Multiplicities of charged kaons from deep-inelastic muon scattering off an isoscalar target

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Multiplicities

of

charged

kaons

from

deep-inelastic

muon

scattering

off

an

isoscalar

target

C. Adolph

h

,

M. Aghasyan

y

,

R. Akhunzyanov

g

,

M.G. Alexeev

aa

,

G.D. Alexeev

g

,

A. Amoroso

aa

,

ab

,

V. Andrieux

u

,

ac

,

N.V. Anfimov

g

,

V. Anosov

g

,

K. Augsten

g

,

s

,

W. Augustyniak

ad

,

A. Austregesilo

p

,

C.D.R. Azevedo

a

,

B. Badełek

ae

,

F. Balestra

aa

,

ab

,

M. Ball

c

,

J. Barth

d

,

R. Beck

c

,

Y. Bedfer

u

,

J. Bernhard

m

,

j

,

K. Bicker

p

,

j

,

E.R. Bielert

j

,

R. Birsa

y

,

M. Bodlak

r

,

P. Bordalo

l

,

1

,

F. Bradamante

x

,

y

,

C. Braun

h

,

A. Bressan

x

,

y

,

M. Büchele

i

,

L. Capozza

u

,

W.-C. Chang

v

,

C. Chatterjee

f

,

M. Chiosso

aa

,

ab

,

I. Choi

ac

,

S.-U. Chung

p

,

2

,

A. Cicuttin

z

,

y

,

M.L. Crespo

z

,

y

,

Q. Curiel

u

,

S. Dalla Torre

y

,

S.S. Dasgupta

f

,

S. Dasgupta

x

,

y

,

O.Yu. Denisov

ab

,

∗

,

L. Dhara

f

,

S.V. Donskov

t

,

N. Doshita

ag

,

Ch. Dreisbach

p

,

V. Duic

x

,

W. Dünnweber

3

,

M. Dziewiecki

af

,

A. Efremov

g

,

P.D. Eversheim

c

,

W. Eyrich

h

,

M. Faessler

3

,

A. Ferrero

u

,

M. Finger

r

,

M. Finger Jr.

r

,

H. Fischer

i

,

C. Franco

l

,

N. du Fresne von Hohenesche

m

,

J.M. Friedrich

p

,

V. Frolov

g

,

j

,

E. Fuchey

u

,

F. Gautheron

b

,

O.P. Gavrichtchouk

g

,

S. Gerassimov

o

,

p

,

F. Giordano

ac

,

I. Gnesi

aa

,

ab

,

M. Gorzellik

i

,

S. Grabmüller

p

,

A. Grasso

aa

,

ab

,

M. Grosse Perdekamp

ac

,

B. Grube

p

,

T. Grussenmeyer

i

,

A. Guskov

g

,

F. Haas

p

,

D. Hahne

d

,

G. Hamar

x

,

y

,

D. von Harrach

m

,

F.H. Heinsius

i

,

R. Heitz

ac

,

F. Herrmann

i

,

N. Horikawa

q

,

4

,

N. d’Hose

u

,

C.-Y. Hsieh

v

,

5

,

S. Huber

p

,

S. Ishimoto

ag

,

6

_,

_{A. Ivanov}

aa

,

ab

_,

_{Yu. Ivanshin}

g

_,

_{T. Iwata}

ag

_,

_{V. Jary}

s

_,

_{R. Joosten}

c

_,

_{P. Jörg}

i

_,

E. Kabuß

m

,

B. Ketzer

c

,

G.V. Khaustov

t

,

Yu.A. Khokhlov

t

,

7

,

8

,

Yu. Kisselev

g

,

F. Klein

d

,

K. Klimaszewski

ad

,

J.H. Koivuniemi

b

,

V.N. Kolosov

t

,

K. Kondo

ag

,

K. Königsmann

i

,

I. Konorov

o

,

p

,

V.F. Konstantinov

t

,

A.M. Kotzinian

aa

,

ab

,

O.M. Kouznetsov

g

,

M. Krämer

p

,

P. Kremser

i

,

F. Krinner

p

,

Z.V. Kroumchtein

g

,

Y. Kulinich

ac

,

F. Kunne

u

,

K. Kurek

ad

,

R.P. Kurjata

af

,

A.A. Lednev

t

,

A. Lehmann

h

,

M. Levillain

u

,

S. Levorato

y

,

Y.-S. Lian

v

,

9

,

J. Lichtenstadt

w

,

R. Longo

aa

,

ab

,

A. Maggiora

ab

,

A. Magnon

ac

,

N. Makins

ac

,

N. Makke

x

,

y

,

G.K. Mallot

j

,

∗

_,

_{B. Marianski}

ad

_,

_{A. Martin}

x

,

y

_,

_{J. Marzec}

af

_,

_{J. Matoušek}

r

,

y

_,

_{H. Matsuda}

ag

_,

T. Matsuda

n

,

G.V. Meshcheryakov

g

,

M. Meyer

ac

,

u

,

W. Meyer

b

,

Yu.V. Mikhailov

t

,

M. Mikhasenko

c

,

E. Mitrofanov

g

,

N. Mitrofanov

g

,

Y. Miyachi

ag

,

A. Nagaytsev

g

,

F. Nerling

m

,

D. Neyret

u

,

J. Nový

s

,

j

,

W.-D. Nowak

m

,

G. Nukazuka

ag

,

A.S. Nunes

l

,

A.G. Olshevsky

g

,

I. Orlov

g

,

M. Ostrick

m

,

D. Panzieri

ab

,

10

,

B. Parsamyan

aa

,

ab

,

S. Paul

p

,

J.-C. Peng

ac

,

F. Pereira

a

,

M. Pešek

r

,

D.V. Peshekhonov

g

,

N. Pierre

m

,

u

,

S. Platchkov

u

