Article
Reference
Inclusive π
0and K
S0production in two-photon collisions at LEP
L3 Collaboration
ACHARD, Pablo (Collab.), et al.
Abstract
The reactions e+e−→e+e−π0 X and e+e−→e+e−KS0 X are studied using data collected at LEP with the L3 detector at centre-of-mass energies between 189 and 202 GeV. Inclusive differential cross sections are measured as a function of the particle transverse momentum pt and the pseudo-rapidity. For pt⩽1.5 GeV, the π0 and KS0 differential cross sections are described by an exponential, typical of soft hadronic processes. For pt⩾1.5 GeV, the cross sections show the presence of perturbative QCD processes, described by a power-law. The data are compared to Monte Carlo predictions and to NLO QCD calculations.
L3 Collaboration, ACHARD, Pablo (Collab.), et al . Inclusive π
0and K
S0production in two-photon collisions at LEP. Physics Letters. B , 2002, vol. 524, no. 3-4, p. 44-54
DOI : 10.1016/S0370-2693(01)01269-2
Available at:
http://archive-ouverte.unige.ch/unige:43258
Disclaimer: layout of this document may differ from the published version.
1 / 1
Physics Letters B 524 (2002) 44–54
www.elsevier.com/locate/npe
Inclusive π 0 and K 0 S production in two-photon collisions at LEP
L3 Collaboration
P. Achard
t, O. Adriani
q, M. Aguilar-Benitez
x, J. Alcaraz
x,r, G. Alemanni
v, J. Allaby
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f,ag, F. Anselmo
i, A. Arefiev
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c, T. Aziz
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al, A. Bajo
x, G. Baksay
p, L. Baksay
y, S.V. Baldew
b, S. Banerjee
j, Sw. Banerjee
d, A. Barczyk
au,as,
R. Barillère
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af, A. Bay
v, F. Becattini
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b, D. van Dierendonck
b, C. Dionisi
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j, P. Garcia-Abia
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u, G. Grenier
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h,a, M. Guida
am, R. van Gulik
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e, D. Hatzifotiadou
i, T. Hebbeker
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ah,
H. Hofer
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au, S.R. Hou
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ad, B.N. Jin
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x, D. Käfer
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0370-2693/02/$ – see front matter 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 0 - 2 6 9 3 ( 0 1 ) 0 1 2 6 9 - 2
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aaI. Physikalisches Institut, RWTH, D-52056 Aachen, Germany1 III. Physikalisches Institut, RWTH, D-52056 Aachen, Germany1
bNational Institute for High Energy Physics, NIKHEF, and University of Amsterdam, NL-1009 DB Amsterdam, The Netherlands
cUniversity of Michigan, Ann Arbor, MI 48109, USA
dLaboratoire d’Annecy-le-Vieux de Physique des Particules, LAPP, IN2P3-CNRS, BP 110, F-74941 Annecy-le-Vieux Cedex, France eInstitute of Physics, University of Basel, CH-4056 Basel, Switzerland
fLouisiana State University, Baton Rouge, LA 70803, USA gInstitute of High Energy Physics, IHEP, 100039 Beijing, PR China6
hHumboldt University, D-10099 Berlin, Germany1
iUniversity of Bologna, and INFN, Sezione di Bologna, I-40126 Bologna, Italy jTata Institute of Fundamental Research, Mumbai (Bombay) 400 005, India
kNortheastern University, Boston, MA 02115, USA
lInstitute of Atomic Physics and University of Bucharest, R-76900 Bucharest, Romania
mCentral Research Institute for Physics of the Hungarian Academy of Sciences, H-1525 Budapest 114, Hungary2 nMassachusetts Institute of Technology, Cambridge, MA 02139, USA
oPanjab University, Chandigarh 160 014, India pKLTE-ATOMKI, H-4010 Debrecen, Hungary3
qINFN, Sezione di Firenze, and University of Florence, I-50125 Florence, Italy rEuropean Laboratory for Particle Physics, CERN, CH-1211 Geneva 23, Switzerland
sWorld Laboratory, FBLJA Project, CH-1211 Geneva 23, Switzerland tUniversity of Geneva, CH-1211 Geneva 4, Switzerland
uChinese University of Science and Technology, USTC, Hefei, Anhui 230 029, PR China6 vUniversity of Lausanne, CH-1015 Lausanne, Switzerland
