Multiplicities of charged pions and charged hadrons from deep-inelastic scattering of muons off an isoscalar target

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Multiplicities

of

charged

pions

and

charged

hadrons

from

deep-inelastic

scattering

of

muons

off

an

isoscalar

target

C. Adolph

i

, M. Aghasyan

z

,

R. Akhunzyanov

h

, G.D. Alexeev

h

,

M.G. Alexeev

ab

,

A. Amoroso

ab

,

ac

,

V. Andrieux

v

, N.V. Anfimov

h

,

V. Anosov

h

, K. Augsten

h

,

t

,

W. Augustyniak

ae

,

A. Austregesilo

q

,

C.D.R. Azevedo

b

, B. Badełek

af

,

F. Balestra

ab

,

ac

,

J. Barth

e

,

R. Beck

d

, Y. Bedfer

v

, J. Bernhard

n

,

k

,

K. Bicker

q

,

k

, E.R. Bielert

k

,

R. Birsa

z

,

J. Bisplinghoff

d

,

M. Bodlak

s

,

M. Boer

v

,

P. Bordalo

m

,

1

,

F. Bradamante

y

,

z

,

C. Braun

i

,

A. Bressan

y

,

z

,

M. Büchele

j

, L. Capozza

v

, W.-C. Chang

w

,

C. Chatterjee

g

, M. Chiosso

ab

,

ac

,

I. Choi

ad

,

S.-U. Chung

q

,

2

,

A. Cicuttin

aa

,

z

,

M.L. Crespo

aa

,

z

,

Q. Curiel

v

, S. Dalla Torre

z

,

S.S. Dasgupta

g

,

S. Dasgupta

y

,

z

,

O.Yu. Denisov

ac

,

∗

, L. Dhara

g

,

S.V. Donskov

u

,

N. Doshita

ah

,

V. Duic

y

,

W. Dünnweber

3

,

M. Dziewiecki

ag

,

A. Efremov

h

, P.D. Eversheim

d

,

W. Eyrich

i

,

M. Faessler

3

, A. Ferrero

v

,

M. Finger

s

,

M. Finger jr.

s

,

H. Fischer

j

,

C. Franco

m

,

N. du Fresne von Hohenesche

n

, J.M. Friedrich

q

, V. Frolov

h

,

k

,

E. Fuchey

v

,

F. Gautheron

c

,

O.P. Gavrichtchouk

h

,

S. Gerassimov

p

,

q

,

F. Giordano

ad

,

I. Gnesi

ab

,

ac

,

M. Gorzellik

j

,

S. Grabmüller

q

,

A. Grasso

ab

,

ac

,

M. Grosse Perdekamp

ad

,

B. Grube

q

, T. Grussenmeyer

j

,

A. Guskov

h

,

F. Haas

q

, D. Hahne

e

,

D. von Harrach

n

,

R. Hashimoto

ah

,

F.H. Heinsius

j

,

R. Heitz

ad

,

F. Herrmann

j

,

F. Hinterberger

d

,

N. Horikawa

r

,

4

,

19

, N. d’Hose

v

,

C.-Y. Hsieh

w

,

5

,

S. Huber

q

,

S. Ishimoto

ah

,

6

_,

_{A. Ivanov}

ab

,

ac

_,

_{Yu. Ivanshin}

h

_,

_{T. Iwata}

ah

_,

_{R. Jahn}

d

_,

_{V. Jary}

t

_,

R. Joosten

d

, P. Jörg

j

,

E. Kabuß

n

,

B. Ketzer

d

,

G.V. Khaustov

u

,

Yu.A. Khokhlov

u

,

7

,

8

,

Yu. Kisselev

h

,

F. Klein

e

, K. Klimaszewski

ae

,

J.H. Koivuniemi

c

,

V.N. Kolosov

u

, K. Kondo

ah

,

K. Königsmann

j

,

I. Konorov

p

,

q

,

V.F. Konstantinov

u

, A.M. Kotzinian

ab

,

ac

,

O.M. Kouznetsov

h

,

M. Krämer

q

, P. Kremser

j

,

F. Krinner

q

,

Z.V. Kroumchtein

h

,

R. Kuhn

q

,

Y. Kulinich

ad

,

F. Kunne

v

, K. Kurek

ae

,

R.P. Kurjata

ag

,

A.A. Lednev

u

,

A. Lehmann

i

,

M. Levillain

v

,

S. Levorato

z

,

Y.-S. Lian

w

,

9

,

J. Lichtenstadt

x

,

R. Longo

ab

,

ac

,

A. Maggiora

ac

,

A. Magnon

v

,

N. Makins

ad

,

N. Makke

y

,

z

_,

_{G.K. Mallot}

k

,

∗

_,

_{C. Marchand}

v

_,

_{B. Marianski}

ae

_,

_{A. Martin}

y

,

z

_,

J. Marzec

ag

,

J. Matoušek

s

,

z

, H. Matsuda

ah

,

T. Matsuda

o

,

G.V. Meshcheryakov

h

,

M. Meyer

ad

,

v

,

W. Meyer

c

,

T. Michigami

ah

,

Yu.V. Mikhailov

u

, M. Mikhasenko

d

,

E. Mitrofanov

h

,

N. Mitrofanov

h

, Y. Miyachi

ah

,

P. Montuenga

ad

,

A. Nagaytsev

h

,

F. Nerling

n

,

D. Neyret

v

, V.I. Nikolaenko

u

,

J. Nový

t

,

k

,

W.-D. Nowak

n

,

G. Nukazuka

ah

,

A.S. Nunes

m

,

A.G. Olshevsky

h

,

I. Orlov

h

,

M. Ostrick

n

,

D. Panzieri

a

,

ac

,

B. Parsamyan

ab

,

ac

,

S. Paul

q

,

J.-C. Peng

ad

, F. Pereira

b

,

M. Pešek

s

, D.V. Peshekhonov

h

,

N. Pierre

n

,

v

, S. Platchkov

v

,

J. Pochodzalla

n

,

V.A. Polyakov

u

, J. Pretz

e

,

10

_,

_{M. Quaresma}

m

_,

_{C. Quintans}

m

_{, S. Ramos}

m

,

1

_,

C. Regali

j

,

G. Reicherz

c

,

C. Riedl

ad

,

M. Roskot

s

, N.S. Rossiyskaya

h

,

D.I. Ryabchikov

u

,

8

,

A. Rybnikov

h

,

A. Rychter

ag

, R. Salac

t

,

V.D. Samoylenko

u

,

A. Sandacz

ae

,

C. Santos

z

,

S. Sarkar

g

,

I.A. Savin

h

,

T. Sawada

w

,

G. Sbrizzai

y

,

z

,

P. Schiavon

y

,

z

,

K. Schmidt

j

,

11

,

H. Schmieden

e

,

K. Schönning

k

,

12

,

S. Schopferer

j

,

E. Seder

v

,

∗

,

A. Selyunin

h

,

O.Yu. Shevchenko

h

,

22

,

L. Silva

m

,

L. Sinha

g

,

S. Sirtl

j

, M. Slunecka

h

,

J. Smolik

h

,

F. Sozzi

z

,

*

Correspondingauthors.

