Inclusive Charged Hadron Production in Two-Photon Collisions at LEP

Inclusive charged hadron production, e+e- ->e+e- h+- X, is studied using 414 pb-1 of data collected at LEP with the L3 detector at centre-of-mass energies between 189 and 202 GeV. Single particle inclusive differential cross sections are measured as a function of the particle transverse momentum, pt, and pseudo-rapidity, eta. For p_t<1.5 GeV, the data are well described by an exponential, typical of soft hadronic processes. For higher pt, the onset of perturbative QCD processes is observed. The pi+- production cross section for pt>5 GeV is much higher than the NLO QCD predictions.


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 (VDM), each photon can transform into a vector meson with the same quantum numbers, thus initiating a strong interaction process with characteristics similar to hadron-hadron interactions.This process dominates in the "soft" interaction region, where hadrons are produced with a low transverse momentum, p t , with respect to the beam direction.Hadrons with high p t are produced 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 single particle inclusive production in two-photon interactions at next-to-leading order (NLO) precision [1,2].
The L3 collaboration recently published results on inclusive π 0 and K 0 S production [3].The π 0 differential cross section measured as a function of p t exhibits a clear excess over QCD calculations.A comparison of these results with other single particle inclusive production at high p t is therefore important.In this Letter, the inclusive charged hadron production is studied for a centre-of-mass energy of the two interacting photons, W γγ , greater than 5 GeV.The hadrons are measured in the transverse momentum range 0.4 GeV ≤ p t ≤ 20 GeV and in the pseudo-rapidity 1) interval |η| ≤ 1.The contributions from π ± and K ± are also derived.
The data used for this analysis were collected by the L3 detector [4] at centre-of-mass energies √ s = 189 − 202 GeV, with a luminosity weighted average value of √ s = 194 GeV, for an integrated luminosity of 414 pb −1 .Results on inclusive charged hadron production for a smaller data sample at lower √ s were previously reported [5].
The process e + e − → e + e − hadrons is modelled with the PYTHIA [6] event generator for an event sample three times larger than the data.In this generator, each photon can interact as a point-like particle, as a vector meson or as a resolved photon, leading to six classes of events.The fragmentation is simulated with JETSET.Predictions from the PHOJET Monte Carlo program [7] are also compared with the data.The following Monte Carlo generators are used to simulate the relevant background processes: KK2f [8] for e + e − → qq (γ); KORALZ [9] for e + e − → τ + τ − (γ); KORALW [10] for e + e − → W + W − and DIAG36 [11] for e + e − → e + e − τ + τ − .Events are simulated in the L3 detector using the GEANT [12] and GHEISHA [13] programs and passed through the same reconstruction program as the data.Time dependent detector inefficiencies, as monitored during each data taking period, are also simulated.

Event and charged hadron selection
Two-photon events are collected predominantly by the track triggers [14] with a low p t threshold of about 150 MeV.The selection of e + e − → e + e − hadrons events [15] consists of: • A multiplicity cut.To select hadronic final states, at least six objects must be detected, where an object can be a track or a calorimetric cluster with no associated track.
• Energy cuts.The total energy deposited in the calorimeters must be less than 0.4 √ s, in order to exclude e + e − annihilation events.The total energy in the electromagnetic calorimeter is required to be greater than 500 MeV, to suppress beam-gas and beam-wall backgrounds.
• An anti-tag condition.Events with a cluster in the luminosity monitor with an energy greater than 30 GeV and an electromagnetic shower shape are excluded.
• A mass cut.The visible mass of the event must be greater than 5 GeV.
About 2 million hadronic events are selected by these criteria.The overall background level is less than 1% and is mainly due to the e + e − → qq (γ) and e + e − → e + e − τ + τ − processes.
Charged hadrons are measured with high quality tracks in the inner tracking detector.These tracks have a transverse momentum greater than 400 MeV and a distance of closest approach to the primary vertex in the transverse plane less than 4 mm.The number of hits must be greater than 80% of that expected from the track length.Tracks are analysed in the |η| < 1 and p t < 20 GeV range where the detector resolution is optimal.A resolution σ pt /p t ≃ 0.015( GeV −1 ) × p t is achieved.