,

J. Pochodzalla

m

,

V.A. Polyakov

t

,

J. Pretz

d

,

11

,

M. Quaresma

l

,

C. Quintans

l

,

S. Ramos

l

,

1

,

C. Regali

i

,

G. Reicherz

b

,

C. Riedl

ac

,

M. Roskot

r

,

N.S. Rossiyskaya

g

,

D.I. Ryabchikov

t

,

8

_,

A. Rybnikov

g

,

A. Rychter

af

,

R. Salac

s

,

V.D. Samoylenko

t

,

A. Sandacz

ad

,

C. Santos

y

,

S. Sarkar

f

,

I.A. Savin

g

,

T. Sawada

v

,

G. Sbrizzai

x

,

y

,

P. Schiavon

x

,

y

,

K. Schmidt

i

,

12

,

H. Schmieden

d

,

K. Schönning

j

,

13

,

E. Seder

u

,

∗

,

A. Selyunin

g

,

L. Silva

l

,

L. Sinha

f

,

S. Sirtl

i

,

M. Slunecka

g

,

J. Smolik

g

,

F. Sozzi

y

,

A. Srnka

e

,

D. Steffen

j

,

p

,

M. Stolarski

l

,

O. Subrt

j

,

s

,

M. Sulc

k

,

H. Suzuki

ag

,

4

,

A. Szabelski

ad

,

y

,

T. Szameitat

i

,

12

,

P. Sznajder

ad

,

S. Takekawa

aa

,

ab

,

M. Tasevsky

g

,

S. Tessaro

y

,

F. Tessarotto

y

,

F. Thibaud

u

,

A. Thiel

c

,

F. Tosello

ab

,

V. Tskhay

o

,

S. Uhl

p

,

J. Veloso

a

,

M. Virius

s

,

J. Vondra

s

,

S. Wallner

p

,

T. Weisrock

m

,

M. Wilfert

m

,

http://dx.doi.org/10.1016/j.physletb.2017.01.053

0370-2693/©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

R. Windmolders

d

,

J. ter Wolbeek

i

,

12

,

K. Zaremba

af

,

P. Zavada

g

,

M. Zavertyaev

o

,

E. Zemlyanichkina

g

,

N. Zhuravlev

g

,

M. Ziembicki

af

,

A. Zink

h

a_{UniversityofAveiro,DepartmentofPhysics,3810-193Aveiro,Portugal}

b_{UniversitätBochum,InstitutfürExperimentalphysik,44780Bochum,Germany}14,15 c_{UniversitätBonn,Helmholtz-InstitutfürStrahlen- undKernphysik,53115Bonn,Germany}14 d_{UniversitätBonn,PhysikalischesInstitut,53115Bonn,Germany}14

e_{InstituteofScientificInstruments,ASCR,61264Brno,CzechRepublic}16

f_{MatrivaniInstituteofExperimentalResearch&Education,Calcutta700030,India}17 g_{JointInstituteforNuclearResearch,141980Dubna,Moscowregion,Russia}18 h_{UniversitätErlangen–Nürnberg,PhysikalischesInstitut,91054Erlangen,Germany}14 i_{UniversitätFreiburg,PhysikalischesInstitut,79104Freiburg,Germany}14,15 j_{CERN,1211Geneva23,Switzerland}

k_{TechnicalUniversityinLiberec,46117Liberec,CzechRepublic}16 l_{LIP,1000-149Lisbon,Portugal}19

m_{UniversitätMainz,InstitutfürKernphysik,55099Mainz,Germany}14 n_{UniversityofMiyazaki,Miyazaki889-2192,Japan}20

o_{LebedevPhysicalInstitute,119991Moscow,Russia}

p_{TechnischeUniversitätMünchen,PhysikDepartment,85748Garching,Germany}14,3 q_{NagoyaUniversity,464Nagoya,Japan}20

r_{CharlesUniversityinPrague,FacultyofMathematicsandPhysics,18000Prague,CzechRepublic}16 s_{CzechTechnicalUniversityinPrague,16636Prague,CzechRepublic}16

t_{StateScientificCenterInstituteforHighEnergyPhysicsofNationalResearchCenter‘KurchatovInstitute’,142281Protvino,Russia} u_{IRFU,CEA,UniversitéSaclay-Paris,91191Gif-sur-Yvette,France}15

v_{AcademiaSinica,InstituteofPhysics,Taipei11529,Taiwan}

w_{TelAvivUniversity,SchoolofPhysicsandAstronomy,69978TelAviv,Israel}21 x_{UniversityofTrieste,DepartmentofPhysics,34127Trieste,Italy}

y_{TriesteSectionofINFN,34127Trieste,Italy} z_{AbdusSalamICTP,34151Trieste,Italy}

aa_{UniversityofTurin,DepartmentofPhysics,10125Turin,Italy} ab_{TorinoSectionofINFN,10125Turin,Italy}

ac_{UniversityofIllinoisatUrbana-Champaign,DepartmentofPhysics,Urbana,IL61801-3080,USA} ad_{NationalCentreforNuclearResearch,00-681Warsaw,Poland}22

ae_{UniversityofWarsaw,FacultyofPhysics,02-093Warsaw,Poland}22

af_{WarsawUniversityofTechnology,InstituteofRadioelectronics,00-665Warsaw,Poland}22 ag_{YamagataUniversity,Yamagata992-8510,Japan}20

