1 H1prelim-13-031 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 Production of Λ Baryons at high Q^{2} at HERA

8 H1 Collaboration

Abstract

9

10 The production of Λ baryons is studied using deep-inelastic events measured with the 11 H1 detector at HERA. The measurements are made in the phase space defined by the neg-12 ative four-momentum transferred squared of the photon, 145 < Q^{2} < 20000 GeV^{2}, and 13 the inelasticity 0.2 < y < 0.6. Differential Λ(Λ̄) production cross sections are measured. 14 Differential Λ + Λ̄ yields per event are determined. The Λ − Λ̄ asymmetry is measured and 15 found to be consistent with zero. Predictions of leading order Monte Carlo programs are 16 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(Λ̄) 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.

25

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. The 30 dominant source for strange hadron production, however, is the creation of an s\overline{s} pairs in the 31 non-perturbative fragmentation process (figure 1d). While strange mesons are created by all 32 four processes strange baryon production receives only little contributions from the decays of 33 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 Apart from the differences in K_{s}^{0} and Λ production observed in decays of charm and beauty 41 hadrons the production rate of strange baryons is expected to be small relative to strange mesons 42 as a consequence of the fragmentation process. Even if the s quark is directly produced in the 43 hard sub-process, i.e. by the QPM or BGF process, the creation of a strange baryon is expected 44 to be suppressed because a di-quark system from the vacuum is needed to form the baryon.

45 In ep scattering the initial state has a baryon quantum number of B = 1. The study of baryon 46 production may therefore provide information about the process of baryon number transfer. In 47 particular, data on the Λ − Λ̄ production asymmetry may help understanding this mechanism.

48 This paper presents a measurement of Λ and Λ̄ production in DIS at high values of the 49 negative four momentum transferred squared, 145 < Q^{2} < 20000 GeV^{2}, in the range of lepton 50 inelasticity 0.2 < y < 0.6. The results are based on a data sample corresponding to an integrated 51 luminosity of 340 pb^{−1} collected with the H1 detector at HERA at a centre-of-mass energy of 52 319 GeV in the years 2004 to 2007. The analysis is performed in a different kinematic range 53 than covered in previous H1 publications [9,10,13]. Results are presented for differential cross 54 sections of Λ, then Λ yields normalized to DIS, and the Λ– Λ̄ asymmetry. The measurements are 55 shown as a function of various observables characterising the DIS kinematics and the strange 56 particles production dynamics, both in the laboratory frame and in the Breit frame [19]. The 57 results are compared with predictions obtained from leading order Monte Carlo calculations, 58 based on matrix elements with parton shower simulation. The rôle of the parton evolution and 59 the strangeness suppression on Λ production is investigated.

60 2 Monte Carlo Simulation

61 Deep-inelastic ep scattering is modelled using the DJANGH [20] and the RAPGAP [21] pro-62 grams, which generate hard partonic processes at the Born level at leading order in α_{s} (e.g. 63 γ ∗ q → q, γ ∗ q → qg γ ∗ g → q\overline{q}), convoluted with the parton density function (PDF) of the 64 proton. The PDF set CTEQ6L [22] is chosen for this analysis. The factorisation and renormal-65 isation scales a set to μ_{f}^{2} = μ_{r}^{2} = Q^{2}. Two different approaches are used for the simulation of 66 higher order QCD effects: in RAPGAP the parton shower approach (MEPS) is implemented in 67 which the parton emission is ordered in transverse momentum (k_{T}) according to the leading-68 log approximation; and in DJANGOH the colour dipol approach (CDM [23]) available within 69 ARIADNE [24] is adopted in which partons are created by colour dipole radiation between the 70 partons in the cascade, resulting in a k_{T} un-ordered parton emission.

