1 H1prelim-13-032 Submitted to

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3 XXI International Workshop on Deep-Inelastic Scattering and Related Subjects,

4 DIS2013, April 22-26, 2013, Marseille  Parallel Session  QCD and Final States

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6 Electronic Access: www-h1.desy.de/publications/H1preliminary.short list.html

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8 Measurement of charged particle production in deep-inelastic 9 ep scattering at \sqrt{s} = 225GeV at HERA

10 H1 Collaboration

Abstract

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12 Charged particle production is measured in deep inelastic ep scattering at \sqrt{s} = 225 GeV 13 with the H1 detector at HERA. The kinematic range of the analysis covers low photon vir-14 tualities, 5 < Q^{2} < 10 GeV^{2}, and medium to high values of inelasticity y, 0.35 < y < 0.8. 15 The analysis is performed in the virtual photon-proton centre-of-mass system. The charged 16 particle production cross sections is investigated double-differentially as a function of pseu-17 dorapidity η^{∗} and transverse momentum p_{T}^{∗} in the range 0 < η^{∗} < 3.5 and p_{T}^{∗} < 10 GeV. 18 The data are compared to different phenomenological models.

20 1 Introduction

21 Recently, it was found that the shape of charged particle transverse momentum distributions 22 measured in baryon-baryon interactions is distinctly different from that observed in gamma-23 gamma interactions [1]. This is an indication for possible differencee in underlying dynamics 24 of hadron production for these two types of particle collisions. At HERA both photoproduction 25 and DIS processes are mediated by photon exchange, and therefore it provides an unique pos-26 sibility to study the intermediate case of baryon-photon interactions. Naïvely one would expect 27 to observe a change in the hadron production dynamics at central rapidities in photon-proton 28 (γ^{∗}p) centre-of-mass system.

29 Due to the strong asymmetry in the beam energies of electron and proton beams at HERA the 30 previous inclusive hadron production measurements [2] had only limited access to the central 31 rapidity region in the γ^{∗}p frame. This region can be studied more easily by using the data 32 collected at reduced proton beam energy and by restricting the event kinematics to large values 33 of the γ^{∗}p rest mass W_{γ^{∗}p}.

34 2 Event Selection

35 2.1 DIS and detector level selection

36 In 2007 the HERA ep-collider has also been run at reduced proton beam energy (E_{p} = 460 GeV) 37 for three months in which the H1experiment has collected data corresponding to an integrated 38 luminosity of 12.45 pb^{−1}. These data are used in the present analysis of the charged particle 39 spectra shape in the γ^{∗}p rest frame.

40 DIS events are recorded using triggers based on electromagnetic energy deposits in the 41 SpaCal calorimeter. The trigger efficiency is determined using independently triggered data. 42 For DIS events the trigger efficiency is determined to be almost 100% in the kinematic region 43 of the analysis. The scattered lepton, defined by the most energetic SpaCal cluster, is required 44 to have an energy E_{e} larger than 3.4 GeV. The kinematical phase space is defined by 5 < Q^{2} < 45 10 GeV^{2} and 0.35 < y < 0.8, corresponding to the geometric acceptance of the SpaCal.

46 Several cuts are applied to suppress photoproduction background. The electron identifi-47 cation selection criteria are designed to have a high efficiency for the signal while rejecting 48 significantly the background. A detailed description of these cuts can be found elsewhere [3].

49 2.2 Tracks Selection

50 The tracks used in the analysis are measured in the central tracking detector (CTD). The re-51 construction in the central region is based on two drift chambers, CJC1 and CJC2. The tracks 52 are used to define the event vertex. In this analysis only tracks from the primary vertex are 53 considered.

54 In order to provide a higher efficiency of the track reconstruction, the following cuts are 55 applied:

56 • The transverse momentum p_{T} of a track has to be larger than 0.12 GeV.

57 • The polar angular range of a track is required to be 20^{∘} < θ < 160^{∘}.

58 • Tracks are required to have a radial length L (the radial distance between the first and the 59 last hit) larger than 10 cm for the full θ range to ensure good momentum resolution.

60 • Starting point of a track is required to be in CJC1.

61 2.3 Definition of experimental observables

62 The results of this analysis are presented in the γ^{∗}p centre-of-mass frame, to minimise the effect 63 of the transverse boost from the virtual photon. The transformation to the this frame is recon-64 structed with the knowledge of the kinematic variables Q^{2} and y. The transverse momentum 65 and pseudorapidity of charged particles in this frame are labeled as p_{T}^{∗} and η^{∗}. In the photon-66 proton centre-of-mass frame the pseudorapidity is defined as η^{∗} = ln(tan(θ^{∗}/2)), where θ^{∗} 67 is the polar angle of the track with respect to the virtual photon direction, i.e. the positive z^{∗} 68 direction. All hadronic final state particles with η^{∗} > 0 belong to the current hemisphere, and 69 all particles with η^{∗} < 0 are assigned to the target or proton remnant hemisphere.

