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arXiv:0810.4036v2 [hep-ex] 10 Mar 2009

DESY 08-095

December 2008

ISSN 0418-9833

Strangeness Production at low Q2

in Deep-Inelastic ep Scattering at HERA

H1 Collaboration

Abstract

The production of neutral strange hadrons is investigated using deep-inelastic scattering

events measured with the H1 detector at HERA. The measurements are made in the phase

space defined by the negative four-momentum transfer squared of the photon 2 < Q2<

100 GeV2and the inelasticity 0.1 < y < 0.6. The K0

and their ratios are determined. K0

particles in the same region of phase space. The Λ −¯Λ asymmetry is also measured and

found to be consistent with zero. Predictions of leading order Monte Carlo programs are

compared to the data.

sand Λ(¯Λ) production cross sections

sproduction is compared to the production of charged

Accepted by Eur. Phys. J. C

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F.D. Aaron5,49, C. Alexa5, V. Andreev25, B. Antunovic11, S. Aplin11, A. Asmone33,

A. Astvatsatourov4, A. Bacchetta11, S. Backovic30, A. Baghdasaryan38, E. Barrelet29,

W. Bartel11, M. Beckingham11, K. Begzsuren35, O. Behnke14, A. Belousov25, N. Berger40,

J.C. Bizot27, M.-O. Boenig8, V. Boudry28, I. Bozovic-Jelisavcic2, J. Bracinik3, G. Brandt11,

M. Brinkmann11, V. Brisson27, D. Bruncko16, A. Bunyatyan13,38, G. Buschhorn26,

L. Bystritskaya24, A.J. Campbell11, K.B. Cantun Avila22, F. Cassol-Brunner21, K. Cerny32,

V. Cerny16,47, V. Chekelian26, A. Cholewa11, J.G. Contreras22, J.A. Coughlan6, G. Cozzika10,

J. Cvach31, J.B. Dainton18, K. Daum37,43, M. De´ ak11, Y. de Boer11, B. Delcourt27,

M. Del Degan40, J. Delvax4, A. De Roeck11,45, E.A. De Wolf4, C. Diaconu21, V. Dodonov13,

A. Dossanov26, A. Dubak30,46, G. Eckerlin11, V. Efremenko24, S. Egli36, R. Eichler40,

A. Eliseev25, E. Elsen11, S. Essenov24, A. Falkiewicz7, P.J.W. Faulkner3, L. Favart4,

A. Fedotov24, R. Felst11, J. Feltesse10,48, J. Ferencei16, M. Fleischer11, A. Fomenko25,

E. Gabathuler18, J. Gayler11, S. Ghazaryan38, A. Glazov11, I. Glushkov39, L. Goerlich7,

M. Goettlich12, N. Gogitidze25, M. Gouzevitch28, C. Grab40, T. Greenshaw18, B.R. Grell11,

G. Grindhammer26, S. Habib12,50, D. Haidt11, M. Hansson20, C. Helebrant11,

R.C.W. Henderson17, E. Hennekemper15, H. Henschel39, G. Herrera23, M. Hildebrandt36,

K.H. Hiller39, D. Hoffmann21, R. Horisberger36, A. Hovhannisyan38, T. Hreus4,44,

M. Jacquet27, M.E. Janssen11, X. Janssen4, V. Jemanov12, L. J¨ onsson20, A.W. Jung15,

H. Jung11, M. Kapichine9, J. Katzy11, I.R. Kenyon3, C. Kiesling26, M. Klein18, C. Kleinwort11,

T. Klimkovich11, T. Kluge18, A. Knutsson11, R. Kogler26, V. Korbel11, P. Kostka39,

M. Kraemer11, K. Krastev11, J. Kretzschmar18, A. Kropivnitskaya24, K. Kr¨ uger15, K. Kutak11,

M.P.J. Landon19, W. Lange39, G. Laˇ stoviˇ cka-Medin30, P. Laycock18, A. Lebedev25,

G. Leibenguth40, V. Lendermann15, S. Levonian11, G. Li27, K. Lipka12, A. Liptaj26, B. List12,

J. List11, N. Loktionova25, R. Lopez-Fernandez23, V. Lubimov24, A.-I. Lucaci-Timoce11,

L. Lytkin13, A. Makankine9, E. Malinovski25, P. Marage4, Ll. Marti11, H.-U. Martyn1,

S.J. Maxfield18, A. Mehta18, K. Meier15, A.B. Meyer11, H. Meyer11, H. Meyer37, J. Meyer11,

V. Michels11, S. Mikocki7, I. Milcewicz-Mika7, F. Moreau28, A. Morozov9, J.V. Morris6,

M.U. Mozer4, M. Mudrinic2, K. M¨ uller41, P. Mur´ ın16,44, K. Nankov34, B. Naroska12,†,

Th. Naumann39, P.R. Newman3, C. Niebuhr11, A. Nikiforov11, G. Nowak7, K. Nowak41,