wInstitut de Physique Nucléaire de Lyon, IN2P3-CNRS, Université Claude Bernard, F-69622 Villeurbanne, France xCentro de Investigaciones Energéticas, Medioambientales y Tecnologícas, CIEMAT, E-28040 Madrid, Spain4
yFlorida Institute of Technology, Melbourne, FL 32901, USA zINFN, Sezione di Milano, I-20133 Milan, Italy
aaInstitute of Theoretical and Experimental Physics, ITEP, Moscow, Russia abINFN, Sezione di Napoli, and University of Naples, I-80125 Naples, Italy
acDepartment of Physics, University of Cyprus, Nicosia, Cyprus adUniversity of Nijmegen and NIKHEF, NL-6525 ED Nijmegen, The Netherlands
aeCalifornia Institute of Technology, Pasadena, CA 91125, USA
afINFN, Sezione di Perugia, and Università Degli Studi di Perugia, I-06100 Perugia, Italy agNuclear Physics Institute, St. Petersburg, Russia
ahCarnegie Mellon University, Pittsburgh, PA 15213, USA aiINFN, Sezione di Napoli, and University of Potenza, I-85100 Potenza, Italy
ajPrinceton University, Princeton, NJ 08544, USA akUniversity of California, Riverside, CA 92521, USA
alINFN, Sezione di Roma, and University of Rome “La Sapienza”, I-00185 Rome, Italy amUniversity and INFN, Salerno, I-84100 Salerno, Italy
anUniversity of California, San Diego, CA 92093, USA
aoBulgarian Academy of Sciences, Central Laboratory of Mechatronics and Instrumentation, BU-1113 Sofia, Bulgaria ap The Center for High Energy Physics, Kyungpook National University, 702-701 Taegu, South Korea
aqUtrecht University and NIKHEF, NL-3584 CB Utrecht, The Netherlands arPurdue University, West Lafayette, IN 47907, USA
asPaul Scherrer Institut, PSI, CH-5232 Villigen, Switzerland atDESY, D-15738 Zeuthen, Germany
auEidgenössische Technische Hochschule, ETH Zürich, CH-8093 Zürich, Switzerland avUniversity of Hamburg, D-22761 Hamburg, Germany
awNational Central University, Chung-Li, Taiwan, ROC axDepartment of Physics, National Tsing Hua University, Taiwan, ROC
1 Supported by the German Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie.
2 Supported by the Hungarian OTKA fund under contract numbers T019181, F023259 and T024011.
3 Also supported by the Hungarian OTKA fund under contract number T026178.
4 Supported also by the Comisión Interministerial de Ciencia y Tecnología.
5 Also supported by CONICET and Universidad Nacional de La Plata, CC 67, 1900 La Plata, Argentina.
6 Supported by the National Natural Science Foundation of China.
Received 8 September 2001; received in revised form 10 October 2001; accepted 21 October 2001 Editor: L. Rolandi
Abstract
The reactions e+e−→e+e−π0X and e+e−→e+e−K0S X are studied using data collected at LEP with the L3 detector at centre-of-mass energies between 189 and 202 GeV. Inclusive differential cross sections are measured as a function of the particle transverse momentumpt and the pseudo-rapidity. Forpt1.5 GeV, theπ0and K0Sdifferential cross sections are described by an exponential, typical of soft hadronic processes. Forpt 1.5 GeV, the cross sections show the presence of perturbative QCD processes, described by a power-law. The data are compared to Monte Carlo predictions and to NLO QCD calculations.2002 Elsevier Science B.V. All rights reserved.
1. Introduction
Two-photon collisions are the main source of hadron production in the high-energy regime of LEP via the process e+e−→e+e−γ∗γ∗→e+e−hadrons. In the Vector Dominance Model, each photon can transform into a vector meson with the same quantum num- bers, thus initiating a strong interaction process with characteristics similar to hadron–hadron interactions.
This process dominates in the “soft” interaction re- gion, where hadrons are produced with a low trans- verse momentum pt. Hadrons with highpt are pro- duced by the direct QED process γ∗γ∗→qq or by¯ QCD processes originating from the partonic content of the photon. QCD calculations are available for sin- gle particle inclusive production in two-photon inter- actions at next-to-leading order (NLO) [1,2].
In this Letter, inclusive π0 and K0S production from quasi-real photons is studied for a centre-of- mass energy of the two interacting photons, Wγ γ, greater than 5 GeV. The π0’s are measured in the transverse momentum range 0.2 pt 20 GeV and in the pseudo-rapidity7 intervals |η|2.3 and 3.4|η|4.3. The K0S’s are measured in the range 0.4pt4 GeV and|η|1.5.
