1 H1prelim-13-033 Submitted to

2

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

7 K_{s}^{0} Production at Low Q^{2} 8 in Deep-Inelastic ep Scattering at HERA

9 H1 Collaboration

Abstract

10

11 The production of K_{s}^{0} mesons is studied using deep-inelastic events measured with 12 the H1 detector at HERA. The measurements are made in the phase space defined by the 13 negative four-momentum transferred squared of the photon, 7 < Q^{2} < 100 GeV^{2}, and the 14 inelasticity 0.1 < y < 0.6. Differential K_{s}^{0} production cross sections and ratios of K_{s}^{0} 15 production to charged hadron production are measured. Predictions of leading order Monte 16 Carlo programs are compared to data.

18 1 Introduction

19 The measurement of strange particle production in high energy collisions provides valuable 20 information for understanding Quantum Chromodynamics (QCD) in the perturbative and non-21 perturbative regime. The production of K_{s}^{0}, Λ^{1} has been studied at different colliders with 22 complementary characteristics; in e^{+}e^{−} annihilation at LEP [1–4], in pp̄ collisions at Tevatron 23 [6], in pp interactions at RHIC [7], in ep scattering at HERA [8–13] and at the LHC [14–18].

24 In neutral current deep-inelastic ep scattering (DIS) at HERA the four different processes depicted in figure 1 contribute to strange hadron production. Strange quarks may be created

(a)  (b)  (c)  (d)

Figure 1: Schematic diagrams for the processes contributing to strangeness production in ep scattering: (a) direct production from the strange sea, (b) BGF, (c) heavy hadron decays and (d) fragmentation. The diagrams relevant for K^{0} production are shown.

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26 in the hard sub-process of the ep scattering by originating directly from the strange sea of the 27 proton in a quark-parton-model (QPM) like interaction (figure 1a), from boson-gluon-fusion 28 (BGF, figure 1b) or from the decays of heavy flavoured hadrons (figure 1c). In these production 29 mechanisms hard scales are involved allowing for the applicability of perturbative QCD to be 30 tested. The dominant source for strange hadron production, however, is the creation of an 31 s\overline{s} pairs in the non-perturbative fragmentation process (figure 1d). While strange mesons are 32 created by all four processes strange baryon production receives only little contributions from 33 the decays of heavy flavoured hadrons.

34 Since s quarks are heavy compared to u and d quarks the formation rate of s\overline{s} pairs in the 35 fragmentation process is expected to be smaller than for u\overline{u} or d\overline{d} pairs. Therefore the produc-36 tion of strange hadrons is expected to be suppressed relative to non-strange hadrons. In the mod-37 elling of the fragmentation process this suppression is generally controlled by the strangeness 38 suppression factor λ_{s}. Especially, the ratio of K_{s}^{0} to charged particles should strongly depend 39 on this quark mass effect.

40 This paper presents a measurement of K_{s}^{0} production in DIS in the range of negative four 41 momentum transfer squared, 7 < Q^{2} < 100 GeV^{2} and of lepton inelasticity 0.1 < y < 0.6. 42 The results are based on a data sample corresponding to an integrated luminosity of 109 pb^{−1} 43 collected with the H1 detector at HERA at a centre-of-mass energy of 319 GeV in the years 2006 44 and 2007. The analysis is performed in a similar kinematic range than covered in previous H1 45 publications [9, 10, 13]. Results are presented for differential cross sections of K_{s}^{0} production 46 and the ratios of K_{s}^{0} production to charged particles production measured in the same phase 47 space regions. The measurements are shown as a function of various observables characterising 48 the DIS kinematics and the strange particles production dynamics in the laboratory frame. The 49 results are compared with predictions obtained from leading order Monte Carlo calculations, 50 based on matrix elements with parton shower simulation. The rôle of the parton evolution, the 51 strangeness suppression on K_{s}^{0} mesons is investigated.

1If not stated differently the charge conjugate state is always implied.