M. Nozicka11, B. Olivier26, J.E. Olsson11, S. Osman20, D. Ozerov24, V. Palichik9,

I. Panagouliasl,11,42, M. Pandurovic2, Th. Papadopouloul,11,42, C. Pascaud27, G.D. Patel18,

O. Pejchal32, H. Peng11, E. Perez10,45, A. Petrukhin24, I. Picuric30, S. Piec39, D. Pitzl11,

R. Plaˇ cakyt˙ e11, R. Polifka32, B. Povh13, T. Preda5, V. Radescu11, A.J. Rahmat18, N. Raicevic30,

A. Raspiareza26, T. Ravdandorj35, P. Reimer31, E. Rizvi19, P. Robmann41, B. Roland4,

R. Roosen4, A. Rostovtsev24, M. Rotaru5, J.E. Ruiz Tabasco22, Z. Rurikova11, S. Rusakov25,

D. Salek32, F. Salvaire11, D.P.C. Sankey6, M. Sauter40, E. Sauvan21, S. Schmidt11,

S. Schmitt11, C. Schmitz41, L. Schoeffel10, A. Sch¨ oning11,41, H.-C. Schultz-Coulon15,

F. Sefkow11, R.N. Shaw-West3, I. Sheviakov25, L.N. Shtarkov25, S. Shushkevich26, T. Sloan17,

I. Smiljanic2, P. Smirnov25, Y. Soloviev25, P. Sopicki7, D. South8, V. Spaskov9, A. Specka28,

Z. Staykova11, M. Steder11, B. Stella33, U. Straumann41, D. Sunar4, T. Sykora4,

V. Tchoulakov9, G. Thompson19, P.D. Thompson3, T. Toll11, F. Tomasz16, T.H. Tran27,

D. Traynor19, T.N. Trinh21, P. Tru¨ ol41, I. Tsakov34, B. Tseepeldorj35,51, I. Tsurin39, J. Turnau7,

E. Tzamariudaki26, K. Urban15, A. Valk´ arov´ a32, C. Vall´ ee21, P. Van Mechelen4, A. Vargas

Trevino11, Y. Vazdik25, S. Vinokurova11, V. Volchinski38, D. Wegener8, M. Wessels11,

Ch. Wissing11, E. W¨ unsch11, V. Yeganov38, J.ˇZ´ aˇ cek32, J. Z´ aleˇ s´ ak31, Z. Zhang27,

A. Zhelezov24, A. Zhokin24, Y.C. Zhu11, T. Zimmermann40, H. Zohrabyan38, and F. Zomer27

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1I. Physikalisches Institut der RWTH, Aachen, Germanya

2Vinca Institute of Nuclear Sciences, Belgrade, Serbia

3School of Physics and Astronomy, University of Birmingham, Birmingham, UKb

4Inter-University Institute for High Energies ULB-VUB, Brussels; Universiteit Antwerpen,

Antwerpen; Belgiumc

5National Institute for Physics and Nuclear Engineering (NIPNE) , Bucharest, Romania

6Rutherford Appleton Laboratory, Chilton, Didcot, UKb

7Institute for Nuclear Physics, Cracow, Polandd

8Institut f¨ ur Physik, TU Dortmund, Dortmund, Germanya

9Joint Institute for Nuclear Research, Dubna, Russia

10CEA, DSM/Irfu, CE-Saclay, Gif-sur-Yvette, France

11DESY, Hamburg, Germany

12Institut f¨ ur Experimentalphysik, Universit¨ at Hamburg, Hamburg, Germanya

13Max-Planck-Institut f¨ ur Kernphysik, Heidelberg, Germany

14Physikalisches Institut, Universit¨ at Heidelberg, Heidelberg, Germanya

15Kirchhoff-Institut f¨ ur Physik, Universit¨ at Heidelberg, Heidelberg, Germanya

16Institute of Experimental Physics, Slovak Academy of Sciences, Koˇ sice, Slovak Republicf

17Department of Physics, University of Lancaster, Lancaster, UKb

18Department of Physics, University of Liverpool, Liverpool, UKb

19Queen Mary and Westfield College, London, UKb

20Physics Department, University of Lund, Lund, Swedeng

21CPPM, CNRS/IN2P3 - Univ. Mediterranee, Marseille - France

22Departamento de Fisica Aplicada, CINVESTAV, M´ erida, Yucat´ an, M´ exicoj

23Departamento de Fisica, CINVESTAV, M´ exicoj

24Institute for Theoretical and Experimental Physics, Moscow, Russia

25Lebedev Physical Institute, Moscow, Russiae

26Max-Planck-Institut f¨ ur Physik, M¨ unchen, Germany

27LAL, Univ Paris-Sud, CNRS/IN2P3, Orsay, France

28LLR, Ecole Polytechnique, IN2P3-CNRS, Palaiseau, France

29LPNHE, Universit´ es Paris VI and VII, IN2P3-CNRS, Paris, France

30Faculty of Science, University of Montenegro, Podgorica, Montenegroe

31Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republich

32Faculty of Mathematics and Physics, Charles University, Praha, Czech Republich

33Dipartimento di Fisica Universit` a di Roma Tre and INFN Roma 3, Roma, Italy

34Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgariae

35Institute of Physics and Technology of the Mongolian Academy of Sciences , Ulaanbaatar,

Mongolia

36Paul Scherrer Institut, Villigen, Switzerland

37Fachbereich C, Universit¨ at Wuppertal, Wuppertal, Germany

38Yerevan Physics Institute, Yerevan, Armenia

39DESY, Zeuthen, Germany

40Institut f¨ ur Teilchenphysik, ETH, Z¨ urich, Switzerlandi

41Physik-Institut der Universit¨ at Z¨ urich, Z¨ urich, Switzerlandi

42Also at Physics Department, National Technical University, Zografou Campus, GR-15773

Athens, Greece

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43Also at Rechenzentrum, Universit¨ at Wuppertal, Wuppertal, Germany