E-mailaddresses:[email protected](O.Yu. Denisov),[email protected](G.K. Mallot),[email protected](E. Seder).

http://dx.doi.org/10.1016/j.physletb.2016.09.042

A. Srnka

f

, D. Steffen

k

,

q

,

M. Stolarski

m

,

M. Sulc

l

,

H. Suzuki

ah

,

4

,

19

,

A. Szabelski

ae

,

T. Szameitat

j

,

11

,

P. Sznajder

ae

,

S. Takekawa

ab

,

ac

,

M. Tasevsky

h

, S. Tessaro

z

,

F. Tessarotto

z

,

F. Thibaud

v

,

F. Tosello

ac

,

V. Tskhay

p

,

S. Uhl

q

,

J. Veloso

b

,

M. Virius

t

, J. Vondra

t

,

T. Weisrock

n

,

M. Wilfert

n

,

R. Windmolders

e

, J. ter Wolbeek

j

,

11

, K. Zaremba

ag

, P. Zavada

h

,

M. Zavertyaev

p

, E. Zemlyanichkina

h

,

N. Zhuravlev

h

,

M. Ziembicki

ag

, A. Zink

i

a_{UniversityofEasternPiedmont,15100Alessandria,Italy}

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

c_{UniversitätBochum,InstitutfürExperimentalphysik,44780Bochum,Germany}13,14

d_{UniversitätBonn,Helmholtz-InstitutfürStrahlen- undKernphysik,53115Bonn,Germany}13

e_{UniversitätBonn,PhysikalischesInstitut,53115Bonn,Germany}13

f_{InstituteofScientificInstruments,ASCR,61264Brno,CzechRepublic}15

g_{MatrivaniInstituteofExperimentalResearch&Education,Calcutta-700030,India}16

h_{JointInstituteforNuclearResearch,141980Dubna,Moscowregion,Russia}17

i_{UniversitätErlangen–Nürnberg,PhysikalischesInstitut,91054Erlangen,Germany}13

j_{UniversitätFreiburg,PhysikalischesInstitut,79104Freiburg,Germany}13,14

k_{CERN,1211Geneva23,Switzerland}

l_{TechnicalUniversityinLiberec,46117Liberec,CzechRepublic}15

m_{LIP,1000-149Lisbon,Portugal}18

n_{UniversitätMainz,InstitutfürKernphysik,55099Mainz,Germany}13

o_{UniversityofMiyazaki,Miyazaki889-2192,Japan}19

p_{LebedevPhysicalInstitute,119991Moscow,Russia}

q_{TechnischeUniversitätMünchen,PhysikDepartment,85748Garching,Germany}13,3

r_{NagoyaUniversity,464Nagoya,Japan}19

s_{CharlesUniversityinPrague,FacultyofMathematicsandPhysics,18000Prague,CzechRepublic}15

t_{CzechTechnicalUniversityinPrague,16636Prague,CzechRepublic}15

u_{StateScientificCenterInstituteforHighEnergyPhysicsofNationalResearchCenter‘KurchatovInstitute’,142281Protvino,Russia} v_{CEAIRFU/SPhNSaclay,91191Gif-sur-Yvette,France}14

w_{AcademiaSinica,InstituteofPhysics,Taipei11529,Taiwan}

x_{TelAvivUniversity,SchoolofPhysicsandAstronomy,69978TelAviv,Israel}20

y_{UniversityofTrieste,DepartmentofPhysics,34127Trieste,Italy} z_{TriesteSectionofINFN,34127Trieste,Italy}

aa_{AbdusSalamICTP,34151Trieste,Italy}

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

ad

UniversityofIllinoisatUrbana-Champaign,DepartmentofPhysics,Urbana,IL61801-3080,USA ae_{NationalCentreforNuclearResearch,00-681Warsaw,Poland}21

af_{UniversityofWarsaw,FacultyofPhysics,02-093Warsaw,Poland}21

ag_{WarsawUniversityofTechnology,InstituteofRadioelectronics,00-665Warsaw,Poland}21

ah_{YamagataUniversity,Yamagata992-8510,Japan}19

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory: Received15April2016

Receivedinrevisedform17September 2016

Accepted23September2016 Availableonline28September2016 Editor:M.Doser

Keywords:

Deepinelasticscattering Pionmultiplicities Fragmentationfunctions

Multiplicitiesofchargedpionsandchargedhadronsproducedindeep-inelasticscatteringweremeasured in three-dimensionalbins ofthe Bjorken scaling variable x,the relative virtual-photonenergy y and

therelativehadronenergyz.DatawereobtainedbytheCOMPASSCollaborationusinga160GeV muon beamand an isoscalartarget (6_{LiD).They coverthekinematic domaininthe photon virtuality Q}2_>

1(GeV/c)2_{,0.004<x<0.4,0.2<z<0.85 and0.1<y<0.7.Inaddition,aleading-orderpQCDanalysis}

wasperformedusingthepionmultiplicityresultstoextractquarkfragmentationfunctions.

©2016TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

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

1. Introduction

Hadron production in semi-inclusive measurements of deep-inelasticlepton–nucleonscattering(SIDIS)isoneofthemost pow-erfultools toinvestigate thestructure andformation of hadrons. Withinthestandardframeworkofleading-twistperturbative QCD (pQCD), factorisation theorems [1] allow one to write the SIDIS cross section as a convolution of hard scattering cross sections, whichare calculable in pQCD, withnon-perturbative Parton Dis-tributionFunctions(PDFs)andFragmentationFunctions (FFs).The PDFsaccount forthe partonic structure ofhadrons in the initial state. The FFs encode the details aboutthe hadronisation mech-anism that describes the transition from final-state partons into colour-neutral hadrons. Both types of functions are believed to be universal, i.e. process independent, andcan be interpreted in leading-order (LO) as number densities. While PDFs have been studied in detail for severaldecades and are hence known with goodprecision,newaccuratemeasurementsarenecessaryto con-strain the FFs. In what follows, we will restrict ourselves to transverse-momentum-integratedPDFsandFFs.