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received24August2016

Receivedinrevisedform13January2017 Accepted24January2017

Availableonline27January2017 Editor:M.Doser

Keywords:

Deepinelasticscattering Kaonmultiplicities

Quarkfragmentationfunctions Strangequark

Precise measurementsof charged-kaonmultiplicitiesindeep inelastic scatteringwereperformed. The results are presented inthree-dimensional binsofthe Bjorkenscaling variable x, therelative virtual-photon energy y, and the fraction z of the virtual-photon energy carried by the produced hadron. The data wereobtainedby theCOMPASS Collaborationbyscattering 160 GeV muons off anisoscalar 6_{LiDtarget.Theycoverthekinematicdomain1(GeV/c)}2_<Q2_{<60 (GeV/c)}2_{inthephotonvirtuality,} 0.004<x<0.4,0.1<y<0.7,0.20<z<0.85,andW>5 GeV/c2_{intheinvariantmassofthehadronic} system.Theresultsfromthesumofthez-integratedK+andK−multiplicitiesathighx pointtoavalue ofthenon-strangequarkfragmentationfunctionlargerthanobtainedbytheearlierDSSfit.

©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

*

Correspondingauthors.

E-mailaddresses:oleg.denisov@cern.ch(O.Yu. Denisov),gerhard.mallot@cern.ch(G.K. Mallot),erin.seder@cern.ch(E. Seder). 1 _{AlsoatInstitutoSuperiorTécnico,UniversidadedeLisboa,Lisbon,Portugal.}

2 _{AlsoatDepartmentofPhysics,PusanNationalUniversity,Busan609-735,RepublicofKoreaandatPhysicsDepartment,BrookhavenNationalLaboratory,Upton,NY11973,} USA.

3 _{SupportedbytheDFGclusterofexcellence‘OriginandStructureoftheUniverse’(www.universe-cluster.de).} 4 _{AlsoatChubuUniversity,Kasugai,Aichi487-8501,Japan.}

5 _{AlsoatDepartmentofPhysics,NationalCentralUniversity,300JhongdaRoad,Jhongli32001,Taiwan.} 6 _{AlsoatKEK,1-1Oho,Tsukuba,Ibaraki305-0801,Japan.}

7 _{AlsoatMoscowInstituteofPhysicsandTechnology,MoscowRegion,141700,Russia.} 8 _{SupportedbyPresidentialgrantNSh-999.2014.2.}

9 _{AlsoatDepartmentofPhysics,NationalKaohsiungNormalUniversity,KaohsiungCounty824,Taiwan.} 10 _{AlsoatUniversityofEasternPiedmont,15100Alessandria,Italy.}

11 _{Presentaddress:RWTHAachenUniversity,III.PhysikalischesInstitut,52056Aachen,Germany.} 12 _{SupportedbytheDFGResearchTrainingGroupProgramme1102“PhysicsatHadronAccelerators”.} 13 _{Presentaddress:UppsalaUniversity,Box516,75120Uppsala,Sweden.}

14 _{SupportedbytheGermanBundesministeriumfürBildungundForschung.} 15 _{SupportedbyEUFP7(HadronPhysics3,GrantAgreementnumber283286).} 16 _{SupportedbyCzechRepublicMEYSGrantLG13031.}

17 _{SupportedbySAIL(CSR),Govt.ofIndia.} 18 _{SupportedbyCERN-RFBRGrant12-02-91500.}

1. Introduction

The study of strangeness in the nucleon has been arousing

constant interest over the last decades, butthe data sensitive to strangenessarestillratherscarce.Thepartondistributionfunctions (PDFs)ofstrangequarkss

(

x

)

inthenucleonarenotyetwell con-strained.The evaluationof thes-quark helicitydistribution func-tion



s

(

x

)

,where x denotes the fraction oflongitudinal nucleon momentumcarriedby thequark,isparticularlydifficult.Different valuesareobtained foritsfirst moment



s whenusing two dif-ferentmethods.Ontheonehand,asubstantiallynegativevalueis obtainedfromQCDfitsofmeasurementsofdeep-inelastic scatter-ing(DIS)ofapolarisedbeamonapolarisedtarget,whenassuming SU(3)flavoursymmetryinthehyperonsector[1–4].Ontheother hand,thevaluesof



s

(

x

)

extractedusingonly semi-inclusiveDIS measurements(hereafter referred toasSIDIS) ofidentified kaons usingpolarised beamandtargetare foundtobe compatiblewith zerointhemeasuredkinematicrange[5–7].Thelatterevaluations requireknowledgeof thecollinearquark fragmentation functions (FFs),inparticularknowledgeofthequark-to-kaonFF.Thevalues ofthestrangequark-to-kaonFFpresently published differby fac-torsofuptothree[8,9]andthuscanleadtoverydifferentvalues of



s

(

x

)

[4,6].NotethattheauthorsofRef.[3]reconciledthetwo resultsbyusingamoreflexibleshapefor



s

(

x

)

,whichturnedout tobenegativeatlowx wherenodataexistandslightlypositiveat highx toaccommodateSIDISdata.Quark FFsareofgeneral inter-estbythemselves,astheyarenon-perturbativeuniversalfunctions describingprocessesleadingtotheproductionofhadrons.