44Also at University of P.J.ˇSaf´ arik, Koˇ sice, Slovak Republic

45Also at CERN, Geneva, Switzerland

46Also at Max-Planck-Institut f¨ ur Physik, M¨ unchen, Germany

47Also at Comenius University, Bratislava, Slovak Republic

48Also at DESY and University Hamburg, Helmholtz Humboldt Research Award

49Also at Faculty of Physics, University of Bucharest, Bucharest, Romania

50Supported by a scholarship of the World Laboratory Bj¨ orn Wiik Research Project

51Also at Ulaanbaatar University, Ulaanbaatar, Mongolia

†Deceased

aSupported by the Bundesministerium f¨ ur Bildung und Forschung, FRG, under contract

numbers 05 H1 1GUA /1, 05 H1 1PAA /1, 05 H1 1PAB /9, 05 H1 1PEA /6, 05 H1 1VHA /7 and

05 H1 1VHB /5

bSupported by the UK Science and Technology Facilities Council, and formerly by the UK

Particle Physics and Astronomy Research Council

cSupported by FNRS-FWO-Vlaanderen, IISN-IIKW and IWT and by Interuniversity Attraction

Poles Programme, Belgian Science Policy

dPartially Supported by Polish Ministry of Science and Higher Education, grant

PBS/DESY/70/2006 and grant N202 2956 33

eSupported by the Deutsche Forschungsgemeinschaft

fSupported by VEGA SR grant no. 2/7062/ 27

gSupported by the Swedish Natural Science Research Council

hSupported by the Ministry of Education of the Czech Republic under the projects LC527,

INGO-1P05LA259 and MSM0021620859

iSupported by the Swiss National Science Foundation

jSupported by CONACYT, M´ exico, grant 48778-F

lThis project is co-funded by the European Social Fund (75%) and National Resources (25%)

- (EPEAEK II) - PYTHAGORAS II

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1Introduction

The production of strange hadrons in high energy particle collisions allows the investigation

of strong interactions in the perturbative and non-perturbative regimes. Strange quarks are

created in the non-perturbative process of colour string fragmentation, which constitutes the

dominant production mechanism of strange hadrons. In deep-inelastic scattering (DIS), strange

quarks also originate from the strange sea in the nucleon, boson-gluon fusion and heavy quark

decays. Measurements of strangeness production have been used to investigate the suppression

of strangeness relative to lighter flavours in fragmentation. The universality of fragmentation

in different processes can be studied by comparing differential cross sections of the production

of K0

studying the ratios of production rates of Λ(¯Λ) to K0

some model dependencies are expected to cancel.

sand Λ(¯Λ) hadrons in various regions of phase space. Further information is gained by

sand of K0

sto charged hadrons (h±) as

The baryon production mechanism was studied in e+e−annihilation [1, 2, 3, 4, 5], a process

without incident baryons. Data involving a baryon in the initial state, like ep collisions at

HERA, provide additional information. In particular, data on the Λ -¯Λ production asymmetry

from HERA are of interest as an experimental constraint for theories of baryon number transfer

[6]. Fixed target data have shown [7] that the Λ production rate substantially exceeds that of the

¯Λ in the so-called remnant region because the baryon number of the target is conserved.

This paper presents a measurement of neutral strange particle (K0

at negative four momentum transfer squared 2 < Q2< 100GeV2and at low values of Bjorken

x. The study is based on data collected with the H1 detector at HERA at a centre-of-mass

energy of 319GeV in the years 1999 and 2000. This data sample is 40 times larger than that

used in the previous H1 publication [8] and covers a wider kinematic range. Measurements

of K0

collaboration [9]. The differential cross sections of K0

as well as the ratio of K0

variables, both in the laboratory frame and in the Breit frame. The results are compared with

predictions obtained from leading order Monte Carlo calculations, based on matrix elements,

with parton shower simulations. The main feature of the data is a suppression of strange quark

production relative to lighter quarks; this is discussed within the context of the framework of

the LUND [10] fragmentation model.

sand Λ) production in DIS

sand Λ production in different kinematic ranges have also been reported by the ZEUS

smesons, Λ(¯Λ) baryons and their ratio

sto charged hadrons are presented as a function of various kinematic

2Phenomenology

2.1Production of Strange Hadrons

Particles with strangeness can be produced in DIS in the hard sub-process and in the hadronisa-

tion of the colour field, as illustrated schematically in figure 1.

Figure 1a) shows strangeness production within the quark parton model (QPM), where a

strange quark s from the nucleon sea participates in the hard interaction. Figure 1b) illustrates

s production in a boson-gluon fusion (BGF) process, where a gluon emitted from the nucleon

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p

K0

s

s

d

d

e

e

*

γ

p

s

s

d

d

K0

g

ee

*

γ

p

d

d

c

s

g

e

e

c

K0

*

γ

p

d

s

d

s

K0

q

q

e

e

*

γ

Figure 1: Schematic diagrams of the different processes contributing to strangeness production:

a) direct production in the QPM, b) BGF, c) decays of heavy quarks and d) hadronisation.

a)b)

c)d)

splits into a s¯ s quark pair. Figure 1c) depicts heavy quark (charm c and beauty b) production

by boson-gluon fusion (BGF) with subsequent weak decay into s(¯ s) quarks. This process is

suppressed at low Q2due to the masses of the heavy quarks. These production mechanisms

(figures 1a, b, c) are characterised by a hard scale allowing for a perturbative treatment. The

relative rate of the BGF processes depends strongly on the Bjorken scaling variable x due to the

strong rise of the gluon density at low x. In the kinematic region studied in this analysis (low x)

the BGF contributions are expected to be significant. According to the Monte Carlo predictions

described below, roughly 25% of the strange hadrons originate from strange quarks produced

in the hard interaction either directly (figures 1a and b) or through heavy quark production in

BGF processes (figure 1c). In regions of phase space where the quark masses are not relevant

with respect to the process scales (e.g. at very high Q2) this rate can reach up to 50%.