52 2 Monte Carlo Simulation

53 Deep-inelastic ep scattering is modelled using the DJANGH [20] and the RAPGAP [21] pro-54 grams, which generate hard partonic processes at the Born level at leading order in α_{s} (e.g. 55 γ ∗ q → q, γ ∗ q → qg γ ∗ g → q\overline{q}), convoluted with the parton density function (PDF) of the 56 proton. The PDF set CTEQ6L [22] is chosen for this analysis. The factorisation and renormal-57 isation scales a set to μ_{f}^{2} = μ_{r}^{2} = Q^{2}. Two different approaches are used for the simulation of 58 higher order QCD effects: in RAPGAP the parton shower approach (MEPS) is implemented in 59 which the parton emission is ordered in transverse momentum (k_{T}) according to the leading-60 log approximation; and in DJANGOH the colour dipol approach (CDM [23]) available within 61 ARIADNE [24] is adopted in which partons are created by colour dipole radiation between the 62 partons in the cascade, resulting in a k_{T} un-ordered parton emission.

63 The JETSET program [25] is used for simulating the hadronisation process in the Lund 64 colour string fragmentation model [26]. The suppression of strange quarks is predominantly 65 controlled by a single parameter, λ_{s} = P_{s}/P_{q}, where P_{s} and P_{q} are the probabilities for 66 creating strange (s) or light (q = u or d) quarks in the non-perturbative fragmentation pro-67 cess. The most relevant parameters for describing the baryon production are the di-quark sup-68 pression factor λ_{qq} = P_{qq}/P_{q}; i.e., the probability of producing a light di-quark pair qq\overline{q}\overline{q} 69 from the vacuum with respect to a light q\overline{q} pair, and the strange diquark suppression factor 70 λ_{sq} = (P_{sq}/P_{qq})/(P_{s}/P_{q}), which models the relative production of strange di-quark pairs. The 71 values tuned to hadron production measurements in e^{+}e^{−}-annihilation by the ALEPH collabo-72 ration [5] (λ_{s} = 0.286, λ_{qq} = 0.108, and λ_{sq} = 0.690) are taken herein as default values for the 73 simulation of hadronisation within JETSET.

74 Monte Carlo event samples generated both with DJANGOH and RAPGAP are used for the 75 acceptance and efficiency correction of the data. All generated events are passed through the full 76 GEANT [27] based simulation of the H1 apparatus and are reconstructed and analysed using 77 the same programs as for the data.

78 3 Experimental Procedure

79 3.1 The H1 Detector

80 A detailed description of the H1 detector can be found in [28]. In the following, only those 81 detector components important for the present analysis are described. H1 uses a right handed 82 Cartesian coordinate system with the origin at the nominal ep interaction point. The proton 83 beam direction defines the positive z-axis of the laboratory frame and transverse momenta are 84 measured in the (x, y) plane. The polar angle θ is measured with respect to this axis and the 85 pseudorapidity η is given by η = − ln tan \frac{θ}{2}.

86 Charged particles are measured in the Central Tracking Detector (CTD) in the range −1.75 < 87 η < 1.75. The CTD comprises two cylindrical Central Jet Chambers (inner CJC1 and outer 88 CJC2), arranged concentrically around the beam-line, complemented by a silicon vertex detec-89 tor (CST) [29]. The CJCs are separated by a drift chamber which improves the z coordinate 90 reconstruction. A multi-wire proportional chamber mainly used for triggering [30] is situated 91 inside the CJC1. These detectors are arranged concentrically around the interaction region in a 92 solenoidal magnetic field of strength 1.16 T. The trajectories of charged particles are measured 93 with a transverse momentum resolution of σ(p_{T})/p_{T} ≃ 0.2% p_{T} / GeV ⊕ 0.015. In each event 94 the tracks are used in a common fit procedure to determine the ep interaction vertex. The mea-95 surement of the specific energy loss dE/dx of charged particles in this detector is known with a 96 resolution of 6.3% for a minimum ionising track [31].

97 The tracking detectors are surrounded by a Liquid Argon calorimeter (LAr) which measures 98 the positions and energies of particles, including that of the scattered positron, over the polar 99 angle range 4^{∘} < θ < 154^{∘}. The calorimeter consists of an electromagnetic section with lead 100 absorbers and a hadronic section with steel absorbers. The energy resolution for electrons in the 101 electromagnetic section, as measured in beam tests, is σ(E)/E = 11.5%/\sqrt{E} [ GeV] ⊕1% [32]. 102 In the backward region (153^{∘} < θ < 178^{∘}), particle energies are measured by a lead-scintillating 103 fibre calorimeter (SpaCal) [33]

104 The DIS events studied in this paper are triggered by a compact energy deposition in the 105 electromagnetic section of the SpaCal calorimeter. chambers.