Theuniversality ofFFs allows their determinationfrom differ-enthigh-energyprocesses,whichprovidecomplementary

informa-tion on the hadronisation mechanism and cover complementary

kinematicranges.Thestudyofhadronproductionintheelectron– positronannihilationprocessisparticularlywellsuitedbecauseits cross section has no dependence on parton densities and gives directaccesstoFFs.Measurementscoverawiderangeinthe char-acteristichard scale, from10GeV for recentdata fromBELLE [2]

and BaBar [3] to 100GeV at the Z boson mass at LEP [4] and

SLAC [5], at which only the singlet combination ofFFs is acces-sible. In spite of the high precision, these e+e− data cannot be usedto disentangle quarksfrom anti-quarks,as they onlyaccess thesum ofquark andantiquark FFs and hencedo not allow for afullflavourseparation.HadronmultiplicitydatafromSIDIS pro-videchargeandfullflavourseparationoffragmentationfunctions. TheSIDISdatafromfixed targetexperiments explore characteris-tichardscales downto1GeV.Thelargekinematicrangespanned bythe mentionedreactions allowsone tostudyQCD scaling vio-lations,whichalsoconstrainsthegluonFF. Thelatterisindirectly probed by hadron–hadron collisions, e.g. at RHIC [6], via single-inclusivehadronproductionathightransversemomentum[7].

Thepresentpaper reportsonCOMPASSmeasurements of mul-tiplicitiesofchargedpionsandchargedhadrons.The(x,Q2_)range covered by the COMPASS dataextends to much higher valuesof Q2_{andisshiftedtolowervaluesofx whencomparedtotheone} of HERMES [8], while the kinematic range is similar to the one coveredbyEMC[9].

The process lN

→

lhX is described by the negative square of the four-momentum transfer Q2

= −

q2, the Bjorken variable x

= −

q2

_/(

_2P

_·

_q

₎

_{and the fraction of the virtual-photon energy} thatiscarriedby thefinal-statehadron, z

= (

P

·

ph

)/(

P

·

q

)

.Here, q

=

k

−

k, P and phdenotethefour-momentaofthevirtual pho-ton,the nucleonN andthe observedhadron h respectively, with

15 _{SupportedbyCzechRepublicMEYSGrantLG13031.} 16 _{SupportedbySAIL(CSR),Govt.ofIndia.}

17 _{SupportedbyCERN-RFBRGrant12-02-91500.}

18 _{Supportedby the Portuguese FCT – Fundaçãopara a Ciênciae Tecnologia,}

COMPETEandQREN,GrantsCERN/FP109323/2009,116376/2010,123600/2011and CERN/FIS-NUC/0017/2015.

19 _{Supported by the MEXT and the JSPS under the Grants No. 18002006,}

No. 20540299andNo. 18540281;DaikoFoundationandYamadaFoundation.

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

k (k) thefour momentumofthe incident (scattered)lepton. Ad-ditional variables used are the lepton energy fraction carried by the virtual photon, y

= (

P

·

q

)/(

P

·

k

)

,and the invariant mass of the final hadronicsystem, W

=



(

P

+

q

)

2_{. Inorder tostudy the} hadronisation mechanismin SIDIS, therelevant observable is the differential multiplicity forhadronsofa specific type h,which is definedasthedifferentialcrosssectionforhadronproduction nor-malisedtothedifferentialinclusiveDIScrosssection:

dMh

(

x

,

z

,

Q2

)

dz

=

d3

σ

h

₍

_x

_,

_z

_,

_Q2

_)/

_dxdQ2_dz

d2

_σ

DIS

₍

_x

_,

_Q2

_)/

_dxdQ2

.

(1)

InterpretedinpQCD,thecrosssectionsontheright-handsideare expressedintermsofPDFsandFFsandreadatleading-order(LO)

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)

Here,C

(

x

,

Q2

)

=

2

π α

2

₍

₁

_{+ (}

₁

₋

_y

₎

2

_)/

_Q4_with

_α

_{thefinestructure} constant,q

(

x

,

Q2

₎

_{isthequarkPDFfortheflavourq andD}h

q

(

z

,

Q2

)

thequark-to-hadronFF. InLO, Dh

q denotesthenumberdensityof hadronshproducedinthehadronisationofpartonsofspeciesq.

2. TheCOMPASSexperiment

In this Section a short description of the experimental set-up is given, while a more detailed description can be found in Ref.[10].Themeasurementwasperformedin2006withthe natu-rallypolarisedmuon beamoftheCERNSPSusingpositivemuons of160GeV

/

c.Thebeammomentumhadaspreadof5%.The inten-sitywas4

×

107_s−1_{withspillsof4}

_.

_{8s andacycletimeof16}

_.

_8s.

Themomentumofeachincomingmuonwasmeasuredbeforethe

COMPASS experimentwith a precision of0.3%. Before the target, thetrajectoryofeachincomingmuonwasmeasuredinasetof sil-icon andscintillating fibredetectorswithaprecision of0

.

2mrad. The muons were impinging on a longitudinally polarised solid-statetarget positionedinsidealargeaperturesolenoid.Thetarget consistedof three cells, whichwere located along the beamone aftertheother andfilledwith6LiDimmersedinaliquid3He/4He mixture.The admixturesof H, 3Heand7Liintheisoscalartarget leadtoaneffectiveexcessofneutronsofabout0.2%.Thedirection ofthepolarisation inthe60cm longmiddle cellwas oppositeto thatinthetwo 30cm longouter cellsandwasreversedonceper day.Intheanalysis,thedataareaveragedoverthetarget polarisa-tionforthedeterminationofmultiplicities.

Fig. 1. (x, Q2_{) range of the selected DIS sample.}

based on pairs of hodoscopes, selected scatteredmuons above a minimumscatteringangle.