The largest contribution to strange quark production is due to the colour field fragmentation

processes, as illustrated in figure 1d). As these processes occur at large distances they cannot be

treated perturbativelyand thus phenomenological models, such as the LUND string model [10],

are required for their description.

Frames of reference customarily used to study particle production are the laboratory and the

Breit frame [11]. In the Breit frame of reference the virtual space-like photon has momentum Q

butnoenergy. Thephotondirectiondefines thenegativez-axis withtheprotonmovinginthe+z

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direction. The transverse momentum in the Breit frame pBreit

axis. Particles from the proton remnant are almost collinear to the incoming proton direction,

therefore the hemisphere defined by pBreit

z

> 0 is labelled as the target hemisphere. Equally,

in the QPM the struck quark only populates the current hemisphere (pBreit

processes modify this simple picture as they generate transverse momentum in the final state

and may lead to particles from the hard subprocess propagating into the target hemisphere.

T

is computed with respect to this

z

< 0). Higher order

In the current hemisphere, the mechanism of particle production should in principle resem-

ble that of collisions without an incident proton like e+e−. In analogy with e+e−collisions the

fragmentation variable xBreit

p

= 2|? p|/Q is defined, where ? p is the momentum of the particle

in the Breit frame; xBreit

p

corresponds to xp= p/pbeamin e+e−collider experiments. Strange

quarks produced directly in the hard interaction are expected to preferentially populate the cur-

rent hemisphere, which is less sensitive to non-perturbative strangeness contributions. In the

case of baryon production the hemisphere separation is useful to study also baryon transfer,

which is expected to be relevant at high xBreit

p

in the target frame.

2.2Monte Carlo Simulation

The deep-inelastic ep interactions are simulated using the DJANGOH program [12] . It gener-

ates hard partonic processes at Born level and at leading order in αS(e.g. γ∗q → q, γ∗q → qg,

γ∗g → q¯ q ), convolutedwiththepartondistributionfunction(PDF)fortheproton,chosenherein

to be CTEQ6L [13]. The factorisation and renormalisation scales are set to µ2

Within DJANGOH, higher order QCD effects are accounted for using either the parton shower

approach as implemented in LEPTO [14] (referred to as MEPS) or by the so-called colour

dipole model approach available within ARIADNE [15] (referred to as CDM [16]). In LEPTO,

the parton showers are ordered in the transverse momenta (kT) of emissions, according to the

leading log(Q2) approximation. In the ARIADNE program, the partons are generated by colour

dipoles spanned between the partons in the cascade; since the dipoles radiate independently,

there is no kTordering.

f= µ2

r= Q2.

The hadronisation process is modelled according to the LUND colour string fragmentation

model [10], as implemented in the JETSET [17] program. Within this model, the strange quark

suppression is predominantly described by the (constant) factor λs= Ps/Pq, where Psand Pq

are the probabilities for creating strange (s) or light (q = u or d) quarks in a non-perturbative

process from the colour field during the fragmentation process. Further important parameters of

this model are the diquark suppression factor λqq= Pqq/Pq, i.e. the probability of producing a

light diquark pair qq¯ q¯ q from the vacuum with respect to a light q¯ q pair, and the strange diquark

suppression factor λsq= (Psq/Pqq)/(Ps/Pq), which models the relative production of strange

diquark pairs. These are the two most relevant factors for the description of baryon production.

The s¯ s pair production rate is primarily dominated by λs, i.e. u(¯ u) : d(¯d) : s(¯ s) = 1 : 1 : λs.

The values tuned to hadron production measurements by the ALEPH collaboration [4] (λs=

0.286,λqq= 0.108, and λsq= 0.690) are taken herein as default values for the simulation of

hadronisation within JETSET.

Previously published H1 and ZEUS data [8, 18] are better described by a lower value λs=

0.2. A recent ZEUS analysis [9] favours λs= 0.3 from cross section results and λs= 0.22 from

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measurements of the strange mesons to charged hadrons ratio. The same theoretical framework

is also used in e+e−analyses and thus allows for tests of strangeness suppression universality.

Monte Carlo event samples generated with DJANGOH are used for the acceptance and

efficiency correction of the data. All generated events are passed through the full GEANT

[19] based simulation of the H1 apparatus and are reconstructed and analysed using the same

programs as for the data.

3Experimental Procedure

3.1H1 Detector

A detailed description of the H1 detector can be found in [20]. In the following, only those

detector components important for the present analysis are described. H1 uses a right handed

Cartesian coordinate system with the origin at the nominal ep interaction point. The proton

beam direction defines the positive z-axis of the laboratory frame and transverse momenta are

measured in the x − y plane. The polar angle θ is measured with respect to this axis and the

pseudorapidity η is given by η = −lntanθ

Charged particlesaremeasuredintheCentral TrackingDetector(CTD)intherange−1.75 <

η < 1.75. The CTD comprises two cylindrical Central Jet Chambers (CJCs), arranged con-

centrically around the beam-line, complemented by a silicon vertex detector (CST) [21], two

z-drift chambers and two multi-wire proportional chambers for triggering purposes, all within a

solenoidal magnetic field of strength 1.16 T. The transverse momentum resolution is σ(pT)/pT

≃ 0.006pT/GeV ⊕0.015 [22]. In each event the tracks are used in a common fit procedure to

determine the ep interaction vertex.