70 The transverse momenta of charged particles are studied in the pseudorapidity region 0 < 71 η^{∗} < 3.5 which is divided into seven equal intervals. This division in η^{∗}-intervals is made 72 in order to investigate how the charged particle p_{T}^{∗} -spectrum changes with η^{∗} going form the 73 photon direction to the central fragmentation region.The target region, η^{∗} < 0, is not accessible 74 in this analysis. The transverse momenta of charged particles is measured for p_{T}^{∗} > 150 MeV 75 in order to minimize the influence of the boost to virtual photon-proton centre-of-mass frame.

76 2.4 Cross Section Definition

77 The double differential cross section is defined at Born level by the following equation

\frac{d^{2}σ}{dp_{T}^{∗2}dη^{∗}} = \frac{N_{sig}}{L · 2p_{T}^{∗} · Δp_{T}^{∗} · Δη^{∗} · A · ε_{1} … ε_{n}} · RC  (1)

78 where L is the luminosity, Δη^{∗} and Δp_{T}^{∗2} = 2·p_{T}^{∗} ·Δp_{T}^{∗} are the bin widths, ε_{i} is the efficiency of 79 a given cut i, A - the acceptance correction measured at the reconstructed level in the radiative 80 Monte Carlo (with the initial and final state radiation turned on) to the cross section at the 81 generator level:

A = \frac{N_{rec}^{rad}}{N_{gen}^{rad}} ,  (2)

82 and RC is a radiative correction factor extracted using the ratio of the MC calculated cross 83 section excluding initial and final state radiation to that with radiation included:

RC = \frac{σ_{gen}^{norad}}{σ_{gen}^{rad}} .  (3)

84 The bin-center correction is also performed assuming the points to lie in the geometrical 85 centers of p_{T} ∗ bins. The DJANGOH MC was used to correct the data.

86 3 Results and Discussions

87 The measured cross section dσ/dη^{∗} for charged particles with p_{T}^{∗} > 0 GeV is shown in figure 1 88 together with the predictions DJANGOH and RAPGAP normalised to the data. The shape of 89 the pseudorapidity distribution is described by Monte Carlo rather well. 90 The double differential cross sections d^{2}σ/dp_{T}^{∗2}dη^{∗} for charged particles are shown in fig-91 ure 2 together with the absolute predictions from DJANGOH and RAPGAP. The ratio MC over 92 data is shown in figure 3 applying the same normalisation factors to the models predictions as 93 used in figure 1 independently of η^{∗}. Although these models provide a rather good description 94 of the cross section in η^{∗} (figure 1) they fail to describe the shape of the transverse momentum 95 spectra of the charged particles (figure 3). 96 To study the hadroproduction dynamics we use the approximation which has been proposed 97 recently [1]. This approach suggests that the shape of the particle production p_{T}^{∗} spectrum 98 can be described by the sum of an exponential (Boltzmann-like) and a power-law statistical 99 distributions:

\frac{dσ}{p_{T}^{∗} dp_{T}^{∗}} = A_{e} exp (−E_{T kin}/T_{e}) + \frac{A}{(1 + \frac{p_{T}^{∗2}}{T^{2} · N})^{N}} ,  (4)

100 where E_{T kin} = \sqrt{p_{T}^{∗2} + M^{2}} − M with M equal to the produced hadron mass. A_{e}, A, T_{e}, T, N 101 are free parameters to be determined by fit to the data. For charged hadron spectra a hadron 102 mass is assumed to be equal to the pion mass. Detailed arguments for this particular choice are 103 given in [1] and a phenomenological explanation of the formula (4) has been recently given in 104 [4]. The parameterisation in equation (4) provides a much better description of the data than the 105 one traditionally used [5]. 106 The double differential cross sections d^{2}σ/dp_{T}^{∗2}dη^{∗} are shown for seven η^{∗} bins in figure 4 107 together with the fit (4). 108 The relative contribution of the exponential and power-law terms of the approximation (4) 109 can be characterised by ratio R of the power-law term alone to the parameterisation function 110 integrated over p_{T}^{2} . The power-law term can be calculated in the following way:

∫_{0}^{∞} \frac{A}{(1 + \frac{p_{T}^{∗2}}{T^{2}N})^{N}} dp_{T}^{∗2} = \frac{ANT^{2}}{N − 1} .

111 The exponential:

A_{e} ∫_{0}^{∞} e^{− \frac{E_{T kin}}{T_{e}}} dp_{T}^{∗2} = A_{e} ∫_{0}^{∞} e\frac{m − \sqrt{p_{T}^{∗2} + m^{2}}}{T_{e}} dp_{T}^{∗2}

z = \sqrt{p_{T}^{∗2} + m^{2}} − m

dz = \frac{dp_{T}^{∗2}}{\sqrt{p_{T}^{∗2} + m^{2}}} = \frac{dp_{T}^{∗2}}{m + z}

(m + z)dz = dp_{T}^{∗2}

A_{e} ∫_{0}^{∞} e\frac{m − \sqrt{p_{T}^{∗2} + m^{2}}}{T_{e}} dp_{T}^{∗2} = A_{e} ∫_{0}^{∞} e^{− \frac{z}{T_{e}}} 2(m + z)dz = A_{e}(2mT_{e} + 2T_{e}^{2}).