3. Dataanalysis

The data analysis includes eventselection, particle identifica-tion(PID),acceptancecorrectionaswellascorrectionsforradiative effectsanddiffractivevectormesonproduction.Differential multi-plicities are determined in 3-dimensional(x, y, z) bins fromthe acceptance-correctedhadronyields Nhnormalisedbythenumber ofDISevents,NDIS_:

dMh

(

x

,

y

,

z

)

dz

=

1 NDIS

₍

_x

_,

_y

₎

dNh

(

x

,

y

,

z

)

dz 1 A

(

x

,

y

,

z

)

.

(3)

The acceptance correction factor A takes into account the lim-itedgeometric andkinematicacceptanceofthespectrometer and the efficiencyof eventreconstruction. The choice of the z and x variablesisnaturalbecausemultiplicitiesdependmostly onthese variables.Becauseof thestrongcorrelation betweenx and Q2 in theCOMPASSfixed-targetkinematics,itappearsmoreappropriate touse y insteadofQ2 _{asthethirdvariable.}

3.1. Eventandhadronselection

The present analysis is based on events with inclusive trig-gers that use only informationon the scattered muons. Selected eventsarerequiredtohavea reconstructedinteractionvertex as-sociatedtoanincidentandascatteredmuontrack.Thisvertexhas tolieinsidethefiducialtarget volume.Theincident muonenergy isconstrained tothe interval

[

140

,

180

]

GeV. Events are accepted if Q2

>

1

(

GeV

/

c

)

2,0

.

004

<

x

<

0

.

4 and W

>

5GeV

/

c2.These re-quirementsselectthedeep-inelasticscatteringregimeandexclude the nucleon resonanceregion. The relative virtual-photon energy is constrained to the range 0

.

1

<

y

<

0

.

7 to exclude kinematic regions where the momentum resolution degradesand radiative effectsare mostpronounced. Thenumberof inclusiveDISevents selected forthis analysisis 13

×

106_{,corresponding to an} inte-gratedluminosityof0.54 fb−1 _{(forthecovered(x, Q}2_)range,see

Fig. 1).

For a selected DIS event, all reconstructed tracks are consid-ered.Hadrontracksmustbedetectedintrackingdetectorsplaced before and after the magnet in the first stage of the spectrom-eter. The fraction of the virtual-photon energy transferred to a final-statehadronisconstrainedto0

.

2

≤

z

≤

0

.

85,wherebyforan unidentifiedchargedhadronthepionmassisassumed.Thelower limit avoids the contamination from target remnant fragmenta-tion, while the upper one excludesmuons wrongly identified as

hadrons,anditalsoexcludestheregionwithlargediffractive con-tributions. Further constraints on momentum andpolar angle of thehadronsaswellason y arediscussedbelow.

The correctionsforhigher-orderQEDeffectsareappliedonan event-by-event basis taking into account the target composition. For NDIS

₍

_x

_,

_y

₎

_{they are computed according to the scheme} de-scribed in Ref. [12]. For dNh

(

x

,

y

,

z

)

the elastic and quasielastic radiativetailsaresubtractedfromthecorrection.The z-integrated radiativecorrectionfactorforthemultiplicitiesisalwaysbelow5%. A possible z dependenceofradiativecorrectionsisneglected. 3.2. HadronidentificationusingtheRICHdetector

Particleidentification(PID)isperformedusingtheRICH detec-tor [13]. The identificationprocedure relies ona likelihood func-tion,whichisbaseduponthenumberanddistributionofphotons thataredetectedintheRICHdetectorandassociatedtoacharged particletrajectory.Thelikelihoodvaluesarecalculatedby compar-ingthemeasuredphoto-electronpatternwiththeoneexpectedfor differentmasshypotheses(

π

,K,p),takingthedistributionof back-groundphotonsintoaccount.Themassisassignedtothedetected hadron choosingthehypothesis withthemaximumlikelihood.In order to improve the separation between the different mass hy-potheses andthusthe sample purity, constraintsare imposed on theratiosofthemaximumovertheotherlikelihoodvalues.

The purity of the identified hadron samples depends on the probabilities of correct identification and misidentification. The truehadronyieldsNtrue areobtainedbyapplyinganunfolding al-gorithmtothemeasuredhadronyieldsNmeas:

N_truei

=



j

(

P−1

)

i j

·

Nmeasj

.

(4)

The RICH PID matrix P contains as diagonal elements the

effi-ciencies andas off-diagonalelements the misidentification prob-abilities. The elements of this 3

×

3 matrix are constrained by



jPi j

≤

1, wherei

,

j

= {

π

,

K

,

p

}

.They aredetermined fromreal

datausingsamplesof

π

,KorporiginatingfromthedecayofK0_S,

φ

or



into two charged particles. The dependence of the RICH performance on theparticle momentum ph andpolarangle

θ

at the RICHentranceistakenintoaccount bydeterminingthe RICH PID matrix in2-dimensional bins of thesevariables. The ph de-pendence accountsforeffectsarising frommomentum thresholds forparticleidentificationandfromsaturationathighmomentum. The

θ

dependenceaccountsforvaryingoccupancyandbackground level in the RICH photon detectors. The polar angle is selected in the range 10mrad

< θ <

120mrad, where the efficiencies are highandpreciselymeasured.The

θ

dependenceofPi j isrelatively

weak, so that two binsare sufficientin the analysis. In order to achievegoodpion–kaonseparationandhighparticleidentification probabilitiesforkaonsandpions,momentabetween12GeV

/

c and 40GeV

/

c are used. In this range,the momentum dependence of theprobabilitiesof

π

+,K+andptobeidentifiedas

π

+isshown in Fig. 2 for the lower

θ

bin in 10 momentum bins. Pions are identifiedwith98%efficiencyupto30GeV

/

c,wheretheefficiency starts to decrease.The probability to misidentify kaons and pro-tonsaspionsisbelow2%and6%,respectively,overalltheselected momentum range.Similar valuesare obtainedfor

π

−. The num-ber Nπ_true± ofidentifiedpionsavailable fortheanalysisafterallPID cutsis3.4

×

106_{.Withoutlikelihoodcuts,thenumberofcharged} hadronsis4.6

×

106_.