2.

The tracking detectors are surrounded by a Liquid Argon calorimeter (LAr) in the forward

and central region (−1.5 < η < 3.4) and by a lead-scintillating fibre calorimeter (SpaCal)

in the backward region [23] (−4 < η < −1.4). The SpaCal is designed for the detection

of scattered positrons in the DIS kinematic range considered here and has an electromagnetic

energy resolution of σE/E ≃ 7%/?E/ GeV ⊕ 1%. The backward drift chamber (BDC),

positioned in front of the SpaCal, improves the measurement of the positron polar angle and is

used to reject neutral particle background. The DIS events studied in this paper are triggered by

an energy deposition in the SpaCal, complemented by signals in the CJCs and in the multi-wire

proportional chambers.

The luminosity is determined from the rate of the Bethe-Heitler process, ep → epγ, mea-

sured using a calorimeter located close to the beam pipe at z = −103 m.

3.2Selection of DIS Events

The analysis is based on a data sample corresponding to an integrated luminosity of L =

49.9pb−1, recorded when HERA collided positrons at an energy Ee= 27.6GeV with protons at

920GeV in the years 1999 and 2000.

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The selection of DIS events is based on the identification of the scattered positron as a

compactcalorimetricdepositintheSpaCal. Theclusterradiusisrequiredtobelessthan3.5 cm,

consistent with an electromagnetic energy deposition. The cluster centre must be geometrically

associated with a charged track candidate in the BDC. These conditions reduce background

from photoproduction processes.

At fixed centre of mass energies√s the kinematics of the scattering process are described

usingtheLorentzinvariantvariables Q2, y and x. Thesevariablescan beexpressed as afunction

of the scattered positron energy E′

eand its scattering angle θein the laboratory frame:

Q2= 4EeE′

ecos2

?θe

2

?

,y = 1 −E′

e

Eesin2

?θe

2

?

,x =Q2

ys.

(1)

The negative four-momentum transfer squared Q2and the inelasticity y are required to lie

in the ranges 2 < Q2< 100GeV2and 0.1 < y < 0.6. Background from events at low Q2,

in which the electron escapes undetected down the beam pipe and a hadron fakes the electron

signature, is suppressed by the requirement that the difference Σ(E − pz) between the total

energy and the longitudinal momentum must be in the range 35 < Σ(E −pz) < 70GeV, where

the sum includes all measured hadronic final state particles and the scattered electron candidate.

Events are accepted if the z-coordinate of the event vertex, reconstructed using the tracking

detectors, lies within ±35 cm of the mean position for ep interactions.

3.3Selection of Hadron Candidates

The neutral strange K0

tion of their decays K0

cles measured in the central region of the H1 detector with a minimum transverse momentum

pT ≥ 0.12GeV. The neutral strange hadrons K0

sitely charged tracks in the x − y plane to their secondary decay vertices, with the direction of

flight of the mother particle constrained to the primary event vertex. K0

retained if the fit probability is above 1%. In order to reduce background, the radial distance

L of the secondary vertex to the beam line is required to be larger than 5 mm and the vertex

separation significance L/σL> 4, where σLis the uncertainty of L. The transverse momentum

and the pseudorapidity of the K0

and |η| < 1.3. A detailed description of the analyses can be found in [24, 25].

For K0

construction the track with the higher momentum is assumed to be the proton and the other

track is assumed to be the pion. The contamination from Λ (K0

suppressed by a rejection of the corresponding invariant mass region: | M(πp)−mΛ|> 6MeV

for the K0

by the electrical charge of the decay proton (antiproton). The invariant mass spectra M(π+π−)

and M(pπ) of all candidates passing these criteria are shown in figures 2 and 3, respectively.

smeson and Λ baryon states1are measured by the kinematic reconstruc-

s→ π+π−and Λ → pπ−. The analysis is based on charged parti-

sand Λ are identified by fitting pairs of oppo-

sand Λ candidates are

s(Λ) candidates are required to satisfy 0.5 < pT < 3.5 GeV

scandidate reconstruction both tracks are assumed to be pions, while for the Λ re-

s) decays in K0

s(Λ) candidates is

sand | M(ππ) − mK0

s|> 10MeV for the Λ selection. The Λ (¯Λ) baryons are tagged

1Unless explicitly mentioned, a reference to a state implicitly includes the charge conjugate of that state.

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The number of signal particles NSis obtained by fitting the invariant mass spectra with the

sumofasignaland abackgroundfunction. ThesignalfunctionS has thesameshapeforK0

Λ and is composed oftwo Gaussian functionsofidentical central valueµ and ofdifferent widths

σ1and σ2that account for different resolution effects. The background functions BK0

BΛ(M) are chosen with different shapes for the K0

according to

sand

s(M) and

sand Λ cases. These functions are defined

S(M) = P0· G(NS,µ,σ1) + (1 − P0) · G(NS,µ,σ2),

BK0

BΛ(M) = P1· (M − mΛ)P2· e(1+P3·M+P4·M2).