71 The JETSET program [25] is used for simulating the hadronisation process in the Lund 72 colour string fragmentation model [26]. The suppression of strange quarks is predominantly 73 controlled by a single parameter, λ_{s} = P_{s}/P_{q}, where P_{s} and P_{q} are the probabilities for 74 creating strange (s) or light (q = u or d) quarks in the non-perturbative fragmentation pro-75 cess. The most relevant parameters for describing the baryon production are the di-quark sup-76 pression factor λ_{qq} = P_{qq}/P_{q}; i.e., the probability of producing a light di-quark pair qq\overline{q}\overline{q} 77 from the vacuum with respect to a light q\overline{q} pair, and the strange diquark suppression factor 78 λ_{sq} = (P_{sq}/P_{qq})/(P_{s}/P_{q}), which models the relative production of strange di-quark pairs. The 79 values tuned to hadron production measurements in e^{+}e^{−}-annihilation by the ALEPH collabo-80 ration [5] (λ_{s} = 0.286, λ_{qq} = 0.108, and λ_{sq} = 0.690) are taken herein as default values for the 81 simulation of hadronisation within JETSET.

82 Monte Carlo event samples generated both with DJANGOH and RAPGAP are used for the 83 acceptance and efficiency correction of the data. All generated events are passed through the full 84 GEANT [27] based simulation of the H1 apparatus and are reconstructed and analysed using 85 the same programs as for the data.

86 3 Experimental Procedure

87 3.1 The H1 Detector

88 A detailed description of the H1 detector can be found in [28]. In the following, only those 89 detector components important for the present analysis are described. H1 uses a right handed 90 Cartesian coordinate system with the origin at the nominal ep interaction point. The proton 91 beam direction defines the positive z-axis of the laboratory frame and transverse momenta are 92 measured in the (x, y) plane. The polar angle θ is measured with respect to this axis and the 93 pseudorapidity η is given by η = − ln tan \frac{θ}{2}.

94 Charged particles are measured in the Central Tracking Detector (CTD) in the range −1.75 < 95 η < 1.75. The CTD comprises two cylindrical Central Jet Chambers (inner CJC1 and outer 96 CJC2), arranged concentrically around the beam-line, complemented by a silicon vertex detec-97 tor (CST) [29]. The CJCs are separated by a drift chamber which improves the z coordinate 98 reconstruction. A multi-wire proportional chamber mainly used for triggering [30] is situated 99 inside the CJC1. These detectors are arranged concentrically around the interaction region in a 100 solenoidal magnetic field of strength 1.16 T. The trajectories of charged particles are measured 101 with a transverse momentum resolution of σ(p_{T})/p_{T} ≃ 0.2% p_{T} / GeV ⊕ 0.015. In each event 102 the tracks are used in a common fit procedure to determine the ep interaction vertex. The mea-103 surement of the specific energy loss dE/dx of charged particles in this detector is known with a 104 resolution of 6.3% for a minimum ionising track [31].

105 The tracking detectors are surrounded by a Liquid Argon calorimeter (LAr) which measures 106 the positions and energies of particles, including that of the scattered positron, over the polar 107 angle range 4^{∘} < θ < 154^{∘}. The calorimeter consists of an electromagnetic section with lead 108 absorbers and a hadronic section with steel absorbers. The energy resolution for electrons in the 109 electromagnetic section, as measured in beam tests, is σ(E)/E = 11.5%/\sqrt{E} [ GeV] ⊕1% [32]. 110 In the backward region (153^{∘} < θ < 178^{∘}), particle energies are measured by a lead-scintillating 111 fibre calorimeter (SpaCal) [33]

112 The DIS events studied in this paper are triggered by a compact energy deposition in the 113 electromagnetic section of the LAr calorimeter and a signal from the multi-wire proportional 114 chambers.

115 The luminosity is determined from the rate of the elastic QED Compton process ep → eγp, 116 with the electron detected in the SpaCal calorimeter, and the rate of DIS events measured in the 117 SpaCal calorimeter [34].

118 3.2 Selection of DIS Events

119 The data used in this analysis correspond to an integrated luminosity of 340 pb^{−1} and were taken 120 by H1 in the years from 2004 to 2007 when protons with an energy of 920 GeV collided with 121 electrons^{1} with an energy of 27.6 GeV producing a centre-of-mass energy of \sqrt{s} = 319 GeV.