3.3. Acceptancecorrection

Fig. 2. ProbabilitiesofRICHidentificationofπ+,K+andpasaπ+versus momen-tumforthesmallerθbin10mrad< θ <40mrad.Statisticaluncertaintiesarelower thanthesizeofthesymbols.

detectorinefficiencies,resolutionsandbinmigration.Thefull cor-rectionis evaluated using a Monte Carlo(MC) simulation of the muon–nucleondeep-inelasticscatteringprocess.Eventsare gener-atedwiththeLEPTO

[14]

generator,where theparton hadronisa-tionmechanismis simulatedusing theJETSETpackage

[15]

with thetuningfromRef.[16].Thespectrometerissimulatedusingthe GEANT3toolkits[17],andtheMCdataarereconstructedwiththe same software as the experimental data [10]. Secondary hadron interactionsaresimulatedusingtheFLUKApackage[18].The kine-maticdistributionsoftheexperimentaldataarereproducedwithin 5%by theMCsimulationwithdifferencesgoingup to10%atthe edges.

Inordernot to introducea strongdependence onthe physics generatorusedinthe simulation,theextractionof hadron multi-plicities isperformedin narrow kinematicbins of x, y and z.In each(x,y,z)bin,theacceptancecorrectioniscalculatedfromthe ratioofreconstructedandgeneratedmultiplicitiesaccordingto

A

(

x

,

y

,

z

)

=

dN

h

rec

(

x

,

y

,

z

)/

NrecDIS

(

x

,

y

)

dNhgen

(

x

,

y

,

z

)/

NDISgen

(

x

,

y

)

.

(5)

Thegeneratedkinematicvariablesareusedforthegenerated par-ticles,whilethereconstructedkinematicvariablesareusedforthe reconstructedparticles.Afterreconstruction, all particlesare sub-jecttothesamekinematicandgeometricselectioncriteriaasthe data,while the generated onesare subject to kinematic require-mentsonly.Atthisplace,thecorrectionforpossible misidentifica-tionofelectronsaspionsisincludedintheacceptancecorrection. The average value of the acceptance correction is about 70% for y

<

0

.

3 andabout50%fory

>

0

.

3.Theacceptancecorrectionis al-mostflatinz andx,exceptathighy andlowx,andalwayslarger than40%. Generatedhadrons arelost mainly by secondary inter-actions inthe long solid-statetarget, due totrack reconstruction inefficiency andbecauseof constraintsrequired forRICH particle identification.

Withthehadron momentumcut, the y rangeismorelimited forthehadronsample thanfortheDISsample.Thusforeachbin in z,the y range isrestricted to the kinematicregion accessible withhadronmomentabetween12GeV

/

c and40GeV

/

c.

3.4.Vectormesoncorrection

A fraction of the mesons measured in SIDIS originates from diffractive production of vector mesons, which subsequently de-cay into lighter hadrons. This fraction can be considered as a higher-twistcontribution tothe SIDIScross section [8]. It cannot

be described by the QCD parton model with the

independent-fragmentationmechanism,whichisencodedintheFFs.Moreover,

Fig. 3. Correctionduetodiffractiveρ0_{contamination,shownfornegative-pion}

mul-tiplicitiesasafunctionofz forthreeQ2_bins.

fragmentationfunctionsextractedfromdataincludingthisfraction wouldbebiased,whichviolatesinparticulartheuniversality prin-ciple of the model. Therefore, the fraction of final-state hadrons originatingfromdiffractive

ρ

0 _{decayisestimated. Ourevaluation} isbasedontwo MCsimulations, oneusingtheLEPTOevent gen-erator simulating SIDIS free of diffractive contributions (see Sec-tion 3.3), and the other one using the HEPGEN [19] generator simulatingdiffractive

ρ

0 _{production.Further channels, whichare} characterisedbysmallercrosssections,arenottakenintoaccount. Events with diffractive dissociation of the target nucleon are alsosimulatedandrepresentabout25%ofthosewiththenucleon staying intact.Thesimulationoftheseeventsincludesnuclear ef-fects,i.e.coherentproductionandnuclearabsorptionasdescribed inRef. [19].A correction factorforthemultiplicitiesis calculated taking into account the diffractive contribution to pion (hadron) andDISyields.Asanexample,thez dependenceofthecorrection factor f π

ρ0 for

π

+ multiplicities is shown in Fig. 3 forthree Q2

bins.The correctionvariesbetween1.02 and0.55forpions,with thelargestvalue appearing atsmall Q2 _{andhighz,whereby the} latterregionischaracterisedbyverysmallmultiplicities.

3.5. Systematicuncertainties

The main contributions to the systematic uncertainties arise fromtheuncertaintiesonthedeterminationoftheacceptance,of theRICH performance andofthe diffractive

ρ

0 _{contribution.The} uncertaintyonthe acceptancecorrectionisevaluated bytwo dif-ferentmethods: first,byvarying intheMC thePDF setusedand the JETSET parameters related to the hadronisation mechanism; secondly,by determining theacceptance correction ina different dimensionalspaceaddingadditionalvariables.The validityofthe correction for electron contamination is confirmedby comparing the simulated and measured electron distributions for momenta below8GeV

/

c,whereelectrons areidentifiedusing theRICH de-tector.Anuncertaintyof4%isfoundthatincludestheuncertainty oftheelectroncontamination.Withthethreedifferenttargetcells threeindependentmeasurementsofthemultiplicitiescanbe per-formed.Themultiplicitiesfromtheupstreamandthedownstream target cellsarefound toagreewithintwo tothreepercent,while theagreementisbetterwiththemiddlecell.Thesedifferencesare wellcoveredbytheacceptancecorrectionuncertainty.

ob-Table 1

Binlimitsforthethree-dimensionalbinninginx,y andz. 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. Positivepionmultiplicitiesversusz forninex binsandfivey bins(forclaritystaggeredverticallybyα).Thebandscorrespondtothetotalsystematicuncertainties fortherange0.30<y<0.50.ThecurvescorrespondtotheCOMPASSLOfit(seeSection5).(Colouredversiononline.)

servedwhen comparingtheresults obtainedfromthe datataken insixdifferentweeks.

The crosssection forexclusive productionof

ρ

0 _{calculated in} HEPGENisnormalisedtothephenomenologicalmodelofRef.[20]. Thetheoreticaluncertaintyonthepredictedcrosssectioncloseto COMPASSkinematicsamountstoabout30%.Thisresultsinan un-certaintyonthediffractive

ρ

0 _{correctionfactor,whichamountsto} atmost30%anddependsonthekinematicrange.