(2)

(3)

s(M) = P1+ P2· M,

(4)

Here, M denotes the ππ and the pπ invariant mass, respectively, and mΛthe nominal mass

of the Λ baryon [26]. The normalisation NS, the central value µ, the widths σ1and σ2of the

Gaussian function G and the parameters Piare left free in the fit. P0represents the relative

normalisation of the two signal Gaussians. For the differential distributions the fit is repeated in

each of the kinematic bins.

Thefityieldsapproximately213000K0

is consistent with the world average [26] and the measured mean width 13.8 ± 0.4( stat.) MeV

is described by the simulated detector resolution within 20%. In the case of the Λ the fit yields

approximately 22000 Λ and 20000¯Λ baryons. The fitted mass of 1115.8 ± 0.1( stat.) MeV is

also consistent with the world average [26] and the measured width of 4.3 ± 0.3( stat.) MeV

is consistent with the detector resolution within 20%.

smesons. Thefittedmassof496.9±0.1( stat.) MeV

Charged hadrons h±used for the ratio R(K0

a lifetime > 10−8s detected in the same kinematic region as strange particles (|η| < 1.3,

0.5 < pT < 3.5GeV), with the following additional requirements: each track must point to

the primary vertex, the number of associated hits in the CJC must be greater than eight, the

radial track length must be longer than 10 cm and the radial distance from the beam line to the

innermost hit associated with the track must be less than 50 cm.

s/h±) are defined as long-lived particles with

4Results

4.1 Determination of Cross Sections

The total inclusivecross section σvisin the accessible kinematicregion is given by the following

expression:

σvis(ep → e[K0

s,Λ,h±]X) =

N

L · ǫ · BR · (1 + δrad)

s, the sum of Λ and¯Λ baryons or the charged

,

(5)

where N represents the observed number of K0

hadrons h±, respectively. L denotes the integrated luminosity. The branching ratios BR for the

K0

Λ particles are determined by fitting the mass distributions as explained in section 3.3. In the

case of differential distributions the same formula is applied in each bin.

sand Λ decays are taken from [26] and BR = 1 for charged hadrons. The number of K0

sand

9

Page 11

Theefficiency ǫ is givenby ǫ = ǫrec·ǫtrig, where ǫrecis the reconstructionefficiency and ǫtrig

is the trigger efficiency. The reconstruction efficiency is estimated using CDM Monte Carlo

event samples for the kinematic region and the visible range defined in sections 3.2 and 3.3,

and amounts to 33.3% and 19.5% for the K0

numbers include the geometric acceptance and the efficiency for track and secondary vertex

reconstruction. The geometric acceptance to find both decay particles in the CTD is about 80%

for the K0

smesons and the Λ baryons, respectively. These

smesons and 70% for the Λ baryons, respectively

The trigger efficiency is extracted from the data using monitor triggers and amounts to

81.5% and 83.3% for the K0

measured cross section to the Born level and is calculated using the program HERACLES [27].

It amounts to δrad= 6.6(4.3)% for the K0

over the kinematic range considered. The trigger efficiency and radiative corrections are as-

sumed to be the same for particles and antiparticles.

sand the Λ, respectively. The radiative correction δradcorrects the

s(Λ) on average and varies between −8% and +19%

In the case of charged hadrons h±, the reconstruction efficiency ǫrecis defined such that it

includes corrections for K0

track reconstruction efficiency. The total correction ǫ(1 + δrad) amounts to 81.1%.

sand Λ decays, secondary interactions, photon conversions and the

4.2 Systematic Uncertainties

The systematic uncertainties are studied using the CDM Monte Carlo simulation, unless oth-

erwise stated. For the inclusive cross sections, the resulting systematic uncertainties are sum-

marised in table 1. For the differential cross sections, the systematic uncertainties are estimated

in each bin. The following contributions are considered:

• The energy scale in the Spacal measurements is known to 1%, except for the lowest Q2

bin (2 < Q2< 2.5 GeV2) where the uncertainty on the energy measurement is 2.5%.

• The uncertainty of the measurement of the polar angle of the scattered positron is 1mrad.

• The uncertainty on the overall number of reconstructed K0

from data by comparing the numbers obtained from the fit of the mass spectra with the

number obtained by simply counting the events within ±6σ of the nominal mass after

subtracting the expected background. The number of background events is estimated

by integrating the background function described in equation 4 over the corresponding

interval (0.42−0.58GeV for K0

by performing the fit in different mass ranges.

sand Λ particles is determined

sand 1.085−1.2 for Λ). The procedure is cross checked

• Theuncertaintyofthereconstructionefficiency isdeterminedby comparingitsestimation

using different models. The uncertainty is taken as 50% of the difference between the

CDM and the MEPS Monte Carlo simulations.

• The uncertainty on the trigger efficiency is obtained by comparing estimates using differ-

ent monitor triggers (MT).

• The uncertainty on the luminosity measurement is 1.5%.

10

Page 12

• The uncertainty of the charged hadron reconstruction is 2% per track. For the measure-

ment of the Λ to K0

decays is assumed to cancel. The systematic uncertainty on the ratio K0

to be 2.0%.

sratio the uncertainty caused by the pion track appearing in both

s/h±is estimated

• The uncertainty due to the decay branching ratios is taken as 0.8% for Λ and is negligible

for K0

s[26].