Differential cross section
The differential cross sections of inclusive charged hadron production as a function of p t are measured for an effective mass of the γγ system W γγ ≥ 5 GeV, with a mean value of W γγ ≃ 30 GeV, a photon virtuality Q 2 ≤ 8 GeV 2 and an average photon virtuality Q 2 ≃ 0.2 GeV 2 .This phase space is defined by cuts at the Monte Carlo generator level.Results are presented in 12 p t bins between 0.4 and 20 GeV.
The distribution of the detected charged hadrons in these p t bins is presented in Figure 1a.The background remains very low over the whole p t range.Events from the e + e − → e + e − τ + τ − process dominate the background at low p t while annihilation events dominate it at high p t .To measure the cross section, the background is subtracted bin-by-bin and the data are corrected for the selection efficiency, including acceptance, calculated bin-by-bin with PYTHIA.This selection efficiency varies from 62% to 84%.At low p t , the efficiency decreases due to the effect of the mass and energy cuts.At high p t , it decreases because of the multiplicity cut, since high p t particles are mainly produced in low multiplicity events.
The level 1 trigger efficiency is obtained by comparing the number of events accepted by the independent track and calorimetric energy [16] triggers.It varies from 95% to 98%.The efficiency of higher level triggers is about 95% and is measured using prescaled events.The overall efficiency, taking into account selection and trigger efficiencies is given in Table 1.
Sources of systematic uncertainties on the cross section measurements are the trigger efficiency estimation, the background subtraction, the selection procedure and the Monte Carlo modeling.Their contributions are shown in Table 2.The uncertainty on the trigger efficiency and on the background subtraction are of a statistical nature.The uncertainty due to the selection procedure is evaluated by repeating the analysis with different selection criteria: the multiplicity cut is moved from 5 to 7 objects, the energy cut is moved to 0.35 √ s and the number of hits of the tracks is moved to 70% of that expected.The sum in quadrature of the differences between these and the reference results is listed in Table 2. Varying other criteria give negligible contributions.To evaluate the uncertainty on the Monte Carlo modeling, the selection efficiency is determined using only one of the PYTHIA subprocesses: VDM-VDM, direct-direct or resolved-resolved.The systematic uncertainty is assigned as the average difference between these values and the reference Monte Carlo.The larger contribution comes from the difference between direct and other processes.
The differential cross section of charged hadron production as a function of p t is presented in Figure 1b and in Table 1.The migration due to the p t resolution does not affect these results.This was verified by performing a one-step Bayesian unfolding [17] of the track p t distribution which give results compatible, within errors, with those obtained using the bin-bybin correction.
The steep decrease of dσ/dp t in the range 0.4 < p t < 1.5 GeV is described by an exponential of the form A exp(−p t / p t ) with a mean value of p t ≃ 232 MeV.This behaviour is characteristic of hadrons produced by soft interactions and is similar to that obtained in hadron-hadron and photon-hadron collisions [18].At higher p t the differential cross section is better represented by power law functions Ap −B t , as expected by the onset of QCD processes.For 1.5 GeV < p t < 5 GeV, B ≃ 4.2 and for 5 GeV < p t < 20 GeV, B ≃ 2.6.The results of the fits are drawn on Figure 1b where the data are also compared to Monte Carlo predictions.PYTHIA is slightly above the data, whereas PHOJET is too low by more than one order of magnitude.These results are consistent with our findings in inclusive π 0 production [3].