Thereasonfor thepresently large uncertainties on thevalues of the strange quark-to-kaon FF is the lack of appropriate kaon data.Existingdataonkaonproductionfrome+e−annihilation[10]

andppcollision[11]experimentsareonlyweaklysensitivetothe quark andanti-quarkflavoursindividually.In contrast,SIDISdata allowforafullflavourdecompositionofFFs[12].Comparedtothe kinematicrange of the only published SIDIS results,which

orig-inatefrom HERMES [13], COMPASS measurements cover a wider

kinematicdomain.Inaddition,theybettersatisfytheBerger crite-rion[14] that ensures thevalidity offactorisationin the descrip-tionofSIDIS. Kaonmultiplicities measured by COMPASSare thus expectedtoplayanimportantroleinfuturenext-to-leadingorder (NLO)pQCDanalysesaimingtoconstrainquark-to-kaonFFs.

InthisLetter,wepresentCOMPASSresultsondifferential mul-tiplicities for charged kaons, which are derived from data taken simultaneouslyto thoseused forthe determinationofthe differ-ential multiplicitiesfor chargedpions [15]. In bothcases, similar analysis methods are used. The multiplicity results are derived fromSIDISmeasurementswithpolarisedbeamandtargetafter av-eragingover the target polarisation,so that they coverthe same kinematicrangeasusedfortheextractionof



s

(

x

)

[6],aswell as alarge Q2 _{rangetoprobeevolution.}

Themultiplicityforahadronoftypeh fromtheSIDIS measure-ment lN

→

lhX is definedas the differential hadron production crosssection

σ

h_{normalisedtotheinclusiveDIScrosssection}

_σ

DIS

andthus represents the mean number of hadronsproduced per

DISeventwhenintegratedover z:

dMh

(

x

,

z

,

Q2

)

dz

=

d3

σ

h

₍

_x

_,

_z

_,

_Q2

_)/

_dxdQ2_dz

d2

_σ

DIS

_/

_dxdQ2

.

(1)

19 _{Supportedby the Portuguese FCT – Fundaçãopara a Ciênciae Tecnologia,} COMPETEandQREN,GrantsCERN/FP109323/2009,116376/2010,123600/2011and CERN/FIS-NUC/0017/2015.

20 _{Supportedbythe MEXT and the JSPS under the GrantsNo. 18002006, No.} 20540299andNo.18540281;DaikoFoundationandYamadaFoundation.

21 _{SupportedbytheIsraelAcademyofSciencesandHumanities.} 22 _{SupportedbythePolishNCNGrant2015/18/M/ST2/00550.}

Here, x

= −

q2

_/(

_2P

_·

_q

₎

_{istheBjorken variable,z}

_{= (}

_P

_·

_p

h

)/(

P

·

q

)

the fraction of the virtual-photon energy that is carried by the final-state hadronand Q2

= −

q2 thenegative square ofthe lep-tonfour-momentumtransfer.Thesymbolsq,P and phdenotethe four-momenta of the virtual photon, the nucleon N and the ob-servedhadronhrespectively.Additionalvariablesusedarethe lep-tonenergyfractioncarriedbythevirtualphoton, y

= (

P

·

q

)/(

P

·

k

)

withk thefour-momentumoftheincidentlepton,andthe invari-ant massof thefinal hadronicsystem, W

=



(

P

+

q

)

2_{. AtLO in} pQCDthecrosssectionsarenotsensitivetothegluoncontribution andcanbeexpressedintermsofonlyquarkPDFsandFFs:

d2

σ

DIS dxdQ2

=

C

(

x

,

Q 2

₎



q e2_qq

(

x

,

Q2

),

d3

σ

h dxdQ2_dz

=

C

(

x

,

Q 2

₎



q e2_qq

(

x

,

Q2

)

Dh_q

(

z

,

Q2

),

(2)

where the sumis over quarks and antiquarks. Here, q

(

x

,

Q2

)

is the quark PDF for flavour q, Dh

q

(

z

,

Q2

)

denotes the FF that de-scribes the fragmentationof a quark offlavour q to a hadron of typeh,C

(

x

,

Q2

)

=

2

π α

2

₍

₁

_{+ (}

₁

₋

_y

₎

2

_)/

_Q4_and

_α

_isthefine struc-tureconstant.

2. Experimentalsetupanddataanalysis

Thedatawere takenin2006usingmuonsfromthe M2beam

lineoftheCERNSPS.Thebeammomentumwas160 GeV

/

c witha spreadof

±

5%.Thesolid-state6_{LiDtargetwaseffectivelyisoscalar,} with a small excess of neutrons over protons of about 0.2% due to the presence of additional material in the target (H, 3He and 7_{Li). The target was longitudinally polarised but in the present} analysis the data are averaged over the target polarisation. The

experimental setupusedthesametwo-stageCOMPASS

spectrom-eter[16] asdescribedinthe recentpublicationon thepion mul-tiplicitymeasurement[15].Forpion,kaonandprotonseparation, thering imagingCerenkov counter (RICH)was used.It wasfilled withC4F10 radiator gas leading to thresholds forpion,kaon and proton detection of about 2

.