1The this paper ”electron” is used to denote both electrons and positrons

DIS kinematics 145 < Q^{2} < 20000 GeV^{2} 0.2 < y < 0.6 Hadron kinematics p_{T} > 0.3 GeV −1.5 < η < 1.5

Table 1: Analysis phase space

122 The selection of DIS events is based on the identification of the scattered electron as a 123 compact calorimetric deposit in the electromagnetic section of the LAr calorimeter in the polar 124 angular range 10^{∘} < θ_{e} < 150^{∘}, with energy greater than 11 GeV and associated with a charged 125 track in the CTD.

126 At fixed centre-of-mass energies \sqrt{s} the kinematics of the scattering process are described 127 using the Lorentz invariant variables Q^{2}, y and x. These variables can be expressed as a function 128 of the scattered electron energy E′_{e} and its scattering angle θ_{e} in the laboratory frame:

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)

129 The negative four-momentum transfer squared Q^{2} and the inelasticity y are required to lie 130 in the ranges 145 < Q^{2} < 20000 GeV^{2} and 0.2 < y < 0.6. Background from photo-production 131 events (Q^{2} ≈ 0 GeV^{2}) in which the electron escapes undetected down the beam pipe and a 132 hadron fakes the electron signature, is suppressed by the requirement that the difference Σ(E − 133 p_{z}) between the total energy and the longitudinal momentum must be in the range 35 < Σ(E − 134 p_{z}) < 70 GeV, where the sum includes all measured hadronic final state particles [35] and 135 the scattered electron candidate. The z-coordinate of the event vertex, reconstructed using the 136 tracking detectors, has to be within ±35 cm of the mean position for ep interactions.

137 3.3 Selection of Λ Baryons

138 The Λ baryons^{2} are measured by the kinematic reconstruction of its decay Λ → pπ^{−}. The anal-139 ysis is based on charged particles measured by the CTD with a minimum transverse momentum 140 p_{T} ≥ 0.12 GeV. The Λ baryons are identified by fitting pairs of oppositely charged tracks in the 141 (x, y) plane to their secondary decay vertices, with the direction of flight of the mother particle 142 constrained to the primary event vertex. Candidates are required to have a minimum radial de-143 cay length of 2 cm, a minimum transverse momentum p_{T} of more than 300 MeV and to lie in 144 the pseudorapidity range |η| < 1.5. The phase space of the analysis is summarised in table 1.

145 For the reconstruction of Λ candidates the track with the higher momentum is assumed to be 146 the proton and the other track is assumed to be the pion. Furthermore, the observed energy loss, 147 dE/dx, of the proton candidates in Λ decays have to have a likelihood of being a proton of more 148 than 0.003. The distinction between Λ and Λ̄ baryon candidates is made by the electrical charge 149 of the decay proton (antiproton) candidate. The contamination from K_{s}^{0}decays in the Λsample 150 is suppressed by a rejection of the corresponding invariant mass region: 475 < M(ππ) < 151 530 MeV for the Λ selection. The contamination from gamma conversions is suppressed by 152 requiring that the invariant mass, computed under the assumption that the tracks correspond to 153 an electron–positron pair, is bigger than 50 MeV.

2Unless otherwise noted, charge conjugate states are always implied.

154 The number of Λ baryons is obtained by fitting the invariant mass spectra with the sum of 155 a signal and background function. For the signal fuction a skewed t-student function is used 156 while the background distributions are parameterised as

B_{Λ}(M) = p_{0} (p_{1} + p_{2}(M − m_{Λ}) + p_{3}(M − m_{Λ})^{2})(M − (m_{p} + m_{π}))^{p_{4}}.  (2)

157 Here, M denotes the pπ invariant mass, and m_{Λ}, m_{p} and m_{π} are the nominal masses of the 158 Λ, the proton and the pion [36]. For the differential distribution the fit is performed in each 159 kinematic bin.