106 The luminosity is determined from the rate of the elastic QED Compton process ep → eγp, 107 with the electron detected in the SpaCal calorimeter, and the rate of DIS events measured in the 108 SpaCal calorimeter [34].

109 3.2 Selection of DIS Events

110 The data used in this analysis correspond to an integrated luminosity of 109 pb^{−1} and were 111 taken by H1 in the years 2006 and 2007 when protons with an energy of 920 GeV collided with 112 electrons^{2} with an energy of 27.6 GeV producing a centre-of-mass energy of \sqrt{s} = 319 GeV.

113 The selection of DIS events is based on the identification of the scattered electron as a 114 compact calorimetric deposit in the electromagnetic section of the SpaCal calorimeter in the 115 polar angular range 153^{∘} < θ_{e} < 173^{∘}, with energy greater than 11 GeV.

116 At fixed centre-of-mass energies \sqrt{s} the kinematics of the scattering process are described 117 using the Lorentz invariant variables Q^{2}, y and x. These variables can be expressed as a function 118 of the scattered electron energy E′_{e} and its scattering angle θ_{e} in the laboratory frame:

2The this paper ”electron” is used to denote both electrons and positrons

Q^{2} = 4E_{e}E′_{e} cos^{2} (\frac{θ_{e}}{2} ) , y = 1 − \frac{E′_{e}}{E_{e}} sin^{2} (\frac{θ_{e}}{2} ) , x = \frac{Q^{2}}{ys} .  (1)

119 The negative four-momentum transfer squared Q^{2} and the inelasticity y are required to lie in 120 the ranges 7 < Q^{2} < 100 GeV^{2} and 0.1 < y < 0.6. Background from photo-production events 121 (Q^{2} ≈ 0 GeV^{2}) in which the electron escapes undetected down the beam pipe and a hadron 122 fakes the electron signature, is suppressed by the requirement that the difference Σ(E − p_{z}) 123 between the total energy and the longitudinal momentum must be in the range 35 < Σ(E − 124 p_{z}) < 70 GeV, where the sum includes all measured hadronic final state particles [35] and 125 the scattered electron candidate. The z-coordinate of the event vertex, reconstructed using the 126 tracking detectors, has to be within ±35 cm of the mean position for ep interactions.

127 Primary-vertex-fitted charged-particles are selected requiring that the candidates have a min-128 imal radial length of 10 cm and the radial distance from the innermost hit associated with the 129 track to the beam line has to be less than 30 cm. All selected particles have to be in the kine-130 matic region defined by a transverse momentum greater than 500 MeV and the absolute value

of their pseudorapidity less than 1.3.

131

3.3 Selection of K_{s}^{0} Mesons

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The K_{s}^{0} mesons are measured by the kinematic reconstruction of its decay K_{s}^{0} → π^{+}π^{−}. The

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analysis is based on charged particles measured by the CTD with a minimum transverse mo-

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mentum p_{T} ≥ 0.12 GeV. The K_{s}^{0} mesons are identified by fitting pairs of oppositely charged

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tracks in the (x, y) plane to their secondary decay vertices, with the direction of flight of the

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mother particle constrained to the primary event vertex. Candidates are required to have a mini-

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mum radial decay length of 2 cm, a minimum transverse momentum p_{T} of more than 500 MeV

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and to lie in the pseudorapidity range |η| < 1.3. The phase space of the analysis is summarised

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in table 1. The contamination from Λ decays is suppressed by rejecting candidates having an

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invariant mass M(πp) > 1.125 GeV where the proton hypothesis is assigned to the secondary

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particle with the larger transverse momentum. The contamination from gamma conversions is

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suppressed by requiring that the invariant mass, computed under the assumption that the tracks

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correspond to an electron–positron pair, is bigger than 50 MeV.