9 GeV

/

c, 9 GeV

/

c and 18 GeV

/

c re-spectively. The central region from the RICH is excluded in the analysisinorderto avoidparticlescrossing thebeampipeinside theRICH.

The data analysisincludes event selection, particle identifica-tionandacceptancecorrection,aswell ascorrectionsforQED ra-diative effects anddiffractive vector-meson production. The kaon multiplicities MK

₍

_x

_,

_y

_,

_z

₎

_{aredeterminedfromthekaonyields N}K normalisedbythenumberofDISevents,NDIS_{,anddividedbythe} acceptancecorrection A: dMK

(

x

,

y

,

z

)

dz

=

1 NDIS

₍

_x

_,

_y

₎

dNK

(

x

,

y

,

z

)

dz 1 A

(

x

,

y

,

z

)

.

(3)

Here, y isused asa third variableinstead of Q2 _{becauseof the} strongcorrelationbetweenx and Q2 intheCOMPASSfixed-target kinematics.

2.1. Eventandhadronselection

The present analysis is based on events with inclusive trig-gers thatonly useinformation onthe scatteredmuon. Atotal of 13

×

106 DISeventswerecollectedforanintegratedluminosityof 0.54 fb−1_{.Thedatacoverawidekinematicrangeof1}

₍

_GeV

_/

_c

₎

2

_<

Q2

<

60

(

GeV

/

c

)

2,0

.

004

<

x

<

0

.

4 and W

>

5 GeV

/

c2.The rela-tivevirtual-photonenergy y isconstrainedtotherange0

.

1

<

y

<

resolutiondegradesandradiativeeffectsaremostpronounced. Fur-therconstraintson y arediscussed inSect.2.3.Fortheselection ofkaonsintheSIDISfinalstate,z isconstrainedto0

.

2

≤

z

≤

0

.

85.

The lower limit avoids the contamination from target remnant

fragmentation,whiletheupperlimitissettokeepthesamephase spaceaswasused forpions [15].Further constraintson momen-tumandpolarangleofhadronsarediscussedinSect.2.2.

The correctionsforhigher-orderQED effectsare calculatedon an event-by-eventbasis anddepend on x and y ata givenbeam energy. The correction factors are calculated separately for de-nominator and numerator of Eq. (3), i.e. for the number of DIS eventsandthe number ofkaons, respectively.The Dubna TERAD code[17]isusedfortheDIScorrectionfactor.Forthekaonyields, theTERADcorrectioniscalculatedexcludingtheelasticand quasi-elastictails.As TERADcannot account fora z dependence,which leads to an overestimate of the correction,23 _{a conservative}

ap-proach is adopted here. The correction is calculated for the two extremecases,nocorrection andfullcorrection tothenumberof kaonsenteringthenumerator;halfofthecorrectionisappliedto themultiplicities.Thisapproachleads toan overallcorrection be-tween1% and7% dependingonkinematics.

2.2. KaonidentificationusingtheRICHdetector

ThehadronidentificationusingtheRICHdetector[20]andthe unfolding procedure foridentified hadrons ofdifferent types fol-low the method described in Ref. [15]. Only the main features arerecalledhereforcompleteness.Amaximumlikelihoodmethod is used, based on the pattern of photons detected in the RICH detector. The likelihood values are calculated by comparing the measuredphoto-electronpatternwiththoseexpectedfordifferent masshypotheses (

π

,K, p), takingthedistribution of background photonsintoaccount.

Theyieldsofidentifiedhadrons,Ntrue,areobtainedbyapplying anunfolding algorithmtotheyields ofmeasuredhadrons, Nmeas, inordertocorrectfortheidentificationandmisidentification prob-abilities:

Ni_true

=



j

(

P−1

)

i j

·

Nmeasj

.

(4)

These probabilities are calculated in a matrix Pi j with i

,

j

∈

{

π

,

K

,

p

}

,whichcontainsasdiagonalelementstheefficienciesand asoff-diagonalelementsthemisidentificationprobabilities.The el-ementsof this3

×

3 matrix are constrained by



_jPi j

≤

1. They

aredeterminedfromdatausingsamplesof

π

,Kandpthat origi-natefromthedecayofK0_S,

φ

,and



respectively,intotwocharged particles.The probabilitiesdepend mostly onparticlemomentum phandpolarangle

θ

attheentranceoftheRICHdetector.The ph dependenceaccounts foreffects arising frommomentum thresh-olds (see the beginning of Sect. 2) and from saturation at high momentum(

β

→

1).The

θ

dependencethat accountsforvarying

occupancy and background levels in the RICH photon detectors

is weak, so that it is sufficient to divide in two the full polar angle region where the efficiencies are high and precisely mea-sured(10 mrad

< θ <

40 mrad and40 mrad

< θ <

120 mrad).In ordertoachieveexcellentkaon–pionseparationandhigh particle-identificationprobabilitiesforkaons,onlyparticleswithmomenta between 12 GeV

/

c and 40 GeV

/

c are selected. Fig. 1 shows the

23 _{Wealso estimatedtheradiative correctionsusingthe RADGENcode[18]} to-getherwiththe LEPTOgenerator,whicheffectivelyincorporatesa z dependence.