160 The invariant mass spectrum M(pπ) of all candidates passing the selection criteria are 161 shown in figure 2 together with the result from the fits. In total approximately 7000 Λ(Λ̄) 162 baryons are reconstructed in the phase space given in table 1. The fitted Λ mass agrees with the 163 world average [36].

164 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 → eΛX) = \frac{N}{L · ϵ · BR · (1 + δ_{rad})}  ,  (3)

165 where N represents the observed number of Λ, baryons. L and ϵ denote the integrated luminos-166 ity and the efficiency, respectively. The branching ratios BR for Λ decays are taken from [36]. 167 The radiative corrections (1 + δ_{rad}) needed to correct the measured cross section to the Born 168 level are calculated using the program HERACLES [37]. The number of Λ(Λ̄) particles is de-169 termined by fitting the mass distribution as explained in section 3.3. In the case of differential 170 distributions the same formula is applied for each analysis bin.

171 The efficiency ϵ is given by ϵ = ϵ_{rec}·ϵ_{trig}, where ϵ_{rec} is the reconstruction efficiency and ϵ_{trig} 172 is the trigger efficiency. The reconstruction efficiency includes the geometric acceptance and 173 the efficiency for track and secondary vertex reconstruction. It is estimated using CDM Monte 174 Carlo event samples. The trigger efficiency is extracted from the data using monitor triggers 175 and is above 99%.

176 The systematic uncertainties were studied by changing in the Monte Carlo the value of the 177 variables presented below, repeating the analysis procedure and comparing the results to the 178 standard analysis. For the cross section the total uncertainty was calculated adding the different 179 contributions in quadrature, while for the ratios the uncertainties on the energy scale and angle 180 resolution of the scattered electron, as well as on the luminosity, cancel; the other sources are 181 assumed uncorrelated and added in quadrature. For differential distributions the systematic 182 uncertailies are determined in each analysis bin separately. The following sources of systematic 183 uncertainties were considered:

184 • the uncertainty on the energy scale of the LAr calorimeter for scattered electrons,

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

186 • the uncertainty on the trigger efficiency,

187 • the uncertainty on the reconstruction efficiency,

188 • the uncertainty due the dE/dx requirement on the proton candidate,

189 • the uncertainty in the signal extraction due to the two different topologies, 0.2%.

190 • the uncertainty on the extraction of the signal,

191 • The uncertainty in the correction factor arising from using different Monte Carlo models 192 in the correction procedure, taken as half of the dfference between correcting RAPGAP 193 or DJANGO,

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

195 • the uncertainty in the luminosity measurement.

196 5 Results and Discussion

197 5.1 Inclusive Cross Sections

198 The visible inclusive production cross sections σ_{vis} are measured in the kinematic region defined 199 by 145 < Q^{2} < 20000 GeV^{2} and 0.2 < y < 0.6 for the event kinematics; and for the kinematics 200 of the neutral strange hadrons, p_{T} (Λ(Λ̄)) > 300 MeV, |η(Λ(Λ̄))| < 1.5. The cross sections are 201 measured to be:

σ_{vis}(ep → e[Λ + Λ̄]X) = 144.7 ± 4.7(stat.)_{−8.5}^{+9.4}(syst.) pb,
σ_{vis}(ep → eΛX) = 72.6 ± 3.3(stat.)_{−4.5}^{+4.8}(syst.) pb,
σ_{vis}(ep → eΛ̄X) = 72.9 ± 4.0(stat.)_{−4.6}^{+4.9}(syst.) pb

202 The cross section predictions for Λ + Λ̄ production from the MEPS and CDM models are 203 shown in Table 2 for two values of the strangeness suppression parameter λ_{s} . The measured 204 inclusive Λ + Λ̄ cross section is close to the CDM prediction with λ_{s} = 0.22 and to the MEPS 205 prediction with λ_{s} = 0.286.