Nucleareffectsmaybecausedbythepresenceof3_He/4_Heand 6_{Liin thetarget. A detailedstudyof such effects was previously} performedbytheEMC[9]inasimilarkinematicrangeforcarbon, copper and tin. A z-dependent decrease of5% was observed for the multiplicities of copper compared to the ones of deuterium. While theeffect was larger fortin, nosuch effect was found for carbon,so thatpossiblenucleareffectsinthepresentexperiment areexpectedtobeverysmallandarehenceneglected.

All contributions to the systematicuncertainties are addedin quadrature and yield the total systematic uncertainty shown as bandsin Figs. 6 and7,which variesbetween5% and10% ofthe measuredmultiplicities.Notethatnot allsystematicuncertainties arecorrelatedfrombintobin.Itwasestimatedthat,when consid-eringquadratic summation,about0

.

8

σ

syst is correlatedfrom bin to bin.Inthiscase

√

1

−

0

.

82

_σ

_syst

₌

₀

_.

₆

_σ

_{syst is uncorrelatedand} istreatedtogether withthestatisticaluncertaintiesinthefits dis-cussedinSection5.

4. Resultsforchargedpionandchargedhadronmultiplicities

Themultiplicitiespresentedinthefollowingfiguresareall cor-rected for the diffractive

ρ

0 _{contribution. The numerical values} areavailable onHepData

[21]

formultiplicities withandwithout this correction. The separate correction factors for DIS and pion (hadron) yields are provided aswell. The presentresults feature alarger datasample, an extendedkinematic domain,andan

im-provedtreatmentoftheparticleidentification,whencomparedto the resultsofRef. [22].The x, y and z binning usedinthe anal-ysis is given in Table 1. The Q2 values range from 1

(

GeV

/

c

)

2

at the smallest x to about 60

(

GeV

/

c

)

2 at the highest x, with



Q2



=

3

(

GeV

/

c

)

2.

In Figs. 4 and 5, the results for the z and y dependences of the

π

+and

π

− multiplicitiesarepresentedintheninebinsof x. Statistical uncertainties are shownforall points, whilea band at thebottomofthepanelsillustratesthesizeofthetotalsystematic uncertaintyfora typical y bin (0

.

30

<

y

<

0

.

50). Fortheother y bins,thesystematicuncertaintiesaresimilarorsmallerinsize.The curvescorrespondtotheLOpQCDfitasdiscussedinSection5.

In Fig. 6, multiplicities ofpositively (closed circles) and nega-tively (opencircles)chargedpions areshownversus z,separately fortheninex binsbutaveragedover y.Theerrorbarscorrespond tothestatisticaluncertaintiesandthebandstothetotalsystematic ones.

Fig. 7

showstheresultsforthechargedhadronmultiplicities. Bothfiguresexhibitastrongdependenceon z,asalreadyobserved in previous measurements, and a weak one on x. Multiplicities are higher forpositively than fornegatively chargedhadrons be-cause ofu-quarkdominance. Thisdifference is morepronounced forallhadronsthanforpionssincenegativekaonsandantiprotons, whichareincludedinthehadronsample, donot containnucleon valencequarks.

In the next section, we demonstrate that the multiplicities in

the COMPASS kinematic domain are well described at LO pQCD.

In thisapproximation, the sumofmultiplicities ofpositively and negatively chargedhadrons produced onan isoscalartarget is of specialinterestasseveraltermsintheLOcrosssectionexpression cancel.ThisquantityforchargedkaonswasusedbyHERMES[23]

Fig. 5. Same asFig. 4for negative pions. (Coloured version online.)

Fig. 6. Positive (closed) and negative (open) pion multiplicities versus z for nine x bins. The bands correspond to the total systematic uncertainties.

Fig. 8. Left:SumofMπ+andMπ−versusx.TheCOMPASSdata(160 GeV,closedcircles)arecomparedtoHERMESresults(27.5 GeV,opencircles);Right:SumofMh+

andMh−_{versusx.TheCOMPASSdata(160 GeV,closedcircles)arecomparedtoEMCresults(100 GeVto280 GeV,opencircles).Thesystematicuncertaintiesareshownas}

bandsatthebottom.

Fig. 9. Left:RatioMπ+_/Mπ−_{versusx fromCOMPASS(160 GeV,closedpoints),HERMES(27.5 GeV,opencircles)andJLab(5.5 GeV,opensquares).Right:RatioM}h+_/Mh−

versusx forCOMPASS(160 GeV,closedcircles)andEMC(100 GeVto280 GeV,opencircles)results.Thesystematicuncertaintiesareshownasbandsatthebottom. Foranisoscalartarget andtakingintoaccountonly two

inde-pendentquark FFs Dπ_fav andDπ_unf (see Section5), thesumof

π

+

and

π

− multiplicitiesintegratedoverz canbewrittenatLOas

M

π+

₊

_M

π−

₌

_D

π fav

+

D

unfπ

−

2S 5U

+

2S

(

D

π fav

−

D

unfπ

),

(6) with

M

π±

=





Mπ±

(

x

,

y

,

z

)



ydz. Thecombinationsof PDFsU

=

u

+ ¯

u

+

d

+ ¯

d and S

=

s

+ ¯

s dependonx and Q2,and

D

_favπ

(

Q2

)

=



Dπ_fav

(

z

,

Q2

)

dz and

D

_unfπ

(

Q2

)

=



Dπ_unf

(

z

,

Q2

)

dz are integrated

over the measured z range and depend on Q2 only. The pion

multiplicity sumis expected to be almost flat in x, as the term 2S

/(

5U

+

2S

)

is smallandthe Q2 _dependenceof

_D

π

fav

+

D

unfπ is ratherweak(oftheorderof3%)atCOMPASSkinematics[7].

Fig. 8(left) showstheresultforthesum

M

π+

+

M

π− of

π

+

and

π

−multiplicities,integratedoverz from0.2to0.85and aver-agedover y between0.1and0.7,asafunctionof x.Theexpected weak x dependence isindeed observed inthe data. In thesame figure, the results of HERMES [8] integrated over z from 0.2 to 0.8are shownusing the so-calledx representation. The HERMES multiplicities are larger and show a different dependence on x.

Note however that the HERMES data were measured at a lower

energy and correspond to different kinematics, in particular ac-ceptinglower W values.InordertocomparetheCOMPASSresults alsowiththeEMCones[9],thesumofchargedhadron multiplici-tiesisshownin

Fig. 8

(right).TheresultsfromCOMPASSandEMC, whichcorrespondtocomparablekinematics,arefoundinexcellent agreement.