112 Therefore, the relative contribution R can be expressed by the formula:

R = \frac{AnT^{2}}{AnT^{2} + A_{e}(2MT_{e} + 2T_{e}^{2})(n − 1)}.  (5)

113 In figure 5 the parameters of the fit function and the relative contribution R of the power-law 114 type distribution to the charged particle production spectra (equation (5)) are shown as function 115 of the charged particle rapidity (η^{∗}). Close to the virtual photon direction (large values of η^{∗}) 116 the p_{T}^{∗} spectrum can be described by a power-law term only, while at central rapidities the 117 data require a significant exponential (Boltzmann-like) contribution. Moreover, the smaller η^{∗} 118 the larger the exponential statistical contribution is required to describe the inclusive charged 119 particle spectrum. Note, that in the pp interaction at about the same collision energy as here for 120 γ^{∗}p at HERA the data require only about 30% of the power-law type contribution to the charged 121 particle spectrum measured at central rapidities, while the residual 70% of the particle spectrum 122 is described by the exponential contribution [1]. Thus, we observe that the particle production 123 regime changes when particle rapidity values approach the proton hemisphere in the rapidity 124 space of DIS events.

125 4 Conclusion

126 The first measurement of charged particle production spectra in ep collisions at reduced pro-127 ton beam energy E_{p} = 460 GeV with the H1 detector in the virtual photon-proton centre-of-128 mass frame was performed. The kinematic range of the analysis covers low photon virtualities, 129 5 < Q^{2} < 10 GeV^{2}, and from medium to high values of inelasticit, y 0.35 < y < 0.8. The 130 double differential charged particle production cross sections d^{2}σ/dp_{T}^{∗2}dη^{∗} are measured in the 131 pseudorapidity region 0 < η^{∗} < 3.5 in seven equal bins. The measured transverse momentum 132 distributions show different shape, depending on the η^{∗} value. The Monte Carlo models RAP-133 GAP and DJANGOH describe the shape of the cross section in η^{∗} but both fail to describe shape 134 of the cross section d^{2}σ/dp_{T}^{∗2}dη^{∗}.

135 In order to investigate the change in hadroproduction dynamics with η^{∗} the data are ap-136 proximated by the recently introduced approach (4). This parameterisation provides a much 137 better description of the experimental data than those traditionally used. Moreover, the ob-138 served change in the particle production regime when particle rapidity values approach the 139 proton hemisphere in the rapidity space of DIS events, is rather well explained by the newly 140 introduced qualitative model [4].

141 References

142 [1] A. A. Bylinkin and A. A. Rostovtsev, “Parametrization of the shape of hadron-production 143 spectra in high-energy particle interactions,” Phys. Atom. Nucl. 75 (2012) 999 [Yad. Fiz. 144 75 (2012) 1060].

145 [2] C. Adloff et al. [ H1 Collaboration], ”Measurement of Charged Particle Transverse Mo-146 mentum Spectra in Deep Inelastic Scattering”, Nucl. Phys. B 485 (1996)3 ; 147 C. Alexa et al. [ H1 Collaboration], “Measurement of Charged Particle Spectra in Deep-148 Inelastic ep Scattering at HERA”, submitted to Eur. Phys. J. C, [arxiv:1302.1321].

149 [3] F. D. Aaron et al. [ H1 Collaboration], “Measurement of the Inclusive e±p Scattering 150 Cross Section at High Inelasticity y and of the Structure Function F_{L},” Eur. Phys. J. C 71 151 (2011) 1579 [arXiv:1012.4355].

152 [4] A. A. Bylinkin and A. A. Rostovtsev, “A photon-proton mariage,” arXiv:1209.0958 [hep-153 ph].

154 [5] R. Hagedorn, Riv. Nuovo Cim. 6 (1983) 1.

Figure 1: The measured differential ep cross section dσ/dη^{∗} for inclusive production of charged particles. Particles with a p_{T}^{∗} > 0 GeV are considered. The lines represent the normalized prediction of DJANGOH and RAPGAP respectively.

Figure 2: The measured charged particle double differential cross section d^{2}σ/dp_{T}^{2} dη for seven η∗ intervals together with DJANGOH and RAPGAP predictions.

Figure 3: The ratios of normalised MC over data using the same as used in figure 1 for seven η∗ intervals.

Figure 4: Double differential charged particle cross section d^{2}σ/dp_{T}^{2} dη for seven η∗ intervals together results from the fits of the function (4): the red line shows the exponential term and the blue one - the power law. Bin-center correction is performed.

Figure 5: Contribution R of the power law term and fitted parameters of (4) as function of pseudorapidity (η∗). The data points used for the fits included uncorrelated systematics.