λ_{s} = 0.220 λ_{s} = 0.286
σ_{vis}(ep → e[Λ + Λ̄]X) CDM  136 pb  161 pb
σ_{vis}(ep → e[Λ + Λ̄]X) MEPS 120 pb  144 pb

Table 2: Monte Carlo predictions for different settings of the strangeness suppresion factor λ_{s}.

206 5.2 Differential cross sections

207 Differential Λ + Λ̄ cross sections are presented as a function of the kinematics of DIS and of 208 the strange particles, both in the laboratory and in the Breit frame of references. The results in 209 the Breit frame are presented separately for the current and target hemispheres.

210 The measurement of the differential cross section as a function of the kinematic variables 211 of DIS, Q^{2} and x, as well as the kinematic variables of the neutral strange hadrons in the 212 laboratory frame, p_{T} and η, are shown in Figure 3 along with the predictions of the MEPS and 213 CDM models for λ_{s} values of 0.220 and 0.286. The cross sections fall rapidly as Q^{2}, x and p_{T} 214 grow. The models follow the general behaviour of data, but some differences are seen.

215 In the Breit frame of reference the virtual space-like moment transferred in the interaction 216 has no energy. The direction of q_{μ}, where Q^{2} = −q_{μ}q^{μ}, defines the negative z-axis, with the 217 proton moving in the positive z direction. The transverse momentum in the Breit frame is 218 computed with respect to this axis. Particles with a positive z component of their momenta, 219 as expected from those particles produced close to the proton remnant, are assigned to the 220 target hemisphere; while those having negative z component of their momenta, as expected for 221 particles close to the direction of the struck quark in the naive quark-parton model, are assigned 222 to the current hemisphere. In the figures these hemispheres are denoted by BFT and BFC, 223 respectively.

224 It is expected that the production of particles in the current hemisphere resembles that of 225 e^{+}e^{−} collisions. In analogy with the fragmentation variable use in those cases, for ep collisions 226 it is customary to define x^{BF} = 2|p^{BF} |/Q where p^{BF} is the three momentum of the strange 227 particle in the Breit frame. The variables x^{BFT} and x^{BFC} are obvious generalisations to take 228 into account if the particle is assigned to the target or current hemisphere respectively.

229 The measured differential Λ + Λ̄ production cross sections in the Breit frame are shown in 230 Figure 4. The cross sections fall rapidly in all cases. They are bigger in the current than in the 231 target hemisphere, which is opposite to the behaviour observed at lower values of Q^{2} [13]. This 232 is expected due the kinematical effects at high Q^{2} which push the target region more forward 233 while the current region starts to fill the CJC.

234 5.3 Λ Production to DIS Cross Section Ratio

235 By normalising the particle production cross section to the DIS cross section many model de-236 pendent uncertainties, like the cross section dependence on proton PDFs, cancel thus enhancing 237 the sensitivity on details of the fragmentation process. In Figure 5 the ratio of Λ production to 238 DIS cross section is shown as a function of Q^{2}, and x in comparison to the expectations from 239 RAPGAP and DJANGOH both using λ_{s} = 0.286 and λ_{s} = 0.220. The DJANGOH prediction 240 with λ_{s} = 0.286 yields the worst description of the data by overshoots them significantly inde-241 pendent of Q^{2} and x. For the same strangeness suppression factor also RAPGAP tends to yield 242 ratios larger than observed in data for Q^{2} < 200 GeV^{2}. The best description is provided by 243 DJANGHO using λ_{s} = 0.220.

244 5.4 Λ– Λ̄ Asymmetries

245 The Λ– Λ̄ asymmetry is defined as:

A_{Λ} = \frac{σ_{vis}(ep → eΛX) − σ_{vis}(ep → eΛ̄X)}{σ_{vis}(ep → eΛX) + σ_{vis}(ep → eΛ̄X)}.  (4)

This observable could shed light on the mechanism of baryon number transfer in ep scattering. A significant positive asymmetry would be an indication for the baryon number transfer from the proton to the Λ baryon. If present such an effect should be more pronounced in the positive η region in the laboratory frame and in the target hemisphere in the Breit frame. For the kinemaic region defined in table 1 the asymmetry is measured to be

A_{Λ} = 0.002 ± 0.022 (stat.) ± 0.018 (syst.).