However,byincludingRADGENandLEPTOintheCOMPASSfullMCchainwewere notabletocorrectlydescribethedata.NotealsothatanauthorofRADGENadvises cautionwhenusingtheprogramtocorrectdifferentialcrosssectiondistributions forradiativeeffectsbeyondthe(x,y)dependence[19].

Fig. 1. Probabilities ofRICHidentificationofπ+,K+ andpasK+,shownversus momentumforthetwoθregions.

probabilitiesofpositivehadronstobeidentifiedasK+ vs momen-tum ph for the two

θ

regions. Kaons are identified with a 95%

efficiency over most of the momentum range with probabilities

to misidentifypionsandprotonsaskaonsbeingsmallerthan 3%. Similar values are obtained in the case of negative charge. The numberNK±

true ofidentifiedkaonsavailablefortheanalysisafterall particleidentificationcutsis2

.

8

×

106.

2.3. Acceptancecorrection

The overall correction forthe geometricand kinematic accep-tance of the COMPASS apparatus and for detector inefficiencies, resolutions and bin migration is evaluated using a Monte Carlo (MC)simulation.Agooddescriptionofthekinematicdistributions ofexperimental dataisobtainedusingthefollowingtoolsforthe MC simulation: LEPTO[21] for thegeneration ofDISevents, JET-SET [22] for hadronisation (tuning from Ref. [23]), GEANT3 [24]

for the description of the spectrometer and FLUKA [25] for sec-ondaryhadroninteractions.Theacceptancecorrectioniscalculated innarrowregionsof

(

x

,

y

,

z

)

,thusreducingthedependenceonthe choiceofthegeneratorusedinthesimulation.Itisdefinedasratio ofreconstructedandgeneratedmultiplicities:

A

(

x

,

y

,

z

)

=

dN

K

rec

(

x

,

y

,

z

)/

NDISrec

(

x

,

y

)

dNK

gen

(

x

,

y

,

z

)/

NDISgen

(

x

,

y

)

.

(5)

The generated kinematic variables are used for the generated

events, while the reconstructed kinematic variables are used for the reconstructedevents.The reconstructedMC hadronsare sub-jecttothesamekinematicandgeometric selectioncriteriaasthe data,whilethegeneratedhadronsaresubjecttokinematic require-mentsonly.Eventsgeneratedoutsidetheacceptancearetakeninto consideration. The average value of the acceptance correction is about65%.The acceptancecorrection isalmostflatin z,x and y, except athighx andlow y,butit isalways largerthan 35%.For eachbininz,they rangeforDISeventsisrestrictedtotheregion accessiblewithkaonmomentawithintherangefrom12 GeV

/

c to 40 GeV

/

c.

Fig. 2. Correction factorfornegativekaonmultiplicitiesduetodiffractiveproduction ofvectormesonφshownversusz forthreeQ2_regions.

2.4.Vectormesoncorrection

Forboth the DISand the kaon SIDISsamples, it is necessary toestimatethefractionofevents,inwhichdiffractivelyproduced vectormesonshavedecayedintolighterhadrons.Thisfractioncan beconsideredasahigher-twistcontributiontotheSIDIScross sec-tion[26].It cannotbe describedby thepQCD partonmodelwith theindependent-fragmentationmechanismthat isencodedinthe FFs. Hence FFs extracted fromdata includingthis fractionwould bebiasedandinparticulartheuniversalityprincipleofthemodel wouldbeviolated.The correctionfordiffractivevectormeson de-cayisappliedseparatelyintheDISandkaonsamples.MonteCarlo SIDISeventsthatarefreeofdiffractivecontributionsaresimulated usingLEPTO.Diffractiveproductionofexclusive

ρ

0_and

_φ

_eventsis simulatedusingHEPGEN [27],whilefurtherexclusive-meson pro-ductionchannelscharacterisedbysmallercrosssectionsandmore particlesinthefinal state arenottakenintoaccount. Vector me-sonproductionwithdiffractivedissociationofthetargetnucleonis alsosimulatedandrepresentsabout20%ofthecrosssectiongiven

byHEPGEN.

Anexampleofthecorrectionfactorcalculatedforthediffractive contributionof

φ

-mesondecayinto kaons, cφ_K− vsz, isshownin

Fig. 2 forthree different Q2 ranges. It varies between0

.

1% and 22% with the largest contribution appearing at small Q2 _{and z} closeto 0

.

6.Thecorrection toDISyields,cDIS vs Q2,isshownin

Fig. 3.Itisoftheorderofafewpercent. 2.5.Systematicuncertainties

Fortheevaluationofsystematicuncertaintiesthesamestudies arerepeatedastheywereperformedfortheanalysisofpions[15]

andsummarised here. A maximumuncertainty of4% on the

ac-ceptancecorrection isderivedfromthefollowingstudies:varying the PDF set used, varying the JETSET parameters, using a four-dimensionalspace(x

,

y

,

z

,

pT)withthehadrontransverse

momen-tum pT asfourthvariable,varyingthedetectorefficiencyapplied

intheMCsimulationused forthe acceptancecalculation,aswell ascomparingmultiplicity resultsfromupstreamanddownstream target regions. The RICH identification and unfolding procedure leadstouncertaintiestypicallybelow1

.

5%.Theuncertaintyonthe diffractivemesoncorrection factorisonaveragebelow1

.