The data used for this analysis were collected by the L3 detector [3] at centre-of-mass energies from√
s= 189 GeV to 202 GeV, with a luminosity weighted average value of √
s = 194 GeV. The integrated luminosity is 414 pb−1. Previous measurements of
7 η= −ln tan(θ/2), whereθ is the polar angle of the particle relative to the beam axis.
inclusive charged hadron and K0S production were performed at LEP [4] at√
s=161–172 GeV.
2. Monte Carlo simulation
The process e+e−→ e+e− hadrons is modelled with the PHOJET [5] and PYTHIA [6] event gener- ators with, respectively, 2 and 3 times more luminos- ity than the data. Default options are used for the two generators. The following generators are used to simu- late background processes: PYTHIA and KK2f [7] for e+e−→qq(γ ); KORALZ [8] for e¯ +e−→τ+τ−(γ );
KORALW [9] for e+e−→W+W−and DIAG36 [10]
for e+e−→e+e−τ+τ−. The events are simulated in the L3 detector using the GEANT [11] and GEISHA [12] programs and passed through the same recon- struction program as the data. Time dependent detec- tor inefficiencies, as monitored during the data taking period, are also simulated.
3. Event selection
The selection of e+e− →e+e− hadrons events is based on information from the central tracking detectors and from the electromagnetic (BGO) and hadronic calorimeters, as described in Ref. [13]. In order to restrict the Q2 interval, we exclude events with a cluster in the small-angle calorimeter with energy greater than 30 GeV. About 2 million hadronic events are selected. The level of background is less than 1% and is mainly due to the e+e−→qq(γ )¯ and e+e−→e+e−τ+τ−processes.
The particle identification proceeds from charged tracks and electromagnetic clusters. The inner tracking detector extends up to|η| =1.64. The electromagnetic calorimeters extend up to |η|0.96 for the barrel, and cover 1.15 |η| 2.25 for the endcaps and 3.37|η|4.38 for the small-angle detector. A track must have a transverse momentum above 100 MeV and a distance of closest approach to the primary vertex in the transverse plane below 10 mm. An electromagnetic cluster must have an energy greater than 100 MeV formed by the energy deposited in at least 2 neighbouring BGO crystals. There should be no charged track within an angle of 200 mrad and the associated energy in the hadron calorimeter must be less than 20% of the electromagnetic energy.
Clusters in the small-angle detector must have an energy greater than 2 GeV and restrictions on the energy profile in each cluster are applied to distinguish well reconstructed photons from those at the edges of the detector or from residual hadrons.
Forpt<5 GeV, the inclusiveπ0production is mea- sured via the decay of the π0 into two photons as- sociated to two electromagnetic clusters. The distri- bution of the effective mass of the reconstructedγ γ system shows a clear π0 peak in all the detector re- gions. Examples for the central region and the small- angle detector are given in Figs. 1(a) and (b), respec- tively. Over the entire range of|η|andpt, the resolu- tion varies between 6.6 and 13.5 MeV, and is well re- produced by Monte Carlo simulation. Forpt>4 GeV and |η|<0.5, the two final photons are unresolved and theπ0 is associated to a single electromagnetic cluster. To avoid double-counting in the region 4<
pt <5 GeV and |η|<0.5, where both methods are applied, only clusters which do not contribute to com- binations in a 3-σ mass band around theπ0peak are taken into account. In this region, we have checked that the two methods applied separately agree within errors.
Inclusive K0S production is measured using the decay K0S → π+π− that produces two oppositely charged tracks. The K0S’s are selected by reconstruct- ing the secondary decay vertex. The projected dis- tance, in the transverse plane, between the secondary vertex and the primary e+e− interaction point is re- quired to be greater than 3 mm. The angle between the projected flight direction of the K0Scandidate sec- ondary vertex in the transverse plane, and the to-
tal transverse momentum vector of the two outgoing tracks must be less than 75 mrad. After these cuts, about 5×105 events are selected. The distribution of the effective mass of the reconstructedπ+π−sys- tem shows a clear K0Speak. Examples for differentpt
bins are given in Figs. 1(c) and (d). The resolution varies from 8 MeV forpt <1 GeV to 10 MeV around 4 GeV, and is well reproduced by Monte Carlo simu- lation.