Charged pions and charged kaons
Assuming the fragmentation function implemented in JETSET are correct, the π ± and the K ± inclusive cross sections are extracted from the charged hadron cross section.Their ratios relative to charged hadrons are estimated bin-by-bin from Monte Carlo.Above 5 GeV, they are almost constant.Their uncertainty is calculated in the same way as the uncertainty on the Monte Carlo modeling of the selection efficiency, by using different subprocesses in PYTHIA.This gives an additional systematic uncertainty of from 2% to 12% for pions and from 14% to 24% for kaons.
The differential cross sections for π ± and K ± production as a function of p t are presented in Figure 2 and in Table 3.The π ± data are compared to the previous π 0 data [3] scaled up by a factor 4: a factor 2 to correct for the |η| < 0.5 interval used for the π 0 measurement and a factor 2 to take into account the isospin symmetry.A good agreement is found between these two measurements as shown in Figure 2. The K ± data are compared to the previous results of K 0 S data [3] scaled up by a factor 4/3: a factor 2/3 to correct for the |η| < 1.5 interval of the K 0 S measurement and a factor 2 to take into account unobserved K 0 L decays.Good agreement is found between these two measurements as shown in Figure 2.These agreements show a good consistency with the data of the fragmentation functions as implemented in JETSET.
The differential cross section of π ± production as a function of |η| for p t > 1 GeV is shown in Figure 3 and in Table 5.The cross section is almost constant in this η range.It agrees well with the π 0 measurement [3].For different p t cuts, Monte Carlo and QCD predictions describe well the uniform η distribution, while the agreement in the absolute rate depends on the p t range considered.
In Figure 4a the data are compared to analytical NLO QCD predictions [19,2].For this calculation, the flux of quasi-real photons is obtained using the Equivalent Photon Approximation [20], taking into account both transverse and longitudinal virtual photons.The interacting particles can be point-like photons or partons from the γ → qq process, which evolve into quarks and gluons.The NLO parton density functions of Reference 21 are used and all elementary 2 → 2 and 2 → 3 processes are considered.New NLO fragmentation functions [22] are used.The renormalization, factorisation and fragmentation scales are taken to be equal: [2], with ξ = 1 for the central value.The scale uncertainty in the NLO calculation is estimated by varying the value of ξ from 0.5 to 2.0.The agreement with the data is poor in the high-p t range for any choice of scale.
To test NLO QCD calculations in regions where non-perturbative subprocesses are better suppressed, we have also measured differential cross sections of π ± production for W γγ > 10, 30 and 50 GeV.The results are shown in Table 4 and Figure 4b.The discrepancy between the calculations and data at high p t is not significantly reduced by these stringent more W γγ cuts.Similar calculations were previously compared to γp reactions at HERA up to a p t of 12 GeV and to pp collisions up to a p t of 20 GeV.Good agreement was found [23].In the γγ channel, an excess of data with respect to NLO QCD was observed in tagged events at PETRA experiments [2].No discrepancy is observed with the OPAL data which explore a p t range up to 10 GeV.In this range, our data and the OPAL ones are well in agreement within the quoted uncertainties.A discrepancy with NLO QCD is revealed by our data which extend the measurement to higher p t values.6 0.48 62.4 ± 7.7 (23.4 ± 0.1 ± 3.7) ×10 3 0.6 − 0.8 0.68 64.5 ± 6.9 (10.9 ± 0.1 ± 1.5) ×10 3 0.8 − 1.0 0.88 67.7 ± 6.0 (48.0 ± 0.1 ± 5.9) ×10 2 1.0 − 1.      Figure 4: a) Inclusive π ± differential cross section dσ/dp t compared to NLO QCD calculations [19] for W γγ > 5 GeV.The dasheddotted line corresponds to the direct subprocess.The dashed lines represent the scale uncertainty of the calculations.b) Inclusive π ± differential cross section dσ/dp t with different W γγ cuts.The average p t value of each bin, p t , is used.

Figure 1 :Figure 2 :Figure 3 :
Figure 1: a) Number of selected tracks per GeV in each p t bin and main sources of background.b) Inclusive charged hadron differential cross section dσ/dp t fitted with an exponential and power-law functions.Monte Carlo predictions are also presented.Statistical and systematic uncertainties are shown.The average p t value of each bin, p t , is used.

Table 1 :
Transverse momentum range and average value from the data with the corresponding overall efficiency and differential cross section for inclusive charged hadron production for W γγ > 5 GeV and |η| < 1.The uncertainty on the efficiency is systematic.The first uncertainty on the cross section is statistical and the second systematic.

Table 2 :
Systematic uncertainty on the charged hadron cross section due to trigger efficiency, background subtraction, selection procedure and Monte Carlo modeling.

Table 3 :
Differential cross section as a function of p t for inclusive π ± and K ± production for W γγ > 5 GeV and |η| < 1.The first uncertainty on the cross section is statistical and the second systematic.

Table 4 :
Differential cross section as a function of p t for inclusive π ± production for |η| < 1 and different W γγ cuts.The first uncertainty on the cross section is statistical and the second systematic.

Table 5 :
Differential cross section as a function of |η| for inclusive π ± production for W γγ > 5 GeV and p t > 1 GeV.The first uncertainty on the cross section is statistical and the second systematic.