Anotherquantity of interest is the x dependence of the ratio

M

π+

_/M

π−_{,where mostexperimental systematic effects cancel.} Theresultsare shownin

Fig. 9

(left) asafunction ofx.Theyare inreasonableagreementwiththeHERMESvaluesinthemeasured range.ThevaluesobtainedfromtheJLabE00-108experiment[27]

for z

>

0

.

3 at higher x and lower W values are also shown for completeness. In Fig. 9 (right), the ratio

M

h+

_/

_M

h− _calculated forchargedhadronmultiplicitiesisshownforCOMPASSandEMC data.Theseresultsareinexcellentagreement.

5. Extractionofquark-to-pionfragmentationfunctions

The present dataon charged pionandcharged hadron multi-plicitiescoverawidekinematicrangeinx andz andrepresentan important input for theextraction of quark-to-pion FFs in future NLOpQCD analysesoftheworlddata.Wepresentherean extrac-tion of quark-to-pion FFs, howeverrestrictedto the presentpion dataandlimitedtoLOpQCD. Belowitwillbeshownthatthe re-sultsofthisfitarecompatiblewiththoseofanindependentdirect extractionofthetwoquark-to-pionFFsinfixedkinematicbins.

The fragmentationof a quark of a given species into a final-state hadron is called favoured if the quark flavour corresponds to a valencequarkin thehadron, otherwisethe fragmentationis calledunfavoured.Accordingtoisospinandchargesymmetry,and assuminginadditionthatthestrangequarkFFisequaltotheother unfavouredFFs,onlytwoindependentquark-to-pionFFsremain:

Dπ_fav

=

Dπ_u+

=

Dπ+ d

=

D π− d

=

Dπ − u D_unfπ

=

Dπ_d+

=

D_uπ+

=

Dπ_u−

=

Dπ− d

=

D π± s

=

Dπ ± s

.

(7)

followingfunctionalformisassumedforthez dependence ofthe FFs: zDi

(

z

)

=

Ni zαi

₍

₁

−

_z

₎

βi



0.85 0.2 zαi

(

1

−

z

)

βidz

,

(8)

wherethereferencescaleis Q₀2

=

1

(

GeV

/

c

)

2 and i

= {

fav, unf, g

}

. Inordertofit simultaneously Mπ+ and Mπ−,a

χ

2 _minimisation procedureisapplied.Ittakesintoaccountthequadraticsumofthe statisticalanduncorrelatedsystematicuncertainties,



2:

χ

2

=



π+,π− N



j=1

⎡

⎣

⎛

⎝



qe2qq

xj

,

Q2_j



Dπ_q±

zj

,

Q2_j





qe2qq

xj

,

Q2_j



−

Mπ_exp±

xj

,

Q2j

,

zj



⎞

⎠ /

j

⎤

⎦

2

,

(9)

whereN denotesthenumberofdatapoints.Themultiplicitiesare welldescribedbythefitasshownin

Figs. 4 and 5

.

The results for the extracted favoured and unfavoured quark FFsandtheratio Dπ_unf

/

Dπ_fav are shownin Fig. 10asa functionof z evolvedto Q2

₌

₃

₍

_GeV

_/

_c

₎

2_{. Theunfavoured FFis smallerthan} thefavouredone, asexpected, andtheirratioisseen todecrease withz.Theshadedbandsdepictthetotaluncertainty.Thesebands

are determined using a MC sampling method (bootstrapmethod

in Ref. [30]). One hundred replicas of the original data set are builtby generatingstandard normaldeviatesasnoise factorsthat arethen multipliedby thedatapoint uncertainties andaddedto theoriginaldatapoint.Forthestatisticaluncertaintyand uncorre-latedsystematicuncertaintythenoisefactorisgeneratedforeach point separately, while for the correlated systematic uncertainty the noise factor is generated only once per replica. The bands widths are given by the root mean square of the corresponding distributions.Notethatfortheratio Dπ_fav

/

Dπ_unf mostofthe corre-latedsystematicuncertaintiescancel.

In Fig. 10, also recent parametrisations of FFs obtained from NLOanalyses by theLSS [31],DSEHS [32]andHKNS [33] groups are compared to the COMPASS LOfit. While the presentfit dis-agreeswiththeHKNSparametrisationbasedonelectron–positron annihilationdataonly,qualitativeagreementisobtainedwiththe DSEHSandLSSparametrisationsthat include,inadditionto HER-MESdata,preliminary COMPASSdata basedononly afractionof the presently analysed data with a reduced kinematic coverage andlarger systematicuncertainties. Therefore, the impact of the present COMPASS results on the global fits will be considerably enhancedwhen comparingto theimpactofthe preliminarydata discussedinRef.[22].

Analternativemethodto extracttheFFs fromthepion multi-plicitydataistosolvethesystemoftwolinearequationsforMπ+ andMπ− ineach

(

x

,

y

,

z

)

binforthevaluesofDπ_fav

(



z

,



Q2

_)

_and Dπ_unf

(



z

,



Q2

_)

_{by usingEqs.(1) and(2). No functionalformhas} to be assumed, and the DGLAP evolution for FFs is not needed. ThesamePDFsasmentionedaboveareused.Theresultsfromthis directextractionofFFsareingoodagreementwiththeresults ob-tainedfromtheLOfit.Thisisillustrated inFig. 11forone (x, y) bin.

6. Summaryandconclusions

We have presented differential multiplicities of charge-sepa-rated pions and charge-separated hadrons measured in SIDIS of muonsoff an isoscalartarget. The results are given in 3-dimen-sional bins of x, y and z and cover the kinematic range Q2

_>

Fig. 10. Favoured (top)and unfavoured(middle)quark-to-pionFFsand theratio Dπunf/Dπfav(bottom),asobtainedfromtheCOMPASSLOfit,comparedtotheDSEHS,

HKNSandLSSfitsatNLO.ThebandsrepresentthetotaluncertaintiesfortheFFs andthetotalstatisticaluncertaintyfortheratio(seetext).(Colouredversiononline.)