4. Differential cross sections
Differential cross sections as a function of the trans- verse momentumpt and of the absolute pseudorapid- ity|η|are calculated using the number ofπ0and K0S candidates and the overall efficiency for each bin of pt or|η|. The overall efficiency includes reconstruc- tion and trigger efficiencies and takes into account the branching fraction of the K0S intoπ+π−. The recon- struction efficiency includes the effects of the accep- tance and selection cuts and is calculated with the Monte Carlo generators PHOJET and PYTHIA. As both generators reproduce well the shapes of the ex- perimental distributions of hadronic two-photon pro- duction [13], their average is used.
Two-photon events are collected predominantly by the track triggers [14]. The trigger efficiency is de- rived from each year’s data sample by comparing the number of events accepted by the independent track and calorimetric energy [15] triggers. The efficiencies of higher level triggers are measured using prescaled events. For theπ0, it varies from 80% at low pt to 100% at highpt. For the K0S, it is 85% independently ofpt. Those factors are used to correct the data in each bin of the spectra.
The cross sections are calculated for Wγ γ 5 GeV, with a mean value of 30 GeV and a photon virtuality Q28 GeV2. The overall efficiency does not depend on theQ2cutoff.
4.1. e+e−→e+e−π0X analysis
To evaluate the number of π0’s when the two photons are well separated in the detector, fits are made to theγ γ mass distribution in the interval 50<
Mγ γ <200 MeV using a Gaussian to describe the signal and a third degree Chebyshev polynomial for
Fig. 1. Two photon effective mass for (a) 1< pt<1.5 GeV in the central region and (b) forpt>0.2 GeV in the small angle detector. Two charged pion effective mass for (c) 0.2< pt<0.4 GeV and (d) 0.8< pt<1.0 GeV. Theπ0and K0Speaks are fitted with a Gaussian and the background with a Chebyshev polynomial. Values of theπ0and K0Smasses are also indicated.
the background. All the parameters, including mass and width of the peak, are left free.
When single clusters are identified as aπ0, the con- tamination coming from the decays of other mesons (η, ω, η, . . .) is on average 15.1±1.2% over the entire pt and|η| ranges. Single photon production (γq→ γq, qq¯→γg, gq→γq) is predicted to be more than one order of magnitude below our measurements [16].
In addition, a study of the energy profile of each clus- ter reveals no significant background from this source.
The background due to annihilation events increases withpt up to a maximum of 11%.
The reconstruction efficiency varies between 15%
and 50% in the different pt and |η| ranges. The efficiency increases frompt 0.2 GeV, where a low energy photon can go undetected, up topt 2 GeV.
In the region 2< pt<4 GeV, the efficiency decreases due to the increasing percentage of events in which the two photons merge. Forpt>4 GeV, the addition of the single-cluster analysis gives a higher efficiency.
Table 1
Theπ0overall efficiency and differential cross sections as a function ofptfor|η|<0.5. Averageptvalues,pt, after efficiency corrections are given. Forpt<4 GeV, theπ0is only reconstructed from its decay into two photons. Above 5 GeV, theπ0is only detected as a single cluster. In the 4–5 GeV bin, both methods are used yielding a higher efficiency. The first uncertainty on cross sections is statistical and the second one systematic. The cross sections are calculated for Wγ γ>5 GeV and Wγ γ>10 GeV and coincide forpt>3 GeV
pt pt Efficiency dσ/dptfor Wγ γ>5 GeV dσ/dptfor Wγ γ>10 GeV
[GeV] [GeV] [%] [pb/GeV] [pb/GeV]
0.2–0.4 0.28 12.9±1.2 (89±1±8)×102 (62±0.8±6)×102
0.4–0.6 0.48 24.3±2.2 (44±0.3±4)×102 (35±0.3±3)×102
0.6–0.8 0.68 30.7±2.8 (18±0.1±2)×102 (15±0.1±1)×102
0.8–1.0 0.88 35.4±3.2 (73±0.8±7)×101 (59±0.7±6)×101
1.0–1.5 1.14 37.2±3.4 (22±0.3±2)×101 (18±0.3±2)×101
1.5–2.0 1.68 37.4±3.5 (46±1±4) (40±1±4)
2.0–3.0 2.31 35.8±3.5 (11±0.5±1) (95±5±11)×10−1
3.0–4.0 3.36 23.5±4.1 (30±6±5)×10−1
4.0–5.0 4.39 47.5±8.5 (76±14±1)×10−2
5.0–7.5 5.79 26.7±3.0 (26±4±3)×10−2
7.5–10.0 8.46 26.4±3.7 (73±18±10)×10−3
10.0–15.0 11.98 21.7±3.9 (27±9±5)×10−3
15.0–20.0 17.36 15.6±3.8 (14±8±4)×10−3
Table 2
The number of reconstructed π0, overall efficiency and differential cross section as a function of pseudorapidity forpt >1 GeV and Wγ γ>5 GeV. The first uncertainty on the cross section is statistical and the second one systematic
Detector |η| Number ofπ0 Efficiency [%] dσ/d|η|[pb]
Barrel 0.0–0.2 8914 35.6±4.0 303±8±33
0.2–0.4 9263 36.7±4.1 305±8±33
0.4–0.6 8965 34.2±3.8 317±8±34
0.6–0.8 8094 31.7±3.6 308±8±33
Barrel+Endcap 0.8–1.4 8688 12.4±2.1 282±10±47
Endcap 1.4–1.6 3443 16.6±2.9 251±15±42
1.6–1.8 3050 16.4±3.0 225±15±37
1.8–2.0 2313 15.2±2.8 184±15±31
2.0–2.2 2294 12.7±2.5 217±23±36
Small-angle 3.4–4.3 1410 16.4±3.5 23±2±5
The efficiency decreases with polar angle due to the acceptance of the calorimeters. In the endcaps and small-angle detectors, the efficiency takes into account the regionpt>1 GeV.