Source Variation

∆σ(K0

s)∆σ(Λ)R(Λ/K0

s)R(K0

s/h±)

[%][%] [%] [%]

E′

e

±1%

±1 mrad

Nfit−Ncount

Nfit

+3.3

−3.5

+2.8

−3.1

−

−

−

−θe

±1.4

±0.6

±0.4

+0.4

−0.9

±1.5

±1.4

±1.2

+1.0

−1.4

signal extraction

±1.5

±1.2

+1.1

−1.6

±0.6

±3.5

+0.4

−1.0

model

0.5 ∗ǫCDM

ǫMTset1

trig

rec

−ǫMEPS

rec

ǫCDM

rec

−ǫMTset2

trig

ǫMTset1

trig

trigger efficiency

luminosity

±1.5

±4.0

±0.1

±1.5

±4.0

±0.8

−−

track reco.

2.0% per track

±2.0

±0.8

±2.0

±0.1

branching ratio

Total systematic uncertainty

+5.6

−5.8

+5.8

−6.0

+3.1

−3.3

+4.1

−4.2

Table 1: Systematic sources, variations and corresponding relative errors of the inclusive cross

sectionsandoftheratiosofΛtoK0

as percentages.

sandK0

stocharged hadrons. Allrelativeerrors areexpressed

The systematic errors due to these uncertainties are estimated by varying each quantity

within its error in the Monte Carlo simulation and repeating the cross section measurement.

In the cross section calculation, the contributions are added in quadrature and included in the

uncertainty shown in the individual bins of the differential distributions. In the ratios, the un-

certainties on the electron energy scale and polar angle, as well as the luminosity, cancel. The

other sources of uncertainty are assumed to be uncorrelated and are added in quadrature.

4.3Inclusive Production Measurements

The inclusive K0

kinematicregion2 < Q2< 100GeV2and0.1 < y < 0.6, fortheranges0.5 < pT(K0

3.5 GeV and |η(K0

s, Λ and charged hadron h±production cross sections σvisare measured in the

s,Λ,h±) <

s,Λ,h±)| < 1.3.

11

Page 13

The K0

scross section is found to be

σvis(ep → eK0

sX) = 21.18 ± 0.09(stat.)+1.19

−1.23(syst.) nb.

(6)

The measurement is in agreement with the expectation 21.77 nb based on the LO Monte Carlo

program DJANGOH, using the CDM approach and the default value of λs= 0.286.

The cross section for the sum of Λ and¯Λ baryon production is measured in the same kine-

matic region and is found to be

σvis(ep → e[Λ +¯Λ]X) = 7.88 ± 0.10(stat.)+0.45

in agreement with the expectation of 7.94 nb from the DJANGOH calculation. The individual

Λ and¯Λ production rates are measured to be

−0.47(syst.) nb,

(7)

σvis(ep → eΛX) = 3.96 ± 0.06(stat.)+0.23

σvis(ep → e¯ΛX) = 3.94 ± 0.07(stat.)+0.23

and are therefore found to be consistent with each other within the statistical precision. The

measurements are also in agreement with the DJANGOH prediction of 3.97 nb. The systematic

errors are fully correlated.

−0.24(syst.) nb,

−0.24(syst.) nb,

(8)

(9)

The inclusive ratio of strange baryon to meson production is determined to be

σvis(ep → e[Λ +¯Λ]X)

σvis(ep → eK0

sX)

= 0.372 ± 0.005(stat.)+0.011

−0.012(syst.),

(10)

in agreement with the prediction of 0.365 from the DJANGOH calculation.

The ratio of cross sections of K0

smesons to charged hadrons h±is found to be

σvis(ep → eK0

σvis(ep → eh±X)= 0.0645 ± 0.0002(stat.)+0.0019

sX)

−0.0020(syst.),

(11)

in agreement with the DJANGOH prediction of 0.0638 based on MEPS with λs= 0.22.

Similar values of 0.05 − 0.07 are obtained for the ratio of the average K0

average charged pion multiplicity in e+e−annihilation events at centre of mass energies from

10 to 200GeV [26].

smultiplicity over the

4.4Differential Production Cross Sections

Production cross sections and ratios of K0

visible kinematic region differentially in the event variables Q2and x and in the laboratory

frame variables pT and η. Differential cross sections are also measured as a function of the

variables xBreit

p

and pBreit

T

defined in the Breit frame. The results are bin-averaged and no bin-

centre corrections are applied. The distributions are shown in figures 4 to 13 and are compared

with the predictions. The numerical values are also listed in tables 2 to 8.

s, Λ and charged hadrons h±are measured in the

12

Page 14

4.4.1Discussion of K0

sand Λ Results

The measured differential cross sections of K0

listed in tables 2 to 5. The cross sections decrease rapidly as a function of Q2and x, similarly

to the inclusive DIS distributions. The cross sections are also observed to fall rapidly with pT.

In the laboratory frame the overall features of the distributionsare reproduced by the DJAN-

GOH simulations at the level of 10 to 20%. For comparison, the CDM and MEPS model pre-

dictions are each given with two values of the suppression factor λs= 0.3 and λs= 0.22. The

predictionsbased on theCDM model with λs= 0.3 provideareasonably gooddescription ofthe

data for K0

similar in shape to the CDM model predictions but with a different normalisation in the case

of K0

production, both MEPS and CDM predictions are very similar in shape and normalisation and

λs= 0.3 provides a better description of the data. For these comparisons, only the parameter λs

is varied to describe the data. However, in contrast to the K0

also depend significantly on the JETSET parameters that describe diquark and strange diquark

creation.