5%;itis estimatedassuming 30% uncertainty on thecross section for ex-clusiveproductionof

φ

mesons [28], whichis usedto normalise

the HEPGEN MC calculation. Nuclear effects may be caused by

the presence of 3He/4He and 6Li in the target. A detailed study of such effects was previously performed by the EMC [29] in a

Fig. 3. Correction factor for DIS eventsdue to diffractiveproduction ofvector mesonsφandρ0_shownversusQ2_.

kinematicrange similar toCOMPASS one, forcarbon,copper and tin. A decreaseof the multiplicities of5% was observed for cop-per compared to deuterium. While the effect was larger fortin, no such effect was found for carbon within statistical accuracy, sothat possiblenucleareffectsinthepresentexperimentare ex-pectedto be verysmallandhenceneglected. The dependenceof theacceptanceontheazimuthal angleisnegligible[30].Notime dependence is observed in the results obtained in six weeks of datataking.Also,thepresentresultsarefoundinagreementwith an independent setofpreliminary datatakenin 2004before the upgradeofthespectrometer.Wechosetopublishonlythepresent set ofdata, whichis ofbetter quality and benefitsfrom alarger spectrometeracceptanceandanupgradedRICHdetector.

Inaddition,a conservativeestimate of100% systematic uncer-taintyisassumedforthecorrectionsforhigher-orderQEDeffects. Thiscorrespondstoa1% to7% systematicuncertaintyonthe mul-tiplicities.

Allthesecontributionsareaddedinquadratureandyielda to-talsystematicuncertainty,

σ

syst,whichvariesbetween5% and10%

depending onkinematics.Itisgenerallylargerthanthestatistical oneatlowz,whereasathigherz thestatisticaluncertainty domi-nates.

Fromthetotalsystematicuncertaintya largefraction,0

.

8

σ

syst,

is estimatedtobe correlated frombinto bin,andthe remaining fraction,



(

1

−

0

.

82

₎

_σ

_{syst,isuncorrelated.}

3. Resultsforcharged-kaonmultiplicities

The results for K+ and K− multiplicities represent a total of 618 experimental data points. In this section, results are shown first in theinitial three-dimensional (x, y, z) binning, then aver-aged in y, and eventually also integrated over the z range from 0

.

2 to0

.

85 inordertocalculatethesumandratioofK+ andK− multiplicitiesvs x.Thedatapresentedinthefollowingfiguresare all corrected for the diffractive vector-meson contribution as de-scribed in Sect. 2.4. For completeness, the numerical values are availableonHepData[31]formultiplicitieswithandwithoutthis correction.TheseparatecorrectionfactorsforDISandkaonyields arealsoprovided,asare thefactorsusedforthecorrectionof ra-diative effects.The binlimitsin x, y, andz are givenin Table 1. The Q2 _{values rangefrom1}

₍

_GeV

_/

_c

₎

2 _{atthe smallestx toabout} 60

(

GeV

/

c

)

2 _{at the largest x,with}

_

_Q2

_

₌

₃

₍

_GeV

_/

_c

₎

2_{. In Figs. 4}

and 5, the results for the z and y dependences of the K+ and K−multiplicitiesarepresentedseparatelyfortheninerangesin x. Statistical uncertainties are shown forall points, while the band

Table 1

Lowerandupperbinlimitsforthe(x,y,z)binning. Bin limits

x 0.004 0.01 0.02 0.03 0.04 0.06 0.1 0.14 0.18 0.4

y 0.1 0.15 0.2 0.3 0.5 0.7

z 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.85

Fig. 4. Multiplicities forK+ shownvsz fortheninex rangesandthefivey ranges,addingaconstantαforbettervisibility.Thebandcorrespondstothetotalsystematic uncertaintyfortherange0.30<y<0.50.

Fig. 6. Positive (closed) and negative (open) kaon multiplicities vs z for the nine x ranges. The bands correspond to the total systematic uncertainties.

Fig. 7. Ratio of multiplicities(dMK+_/dz)/(dMK−_{/dz)vs z for the nine x ranges. The bands correspond to the total systematic uncertainties.}

onthebottomoftheplotsillustratesthesizeofthetotal system-aticuncertaintyfora single y range(0.30–0.50).Forthe other y ranges, the bands are similar or smaller in size. In Fig. 6, mul-tiplicities of positive (closed circles) and negative (open circles) charged kaons are shownvs z, separately forthe nine x ranges butaveraged over y. The error bars correspond to the statistical uncertaintiesandthebandstothetotalsystematicones.Astrong

dependence on z is observed as in previous measurements [26]

anda weakone onx.The multiplicitiesare systematicallyhigher

for K+ as compared to K− because of u-quark dominance and

sinceK−donotcontainvalencequarksfromthenucleon. InFig. 7,wepresenttheratioRK+/K−

_{= (}

_dMK+

_/

_dz

_)/(

_dMK−

_/

_dz

₎

vs z in the nine x ranges. In this ratio, most of the systematic uncertaintiescancel,includingtheoneonradiativecorrections,so

thatitprovidesabenchmarkforfutureNLOfits.Asteepriseinz isobserved.

Sinceanimportantgoalofthemeasurementofkaon multiplic-itiesisthedeterminationofquark-to-kaonFFs,thesumofpositive and negative charged-kaon multiplicities is of special interest. It was usedby HERMES[13] foraLOpQCD extractionofthe prod-uctofthestrangequarkPDFandthestrangequark-to-kaonFF.For theCOMPASSkinematics,theapplicabilityoftheLOpQCD formal-ism to pionmultiplicities was alreadydemonstrated [15]. Foran isoscalar target and assuming isospin and charge symmetry, the sumof K+ and K− multiplicities can be written in LOin avery simpleway[32].