Sources of systematic uncertainties on the cross- section measurements are selection criteria, Monte Carlo modelling, background subtraction and accu- racy of the trigger efficiency measurement. The un- certainty due to selection criteria is dominated by
the e+e−→e+e−hadrons selection, estimated to be 7.5% [13]. The Monte Carlo modelling uncertainty, taken as half the relative difference between PHOJET and PYTHIA, increases withptfrom 1% to 24%. The background uncertainty varies from 5% to 15% for pt<5 GeV. It is estimated using different background parametrisations during the fitting procedure. In the high pt region, the uncertainty on the annihilation background subtraction is taken as half the difference
Table 3
The K0Soverall efficiency and differential cross sections as a function ofptfor|η|<1.5. Averageptvalues,pt, after efficiency corrections are given. The first uncertainty on cross section is statistical and the second one systematic. The cross section is calculated for Wγ γ>5 GeV and Wγ γ>10 GeV
pt pt Efficiency dσ/dptfor Wγ γ>5 GeV dσ/dptfor Wγ γ>10 GeV
[GeV] [GeV] [%] [pb/GeV] [pb/GeV]
0.4–0.6 0.49 13.6±0.1 1522±20±81 1262±21±65
0.6–0.8 0.69 17.8±0.2 947±14±53 786±16±40
0.8–1.0 0.89 20.0±0.3 521±11±27 428±12±22
1.0–1.5 1.16 22.2±0.4 180±5±9 151±4±8
1.5–2.0 1.67 22.4±1.0 46±3±3 42±2±2
2.0–3.0 2.29 16.1±1.3 10±1±0.6 11±1±0.6
3.0–4.0 3.35 14.8±4.8 2.1±0.8±0.2 1±0.5±0.3
Table 4
The number of reconstructed K0S, overall efficiency and differential cross section as a function of pseudorapidity forpt>1.5 GeV and Wγ γ>5 GeV. The first uncertainty on the cross section is statistical and the second one systematic
|η| Number of K0S Efficiency [%] dσ/d|η|[pb]
0.0–0.3 744 23.3±0.8 25.9±2.0±1.3
0.3–0.6 759 24.5±0.8 25.1±1.9±1.2
0.6–1.5 1473 14.7±1.2 27.1±2.4±3.2
between PYTHIA and KK2f and varies from 0.1%
to 5%. The uncertainty on the trigger efficiency varies from 0.1% to 1.1% due to the statistical accuracy of its determination.
The overall efficiencies and differential cross sec- tions dσ/dpt and dσ/d|η| are given in Tables 1 and 2. The cross sections are also calculated for Wγ γ >10 GeV. The π0 multiplicity in the range 0.2< pt<20 GeV and|η|<0.5 is 0.275±0.001± 0.025 per e+e−→e+e−hadrons event, in agreement with Monte Carlo predictions, 0.281 for PHOJET and 0.285 for PYTHIA.
4.2. e+e−→e+e−K0SX analysis
The number of K0S is evaluated by means of a fit to the π+π− mass distribution in the interval 400< Mπ+π−<600 MeV. A Gaussian describes the signal and a third degree Chebyshev polynomial the background. All parameters, including the mass and width of the peak, are left free.
The reconstruction efficiency is of the order of 20%.
