.022 ± 0.006 0.557 ± 0.023 ± 0.025 ± 0.010 0.611 ± 0.027 ± 0.029 ± 0.015 0.683 ± 0.028 ± 0.030 ± 0.062

radiation is detected together with the scattered electron. A comparison of the data with the existing parameterisations as obtained with the PDFLIB library [24] shows that our data are not well described by the leading-order parton density functions. In Fig. 6 the data are compared with the predictions of the leadingand higher-order parton density functions GRV [25] and the higher-order parton density functions CJK

γ

Q2 range

Q2 

R

11–14 14–20 20–34

12.4 16.7 25.5

0.89 0.89 0.88

11–14 14–20 20–34

12.4 16.7 25.5

0.88 0.88 0.88

γ F2 /α

Q2 = 11–14 GeV2

261

F2 /α

x = 0.01–0.1 0.278 ± 0.006 ± 0.028 ± 0.013 0.287 ± 0.006 ± 0.015 ± 0.015 0.316 ± 0.008 ± 0.016 ± 0.013

x = 0.1–0.2 0.377 ± 0.010 ± 0.039 ± 0.008 0.355 ± 0.009 ± 0.017 ± 0.005 0.399 ± 0.011 ± 0.019 ± 0.010

x = 0.2–0.3 11–14 14–20 20–34

12.4 16.7 25.5

0.88 0.88 0.87

11–14 14–20 20–34

12.4 16.7 25.5

0.89 0.87 0.87

0.464 ± 0.015 ± 0.051 ± 0.009 0.442 ± 0.013 ± 0.020 ± 0.003 0.477 ± 0.015 ± 0.023 ± 0.013

x = 0.3–0.5 0.544 ± 0.017 ± 0.061 ± 0.019 0.545 ± 0.014 ± 0.024 ± 0.012 0.594 ± 0.015 ± 0.029 ± 0.022

[10].10 The best agreement is found for the higherorder GRV [25] predictions. In all cases four quarks, u, d, s and c are used. The pure QPM prediction for γ γ → q¯q is also indicated, as calculated by using GALUGA with a mass of 0.32 GeV for the u and d quarks, 0.5 GeV for the s quark and 1.4 GeV for the c quark. It is clearly insufficient to describe the data. γ

4.4. Q2 -evolution of F2

γ

The Q2 -evolution of F2 , is studied in four x bins, x = 0.01–0.1, x = 0.1–0.2, x = 0.2–0.3 and x = 0.3–0.5 and the results are given in Table 7. In Fig. 7 γ the F2 /α values are presented for the lowest x bin and for a combined bin x = 0.1–0.5, together with our previous results [6]. Corrections for radiative effects are applied. The new measurements at 11 GeV2
Q2
14 GeV2 , 14 GeV2
Q2
20 GeV2 and 20 GeV2
Q2
34 GeV2 are in good agreement with our previous results. The expected linear growth with ln Q2 is observed in both x intervals. The function a + b ln(Q2 /GeV2 ) is fitted to the data, taking into account 10 We thank Pawel Jankowski for providing us the CJK predictions

for the photon structure function.

262

L3 Collaboration / Physics Letters B 622 (2005) 249–264

γ

Fig. 5. The photon structure function F2 /α obtained with PYTHIA and TWOGAM. Only the statistical uncertainties are shown. For clarity, the symbols corresponding to the two Monte Carlo generators are slightly offset. The measurements are correlated as indicated in Tables 3 and 4.

γ

Fig. 6. The photon structure function F2 /α as a function of x for the three Q2 intervals, with statistical and systematic uncertainties. The former √ are indicated by the inner error bars. The new data are presented together with the previous results at s = 183 GeV [6]. The predictions of the higher-order parton density functions GRV and CJK are shown as well as the leading-order predictions of the GRV. The changes in slope of the CJK predictions are due to the c-quark threshold. The QPM predictions for γ γ → q¯q are also shown.

L3 Collaboration / Physics Letters B 622 (2005) 249–264

263

γ

Fig. 7. Evolution of the photon structure function F2 /α as a function of Q2 for two x intervals. The results of a fit to the data of the function a + b(ln Q2 /GeV2 ) are shown together with the predictions of the higher-order parton density functions GRV and CJK as well as the leading-order predictions of GRV.

the total uncertainty calculated from the quadratic sum of statistical and systematic uncertainties. The fit results are: a = 0.141 ± 0.007 and b = 0.060 ± 0.005 for x = 0.01 − 0.1 with a confidence level of 44% and a = 0.05 ± 0.11 and b = 0.13 ± 0.04 for x = 0.1 − 0.5 with a confidence level of 71%. The predictions of the leading- and higher-order parton density functions GRV [25] and the higherorder parton density functions CJK [10] are also indicated in Fig. 7. The evolution is different for the different models and the data are better described by the higher-order GRV model.