Formultiplicitiesintegratedoverz,

M

K±

₌



_

_MK±

₍

_x

_,

_y

_,

_z

₎

_

ydz,

Fig. 8. Sum ofz-integratedmultiplicities,MK+_{+ M}K−_{.COMPASSdata(160 GeV,} fullpoints)arecomparedtoHERMESdata[13](27.5 GeV,openpoints)(seetext). Thebandsshowthetotalsystematicuncertainties.

M

K+

₊

_M

K−

₌

U

D

UK

+

S

D

KS

5U

+

2S

,

(6)

with U

=

u

+ ¯

u

+

d

+ ¯

d, and S

=

s

+ ¯

s. The z-integrated FFs,

D

K

₍

_Q2

₎

₌



_DK

₍

_z

_,

_Q2

₎

_{dz, depend on Q}2 _{only. The symbols}

_D

K

U

and

D

K

S denote the combinations of FFs

D

UK

=

4

D

K

+ u

+

4

D

K + ¯ u

+

D

K+ d

+

D

K+ ¯ d and

D

K S

=

2

D

K + s

+

2

D

K + ¯

s . At high values of x, the strange content of the nucleon can be neglected, and in a good approximation the sumofK+ andK− multiplicities is relatedto

D

K

U

/

5. This value is expected to have a rather weak Q2

depen-dencewhenintegratedoverz,sothatitcanbeusedatsmaller val-uesofx todeterminetheS

D

K_S value.Theresultfor

M

K+

₊

_M

K− _is presentedinFig. 8asafunctionofx atthemeasuredvaluesof Q2. Thedataareintegratedoverz in therange0.20to0.85and aver-agedover y intherange0.1to0.7.Onlythoseeightx binswhich

havea sufficient z coverageare shown. A weak x dependence is

observed. Fig. 8 also shows the HERMES results [13] that were takenat27.5 GeV beamenergyandcorrespond todifferent kine-maticsinparticularacceptinglower W values.Theyliewellbelow theCOMPASSpointsandexhibitadifferentx behaviour.Thex de-pendence oftheHERMES results forpionandkaonmultiplicities gaverisetosomedispute[33–35].NotethatCOMPASS multiplici-tiesarecomputedinbinsof(x

,

y

,

z)beforeintegrationoverz and

averaging over y while in the case of HERMES, the hadron and

DISyields areobtainedandintegratedoverseparately,andfinally combinedinaratiodependingonx only[35].

From the COMPASS result on

M

K+

₊

_M

K− _{at high x (x}

₌

0

.

25)weextract

D

_UK

≈

0

.

65–0

.

70,dependinguponassumptionson strangequarkPDFsandFFs.ThisdiffersfromtheearlierDSSfit re-sultat Q2

=

3

(

GeV

/

c

)

2,

D

_UK

=

0

.

43

±

0

.

04[9],whichwasmainly based onpreliminary HERMES results. The latter differed signifi-cantlyfromthepublishedones[13].Towardslowx,COMPASSdata showaflatbehaviour,unliketherisethatissuggestedbythe HER-MESdataandtheDSSFFparametrisation[9].

Anotherquantity ofinterest is the x dependence of the mul-tiplicityratio

M

K+

/M

K−,inwhichmostexperimentalsystematic effectscancel.The resultsare shownin Fig. 9 asafunction of x. Intheregionofoverlap,COMPASSresultsarefoundtobe system-aticallylower than those ofHERMES. In contrast,for thecaseof pionsCOMPASSandHERMESmultiplicityratiosarefoundingood agreement[15].

4. Summaryandconclusions

Preciseresultsforcharged-kaonmultiplicitiesareobtainedfrom

kaon SIDIS measurements using a muon beam scattering off an

Fig. 9. Ratio ofz-integratedmultiplicities,MK+_/MK−_{.COMPASSdata(160 GeV,} fullpoints)arecomparedtoHERMESdata[26](27.5 GeV,openpoints).Thebands showthetotalsystematicuncertainties.

isoscalartarget.Thedataaregiveninathree-dimensionalx,y,and z binning andcover awide kinematicrange:1

(

GeV

/

c

)

2

_<

_Q2

_<

60

(

GeV

/

c

)

2, 10−3

<

x

<

0

.

4,0

.

1

<

y

<

0

.

7, and0

.

20

<

z

<

0

.

85 withW

>

5 GeV

/

c2.Theyconstituteanimportantinputforfuture world-data analysesinorderto constrainstrangequark PDFsand FFs.ThesumofK+ andK− multiplicitiesintegratedover z shows aflatdistributioninx,withvaluessignificantlyhigherthanthose measuredbyHERMESatlowerenergy.Bycoveringlowerx values, themultiplicity sumdatawillsignificantlyimprovetheconstraint ontheproductofthestrangequarkPDFandFF, S

D

_SK.Thepresent resultpointstoalargervalueof

D

_UKthanobtainedfromtheearlier DSSfit.

Acknowledgements

We gratefully acknowledge the support of theCERN

manage-ment and staffand theskill andeffort ofthe technicians of our collaboratinginstitutes.Thisworkwasmadepossiblebythe finan-cialsupportofourfundingagencies.

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