Thecrosssectionsmeasured as afunctionofxBreit

figures 6 and 7 and listed in tables 4 and 5, for both the target and the current region. The cross

section values in the target regions are about one order of magnitude higher than in the current

region. They are generally well described by both the MEPS and CDM model predictions. The

predicted momentum distributions tend to be softer than in the data. However, in the current

region the sensitivity to λsis clearly reduced with respect to the laboratory frame or the target

region. This is due to both larger errors and an increased fraction of strangeness produced in

perturbativeprocesses, which contributes up to about 50% (compared to about 25% in the target

hemisphere).

To test the mechanism of baryon number transfer, the asymmetry in the production of Λ

with respect to¯Λ is measured by the variable

AΛ=σvis(ep → eΛX) − σvis(ep → e¯ΛX)

σvis(ep → eΛX) + σvis(ep → e¯ΛX).

A significant Λ -¯Λ asymmetry AΛ?= 0 would indicate a transfer of the baryon number from

the proton beam to the final state strange particles. The measured distributions of AΛin the

laboratory and Breit frames are shown in figures 8 and 9, respectively. All distributions are

observed to be compatiblewith zero within errors. Thus, no evidence of baryon number transfer

is visible in the measured Λ/¯Λ data.

In order to test for possible dependencies of strange hadron production on the proton parton

density functions, the measured distributions are compared with different PDF parametrisa-

tions. Figure 10 shows the differential cross sections for K0

the CDM predictions using the CTEQ6L [13], H12000LO [28] and GRV LO [29] parametrisa-

tions and λs= 0.286. The predictions of the Q2dependence of the cross section are notably

different for different PDFs for both the K0

slight dependence while the η distributions do not exhibit any PDF dependence. The small

discrepancy in the forward direction is not resolved by different PDF parametrisations. Similar

results are obtained in the Breit frame.

sand Λ production are shown in figures 4 to 7 and

sand Λ production. The MEPS simulation produces distributions, which are quite

sproduction, where a lower value of λs= 0.22 describes the data better. In the case of Λ

s, the Λ production cross sections

p

and pBreit

T

intheBreit frameare shownin

(12)

sand Λ production compared with

sand the Λ. The pT distributions indicate only a

13

Page 15

4.4.2Ratios of Production Cross Sections

Different aspects of baryon production within the fragmentation models can be tested with

reduced theoretical uncertainties by studying the ratio of the differential cross sections for Λ

baryons and K0

are shown in figures 11 and 12 and listed in tables 6 and 7. The CDM implementation provides

a reasonably good description of the data in the laboratory frame (figure 11), although system-

atic deviations are seen at high Q2and in the shape of the η distribution, whereas the MEPS

predictions clearly underestimate the data. The model predictions are not sensitive to λs, as

expected.

smesons R(Λ/K0

s) = dσ(ep → eΛX) / dσ(ep → eK0

sX). The measurements

The dependence of R(Λ/K0

in both the target and current hemispheres. The predictions are almost independent of the model

implementation (CDM, MEPS) and the λsvalues used.

s) on pBreit

T

and xBreit

p

(figure 12) are reasonably well described

The ratio of differential production cross sections for K0

denoted by R(K0

average multiplicities of K0

correlation of R(K0

the ratio, inadequacies of the model description of the partonic final states and in particular

of the dependence on the proton structure function should cancel to a large extent. The ratio

R(K0

strongly rises with increasing pT and remains approximately constant as a function of all the

other variables. This pTdependence of R(K0

particles receive the larger fraction of the system momentum) and can also be observed in the

Λ/K0

smesons and charged hadrons,

s/h±) = dσ(ep → eK0

sand charged hadrons. In contrast to inclusive K0

s/h±) to the parameter λsis expected to be less model dependent. By taking

sX) / dσ(ep → eh±X), is equivalent to the ratio of the

sproduction, the

s/h±) is shown in figure 13 and listed in table 8 as a function of Q2,x, pTand η. The ratio

s/h±) reflects a general kinematic feature (heavier

sratio in figure 11.

Also shown with the data are the CDM and MEPS model predictions for two values of λs

(0.22 and 0.3). Overall, no singleprediction is ableto fully describe theshapes ofall R(K0

distributions, failing in particular in the low pT, low x and large positive η regions. The pT

spectrumof R(K0

from the cross section measurement.

s/h±)

s/h±) is found to be harder in thedata, consistentwith theconclusionsderived

The shapes of the ratios R(K0

model predictions. However, there is a difference in normalisation between the two models.

The CDM prediction with λs= 0.3 is in better agreement with the data at low Q2, whereas at

high Q2a value of λs= 0.22 is preferred, as observed in the ZEUS data [9]. In contrast, the

MEPS model predictions prefer a lower value of λs= 0.22 over the full phase space.

s/h±) are reasonably described by both CDM and MEPS

A comparison of the predictions, applying different settings for the diquark-quark suppres-

sion factors (λqq,λsq) shows the expected behaviour. In general, no changes are visible in the

shapes of the differential distributions, however some differences are present in the absolute

normalisation. The K0

R(Λ/K0

dicted effects are mostly independent of the choice of the λsvalue, used for the simulation, and

indicate that the “ALEPH-tune” from e+e−collisions also describes the overall features of the

data in ep collisions, supporting the universality of strangeness production.

sdistributions are not affected, as expected, and both the Λ and the ratio

s) show the anticipated correlations to the suppression factors (λqq,λsq). These pre-

14