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DIS kinematics 7 < Q^{2} < 100 GeV^{2} 0.1 < y < 0.6 Hadron kinematics 0.5 < p_{T} < 3.5 GeV −1.3 < η < 1.3

Table 1: Analysis phase space

The number of K_{s}^{0} mesons is obtained by fitting the invariant mass spectra with the sum of

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a signal and background function. For the signal function the t-student function is used while

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the background distribution is parameterised as

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B_{K_{s}^{0}}(M) = p_{0} (M − 2m_{T})^{p_{1}}e^{p_{2}M+p_{3}M^{2}+p_{4}M^{3}},  (2)

(3)

148 Here, M denotes the π^{+}π^{−} invariant mass, and m_{T} corresponds to the the minimum transverse

mass defined as m_{T} = \sqrt{m_{π}^{2} + (p_{T,min}^{rel})^{2}}. For the differential distribution the fit is performed

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150 in each kinematic bin.

151 The invariant mass spectrum M(π^{+}π^{−}) of all candidates passing the selection criteria are 152 shown in figure 2 together with the result from the fits. In total approximately 290000 K_{s}^{0} 153 mesons are reconstructed in the phase space given in table 1. The fitted K_{s}^{0} mass agrees with 154 the world average [36].

155 4 Cross Sections Determination and Systematic Errors

The total inclusive Born-level cross section σ_{vis} in the kinematic region defined in table 1 is given by the following expression:

σ_{vis}(ep → eK_{s}^{0}X) = \frac{N}{L · ϵ · BR · (1 + δ_{rad})}  ,  (4)

156 where N represents the observed number of K_{s}^{0} mesons and L and ϵ denote the integrated 157 luminosity and the efficiency, respectively. The branching ratios BR(K_{s}^{0} → π^{+}π^{−}) is taken 158 from [36]. The radiative corrections (1 + δ_{rad}) needed to correct the measured cross section to 159 the Born level are calculated using the program HERACLES [37]. The number of K_{s}^{0} mesons is 160 determined by fitting the mass distribution as explained in section 3.3. In the case of differential 161 distributions the same formula is applied for each analysis bin.

162 The efficiency ϵ is given by ϵ = ϵ_{rec}·ϵ_{trig}, where ϵ_{rec} is the reconstruction efficiency and ϵ_{trig} 163 is the trigger efficiency. The reconstruction efficiency includes the geometric acceptance and 164 the efficiency for track and secondary vertex reconstruction. It is estimated using CDM Monte 165 Carlo event samples. The trigger efficiency is extracted from the data using monitor triggers 166 and is above 99%.

167 The systematic uncertainties were studied by changing in the Monte Carlo the value of the 168 variables presented below, repeating the analysis procedure and comparing the results to the 169 standard analysis. For the cross section the total uncertainty was calculated adding the different 170 contributions in quadrature, while for the ratios the uncertainties on the energy scale and angle 171 resolution of the scattered electron, as well as on the luminosity, cancel; the other sources are 172 assumed uncorrelated and added in quadrature. For differential distributions the systematic 173 uncertailies are determined in each analysis bin separately. The following sources of systematic 174 uncertainties were considered:

175 • the uncertainty on the energy scale of the SpaCal calorimeter for scattered electrons,

176 • the uncertainty of the measurement of the polar angle of the scattered electron,

177 • the uncertainty on the trigger efficiency,

178 • the uncertainty on the reconstruction efficiency,

179 • the uncertainty in the signal extraction due to the two different decay topologies,

180 • the uncertainty on the extraction of the signal,

181 • The uncertainty in the correction factor arising from using different Monte Carlo models 182 in the correction procedure, taken as half of the difference between the correction factors 183 obtained with RAPGAP and DJANGO, respectively,

184 • the uncertainty on the branching ratio (0.5% [36]) and

185 • the uncertainty in the luminosity measurement.