246 In figure 6 and 7 A_{Λ} is shown as a function of the variables measured in the laboratory frame 247 and the Breit frame, respectively. Also when studying the asymmetry as a function of these 248 variables the data data do not show any evidence for a non-vanishing asymmetry in the phase 249 space region investigated.

250 6 Conclusions

251 This paper presents a study of inclusive Λ production in DIS at high Q^{2} measured with the H1 252 detector at HERA. The kinematic range of the analysis covers the phase space region 145 < 253 Q^{2} < 20000 GeV^{2}, and 0.2 < y < 0.6. The Λ production cross section are measured as a 254 function of the DIS variables Q^{2} and x and of Λ production variables in the laboratory and in 255 the Breit frames of reference. The measurements in the Breit frame are presented separately for 256 the target and current hemispheres. In addition results on the Λ production to DIS cross section 257 ratio and the Λ − Λ̄ asymmetry are presented.

258 The measurements are been compared to model predictions of DJANGOH, based on the 259 colour-dipol model (CDM)and RAPGAP based on DGLAP matrix element calculations sup-260 plemented parton showers (MEPS). Two different values of the strangeness suppression factor 261 λ_{s} (0.220 and 0.286) are used for both models. The measured visible Λ cross section is found 262 to be described best by the CDM using λ_{s} = 0.220 and the MEPS model using λ_{s} = 0.286. 263 When investigating the Λ production to DIS cross section ratio the best agreement is observed 264 for the CDM with λ_{s} = 0.220. The Λ − Λ̄ asymmetry is found to be consistent with zero.

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Figure 2: Mass distributions for Λ + Λ̄ candidates. 12 Figure 3: Differential Λ + Λ̄ production cross sections as a function of (a) the photon virtuality squared Q^{2}, (b) Bjorken scaling variable x, (c) the transverse momentum, p_{T}, of the Λ baryon and (d) its pseudorapidity η in comparison to RAPGAP (MEPS) and DJANGOH (CDM) with two different vaues of λ_{s}. The inner (outer) error bars show the statistical (total) errors. The “MC/Data” ratios are shown for different Monte Carlo predictions. For comparison, the data points are put to one.

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

Figure 4: Differential Λ production cross sections in the Breit frame as a function of (a) p_{T}^{BFC},

(b) x^{BFC}, (c) p_{T}^{BFT}, (d) x^{BFT} in comparison to RAPGAP (MEPS) and DJANGOH (CDM) with two different vaues of λ_{s}. The inner (outer) error bars show the statistical (total) errors. The “MC/Data” ratios are shown for different Monte Carlo predictions. For the ratios the data points are put at one for comparison.

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

Figure 5: Ratio R(DIS) of Λ production to DIS cross section as a function of (a) the photon virtuality squared Q^{2} and (b) Bjorken scaling variable x in comparison to RAPGAP (MEPS) and DJANGOH (CDM) with two different vaues of λ_{s}. The inner (outer) error bars show the statistical (total) errors. The “MC/Data” ratios are shown for different Monte Carlo predictions. For the ratios the data points are put at one for comparison.

a)  b)

Figure 6: Asymmetry A_{Λ} as a function of (a) the photon virtuality squared Q^{2}, (b) Bjorken scaling variable x, (c) the transverse momentum, p_{T} and (d) its pseudorapidity η in the laboratory frame in comparison to RAPGAP (MEPS) and DJANGOH (CDM) with two different vaues of λ_{s}.

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

Figure 7: Asymmetry A_{Λ} as a function of the Breit frame variables (a) p_{T}^{BFC}, (b) x^{BFC}, (c) p_{T}^{BFT},

(d) x^{BFT} in comparison to RAPGAP (MEPS) and DJANGOH (CDM) with two different vaues of λ_{s}.

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