Fig. 11. Thez dependenceofthefavoured(closedsymbols)andunfavoured(open symbols)quark-to-pionfragmentationfunctions,zDπ

favandzDπunf,extracteddirectly

frompionmultiplicitiesatthemeasured Q2_{for one(x, y)bin(0.04<x<0.06,}

0.3<y<0.5).Forcomparison,theresultfromthepresentLOQCDfittothepion multiplicitiesisshownatQ2₌₆

1

(

GeV

/

c

)

2,0

.

004

<

x

<

0

.

4 and0

.

2

<

z

<

0

.

85.Thenumerical val-uesareavailable inRef.[21] withandwithout thesubtractionof thecontributionofdiffractivevectormesonproductiontoSIDIS.In additiontheradiativecorrectionsfactorsareprovided.Thesehigh precision multi-dimensional data provide an important input for futureNLOQCDfitsoffragmentationfunctions.

The sumofthe z-integrated positively andnegatively charged hadron and pion multiplicities shows a flat x behaviour, as ex-pectedinLOpQCD.Forchargedhadronsthissumisinagreement

with EMC results obtained at comparable kinematics, whereas

someinconsistencyisobservedwhencomparingtoHERMES pion data that were taken at different kinematics. The ratio of the z-integrated positive andnegative hadron and pionmultiplicities asafunctionofx nicelyconfirmsthepreviousmeasurementsfrom

HERMESandEMC.

The measured charged pionmultiplicities were used for a LO extraction of the favoured and unfavoured pion FFs. While both FFsaresignificantly differentfromthoseobtainedintheHKNSfit to only theelectron–positron annihilation data,they are ingood agreementwiththoseobtainedinrecentNLOfitsthatalsoinclude apreliminaryreleaseofthepresentdata.

Acknowledgements

We gratefully acknowledgethe support of the CERN manage-ment andstaff andthe skilland effort of thetechnicians ofour collaboratinginstitutes.Thisworkwasmadepossiblebythe finan-cialsupportofourfundingagencies.SpecialthanksgotoM. Hirai andS. KumanoforprovidinguswiththeDGLAPevolutioncodefor fragmentationfunctions.

References

[1]J.C.Collins,D.E.Soper,G.F.Sterman,Nucl.Phys.B261(1985)104. [2]BELLECollaboration,M.Leitgab,etal.,Phys.Rev.Lett.111(2013)062002. [3]BaBarCollaboration,J.P.Lees,etal.,Phys.Rev.D88(2013)032011. [4]ALEPHCollaboration,R.Barate,etal.,Phys.Rep.294(1998)1;

DELPHICollaboration,O.Abreu,etal.,Eur.Phys.J.C5(1998)585;

OPALCollaboration,R.Akers,etal.,Z.Phys.C63(1994)181. [5]SLDCollaboration,K.Abe,etal.,Phys.Rev.D69(2004)072003. [6]PHENIXCollaboration,S.S.Adler,etal.,Phys.Rev.Lett.91(2003)241803;

STARCollaboration,J.Adams,etal.,Phys.Rev.Lett.97(2006)152302; BRAHMSCollaboration,I.Arsene,etal.,Phys.Rev.Lett.98(2007)252001; STARCollaboration,B.I.Abelev,etal.,arXiv:nucl-ex/0607033.

[7]D.deFlorian,R.Sassot,M.Stratmann,Phys.Rev.D75(2007)114010. [8]HERMESCollaboration,A.Airapetian,etal.,Phys.Rev.D87(2013)074029. [9]EMC,J.Ashman,etal.,Z.Phys.C52(1991)361.

[10]COMPASSCollaboration,P.Abbon,etal.,Nucl.Instrum.MethodsA577(2007) 455.

[11]P.Abbon,etal.,Nucl.Instrum.MethodsA616(2010)21.

[12]A.A.Akhundov,D.Bardin,L.Kalinovskaya,T.Riemann,Fortschr.Phys.44(1996) 373.

[13]P.Abbon,etal.,Nucl.Instrum.MethodsA631(2011)26.

[14]G.Ingelman,A.Edin,J.Rathsman,Comput.Phys.Commun.101(1997)108. [15]T.Sjostrand,LU-TP-95-20,CERN-TH-7112-93-REV,arXiv:hep-ph/9508391. [16]COMPASSCollaboration,C.Adolph,etal.,Phys.Lett.B718(2013)922. [17] R.Brun,M.Caillat,M.Maire,G.N.Patrick,L.Urban,CERN-DD/85/1. [18]T.T.Bohlen,etal.,Nucl.DataSheets120(2014)211;

A.Ferrari,P.R.Sala,A.Fasso,J.Ranft,CERN-2005-10(2005),INFN/TC-05/11, SLAC-R-773.

[19]A.Sandacz,P.Sznajder,HEPGEN–generatorforhardexclusiveleptoproduction, arXiv:1207.0333.

[20]S.V.Goloskokov,P.Kroll,Eur.Phys.J.C53(2008)367. [21] TheDurhamHepDataProject,http://durpdg.dur.ac.uk/.

[22]N.Makke,FragmentationfunctionmeasurementatCOMPASS,in:Proceedings ofthe21stInt.WorkshoponDeep-InelasticScatteringandRelatedSubjects, DIS2013,Marseille,France,2013,in:PoSDIS2013,2013,p. 202.

[23]HERMESCollaboration,A.Airapetian,etal.,Phys.Lett.B666(2008)446. [24]E.Leader,A.V.Sidorov,D.B.Stamenov,Phys.Rev.D93(2016)074026. [25]M.Stolarski,Phys.Rev.D92(2015)098101.

[26]E.Aschenauer,etal.,Phys.Rev.D92(2015)098102.

[27]JLabE00-108,R.Asaturyan,etal.,Phys.Rev.C85(2012)015202. [28]M.Hirai,S.Kumano,Comput.Phys.Commun.183(2012)1002. [29]A.D.Martin,W.J.Stirling,R.S.Thorne,G.Watt,Eur.Phys.J.C63(2009). [30]W.H.Press,S.A.Teukolsky,W.T.Vetterling,B.P.Flannery,NumericalRecipesin

C:TheArtofScientificComputing,2nded.,1992.

[31]E. Leader, A.V. Sidorov, D. Stamenov, Importance of semi-inclusive DIS processes in determining fragmentation functions, in: Proceedings of the 15th Workshop on High Energy Physics, DSPIN-13, Dubna, Russia, 2013, arXiv:1312.5200.

[32]D.deFlorian,etal.,Phys.Rev.D91(2015)014035.