5. Conclusions γ

The photon structure function F2 is measured at LEP with √ the L3 detector at centre-of-mass energies 189
s
209 GeV in the Q2 range 11 GeV2
Q2
34 GeV2 and the x range 0.006
x
0.556. The data are better reproduced by the higher-order parton density function of GRV than by other parton distribution functions determined from the low energy data. Combining the present results with previous L3 measurements, the Q2 evolution is studied from 1.5 to 120 GeV2 in the low-x region, 0.01
x
0.1, and from 12.4 to 225 GeV2 in the higher-x region, 0.1 < x
0.5. The measurements at different centre-

of-mass energies are consistent and the ln Q2 evoluγ tion of F2 is clearly confirmed.

References [1] I.C. Brock, et al., Nucl. Instrum. Methods A 381 (1996) 236. [2] L3 Collaboration, B. Adeva, et al., Nucl. Instrum. Methods A 289 (1990) 35; L3 Collaboration, O. Adriani, et al., Phys. Rep. 236 (1993) 1; M. Chemarin, et al., Nucl. Instrum. Methods A 349 (1994) 345; M. Acciarri, et al., Nucl. Instrum. Methods A 351 (1994) 300; A. Adam, et al., Nucl. Instrum. Methods A 383 (1996) 342. [3] V.M. Budnev, et al., Phys. Rep. 15 (1974) 181. [4] C. Berger, W. Wagner, Phys. Rep. 146 (1987) 1. [5] R. Nisius, Phys. Rep. 332 (2000) 165. [6] L3 Collaboration, M. Acciarri, et al., Phys. Lett. B 436 (1998) 403; L3 Collaboration, M. Acciarri, et al., Phys. Lett. B 447 (1999) 147; L3 Collaboration, M. Acciarri, et al., Phys. Lett. B 483 (2000) 373. [7] ALEPH Collaboration, R. Barate, et al., Phys. Lett. B 458 (1999) 152; ALEPH Collaboration, A. Heister, et al., Eur. Phys. J. 30 (2003) 145; OPAL Collaboration, G. Abbiendi, et al., Eur. Phys. J. 18 (2000) 15; OPAL Collaboration, G. Abbiendi, et al., Phys. Lett. B 533 (2002) 207. [8] M. Krawczyk, A. Zembrzuski, M. Staszel, Phys. Rep. 265 (2001) 165. [9] M. Klasen, Rev. Mod. Phys. 74 (2002) 1221. [10] F. Cornet, et al., Phys. Rev. D 68 (2003) 014010.

264

L3 Collaboration / Physics Letters B 622 (2005) 249–264

[11] ALEPH, L3, OPAL Collaborations, Eur. Phys. J. 23 (2002) 201. [12] PHOJET version 1.05c is used; R. Engel, Z. Phys. C 66 (1995) 203; R. Engel, J. Ranft, Phys. Rev. D 54 (1996) 4344. [13] PYTHIA version 6.203 is used; T. Sjostrand, et al., Comput. Phys. Commun. 135 (2001) 238. [14] TWOGAM version 1.71 is used; S. Nova, A. Olshevski, T. Todorov, DELPHI Note 90-35, 1990. [15] A. Capella, et al., Phys. Rep. 236 (1994) 225. [16] JETSET version 7.4 is used; T. Sjostrand, Comput. Phys. Commun. 82 (1994) 74. [17] DIAG36 Monte Carlo; F.A. Berends, P.H. Daverveldt, R. Kleiss, Nucl. Phys. B 253 (1985) 441; F.A. Berends, P.H. Daverveldt, R. Kleiss, Comput. Phys. Commun. 40 (1986) 285. [18] GEANT version 3.15 is used;

[19] [20] [21] [22] [23]

[24] [25]

R. Brun et al., preprint CERN DD/EE/84-1, 1984, revised 1987. H. Fesefeldt, RWTH Aachen report PITHA 85/2, 1985. G. D’Agostini, Nucl. Instrum. Methods A 362 (1995) 487. GALUGA version 2.0 is used; G.A. Schuler, Comput. Phys. Commun. 108 (1998) 279. T.F. Walsh, P. Zerwas, Phys. Lett. B 44 (1973) 195; R.L. Kingsley, Nucl. Phys. B 60 (1973) 45. RADCOR Monte Carlo; F.A. Berends, P.H. Daverveldt, R. Kleiss, Nucl. Phys. B 253 (1985) 421; F.A. Berends, P.H. Daverveldt, R. Kleiss, Comput. Phys. Commun. 40 (1986) 271. H. Plothow-Besch, Comput. Phys. Commun. 75 (1993) 396. M. Glück, E. Reya, A. Vogt, Phys. Rev. D 45 (1992) 3986; M. Glück, E. Reya, A. Vogt, Phys. Rev. D 46 (1992) 1973, the values given in Appendix A2, p. 1977, are used.