186 5 Results and Discussion

187 5.1 Inclusive Cross Sections

188 The visible inclusive production cross sections σ_{vis} are measured in the kinematic region defined 189 by 7 < Q^{2} < 100 GeV^{2} and 0.1 < y < 0.6 for the event kinematics; and for the kinematics of 190 the neutral strange hadrons, p_{T} (K_{s}^{0}, Λ) > 500 MeV, |η(K_{s}^{0}, Λ)| < 1.3. A cross sections of:

σ_{vis}(ep → eK_{s}^{0}X) = 10.66 ± 0.02(stat.)_{−0.53}^{+0.50}(syst.) nb  (5)

191 is obtained. Using a strangeness suppression factor of λ_{s} = 0.286 the models RAPGAP and 192 DJANGOH predict cross sections of 10.93 nb and 9.88 nb, respectively, in reasonable agreement 193 with the measurement.

194 5.2 Differential cross sections

195 Differential K_{s}^{0} cross sections are shown in figure 3 as a function the photon virtuality, Q^{2}, and 196 as a function of the K_{s}^{0} kinematic variables in the laboratory frame, p_{T} and η along with the 197 predictions of RAPGAP and DJANGOH for a λ_{s} values of 0.286. The cross sections fall rapidly 198 as Q^{2} and p_{T} grow. The figure also includes the ratios of predicted to measured cross sections 199 for a better shape comparison. Apart from small normalisation differences the models describe 200 the shapes of the measured cross sections as a function of Q^{2} and η but predict a significantly 201 softer spectrum in p_{T} than observed in data.

202 5.3 Ratio of K_{s}^{0} Production to Charged Particle Production

203 By normalising the K_{s}^{0} production cross section to the cross section of charged particle produc-204 tion many model dependent uncertainties, like the cross section dependence on proton PDFs, 205 cancel thus enhancing the sensitivity to details of the fragmentation process. In Figure ?? the 206 ratio of K_{s}^{0} production to the cross section charged particle procduction is shown as a function 207 of η, and p_{T} in comparison to the expectations from DJANGOH using three different values of 208 λ_{s} ranging from 0.220 to 0.35. The ration in η is well described by the model in shape and a 209 high sensitivity on λ_{s} is observed in the absolute value of this ratio. However, the shape in p_{T} is 210 not described. A better understanding of the concurrent processes of K_{s}^{0} production is needed 211 prior to the extraction of the strangeness suppression factor λ_{s}.

212 6 Conclusions

213 This paper presents a study of inclusive K_{s}^{0} production in DIS at low Q^{2} measured with the 214 H1 detector at HERA. The kinematic range of the analysis covers the phase space region 7 < 215 Q^{2} < 100 GeV^{2}, and 0.1 < y < 0.6. The K_{s}^{0} production cross section are measured as a 216 function of the DIS kinematic variable Q^{2} and of K_{s}^{0} production variables in the laboratory. In 217 addition results on the ratio of K_{s}^{0} production cross section to the charged particle cross section 218 are presented.

219 The measurements are compared to model predictions of DJANGOH, based on the colour-220 dipol model (CDM)and RAPGAP based on DGLAP matrix element calculations supplemented 221 parton showers (MEPS). Within the uncertainties both models provide a reasonable description 222 of the data except for the differential cross section in p_{T}, where the models predict significantly 223 softer spectra than measured. The sensitivity of the ration of K_{s}^{0} to charged particle production 224 cross sections on the strangeness suppression factor λ_{s} is demonstrated, however, a better under-225 standing of the concurrent processes of K_{s}^{0} production is mandatory prior to the determination 226 of λ_{s}.

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Figure 2: Mass distributions for K_{s}^{0} candidates. 11

(a)  (c)  (b)

Figure 3: Differential K_{s}^{0} production cross sections as a function of (a) the photon virtuality squared Q^{2}, (b) the transverse momentum, p_{T}, of the Λ baryon and (c) its pseudorapidity η in comparison to RAPGAP (MEPS) and DJANGOH (CDM). The inner (outer) error bars show the statistical (total) errors. The ratios “MC/Data” are shown for the different Monte Carlo predictions. For comparison, the data points are put to one.

(a)  (b)

Figure 4: Ratio of K_{s}^{0} to charged particle production as a function of (a) η and (b) p_{T}, in comparison to DJANGOH (CDM) for three different vaues of λ_{s}. The inner (outer) error bars show the statistical (total) errors. The ratios “MC/Data” are shown for the different Monte Carlo predictions. For the ratios the data points are put at one for comparison.