Systematic uncertainties, estimated as in theπ0case, are selection criteria (7.5%), Monte Carlo modelling (1–6%), background subtraction (1–7%) and trigger efficiency measurement accuracy (2%). In addition, a 2.5% uncertainty arises from the K0Sselection criteria.
The overall efficiencies and differential cross sec- tionsdσ/dptanddσ/d|η|are given in Tables 3 and 4.
Cross sections for Wγ γ >10 GeV are also given. The multiplicity of K0Sin the range 0.4< pt<4 GeV and
|η|<1.5 is 0.060±0.006±0.003 per e+e−→e+e− hadrons event, in agreement with Monte Carlo predic- tions, 0.067 for PHOJET and 0.056 for PYTHIA.
5. Results
Differential cross sections ofπ0and K0Sproduction with respect toptand|η|are shown in Figs. 2, 3 and 4.
The behaviour ofdσ/dpt in the range 0.2< pt <
1.5 GeV forπ0 and 0.6< pt <1.5 GeV for K0S is
Fig. 2. Inclusive differential cross sectiondσ/dptcompared to Monte Carlo predictions and exponential and power law behaviour for: (a)π0 production for|η|<0.5 and (b) K0Sproduction for|η|<1.5. Ratio of the differential cross sectiondσ/dpt to Monte Carlo predictions for:
(c)π0production and (d) K0Sproduction.
described by an exponential of the form Ae−pt/pt with a mean value of pt 230 MeV for the π0 and pt 290 MeV for the K0S. This behaviour is characteristic of hadrons produced by soft interactions and is similar to that obtained in hadron–hadron and photon–hadron collisions [17]. Due to the direct γ γ →qq process and to hard QCD interactions, two-¯ photon collisions exhibit a cross section higher than the expected exponential behaviour at highpt values.
Forpt 1.5 GeV, the differential cross sections are better represented by a power law function Ap−t B. The value of the power B is compatible with 4 for bothπ0 and K0S. In the framework of Ref. [18], this value is expected in the case of 2→2 hard scattering processes at the parton level.
The differential cross sections are also compared to Monte Carlo predictions in Fig. 2. In theπ0case, the high pt region is not reproduced by PYTHIA
Fig. 3. Inclusive differential cross sectiondσ/dptcompared to NLO QCD predictions for: (a)π0production for|η|<0.5 and (b) K0Sproduction for|η|<1.5. The NLO calculations are given for the QCD scale equal topt (full line) and for the scales 0.5pt (upper dashed line) and 2pt (lower dashed line). The contribution of the direct QED process is indicated as a dashed dotted line. For theπ0case the estimation of the single photon production [16] is indicated as a dotted line. The structure at 3 GeV in (b) is due to the charm threshold in the fragmentation function [3,23].
Fig. 4. Inclusive differential cross sectionsdσ/d|η|compared to NLO QCD predictions for: (a)π0production forpt>1 GeV and (b) K0S production forpt>1.5 GeV. The NLO calculations are given for the QCD scale equal topt(full line) and for the scales 0.5pt(upper dashed line) and 2pt(lower dashed line). The contribution of the direct QED process is indicated as a dotted line.
nor by PHOJET. We verify that the shapes of the|η| distributions of π0 and K0S are well reproduced by both models. Qualitative agreement with earlier data on charged hadrons [4] and neutral pions [19] is found.
In Figs. 3(a) and (b) the data are compared to an- alytical NLO QCD predictions [20]. For this calcu- lation, the flux of quasi-real photons is obtained us- ing the Equivalent Photon Approximation, taking into account both transverse and longitudinal virtual pho- tons. The interacting particles can be photons or par- tons from the γ → qq, which evolves into quarks¯ and gluons. The NLO parton density functions of Ref. [21] are used and all elementary 2→2 and 2→3 processes are considered. New NLO fragmentation functions(FF)[22] are used assuming that FF(π0)= (FF(π+)+FF(π−))/2. The renormalization, factori- sation and fragmentation scales are taken to be equal:
µ=M=MF =ξpt [2]. The scale uncertainty in the NLO calculation is estimated by varying the value ofξ from 0.5 to 2.0. The structure in thept spectrum for the K0Scalculation is due to the charm threshold in the fragmentation function [2,23]. The agreement with the data is satisfactory in the K0Scase, but it is poor for the π0case in the high-ptrange.
The dσ/d|η| differential cross sections, are also compared to QCD calculations as shown in Fig. 4. The shape of the data, and in particular the measurement of theπ0production at|η| =3.85, is reproduced by NLO QCD predictions.
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. Sjöstrand for useful discussions.
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