Collins and Sivers asymmetries in muonproduction of pions and kaons off transversely polarised protons

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Letters

B

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Collins

and

Sivers

asymmetries

in

muonproduction

of

pions

and

kaons

off

transversely

polarised

protons

C. Adolph

h

,

R. Akhunzyanov

g

,

M.G. Alexeev

aa

,

G.D. Alexeev

g

,

A. Amoroso

aa

,

ac

,

V. Andrieux

v

,

V. Anosov

g

,

A. Austregesilo

j

,

q

,

B. Badełek

ae

,

F. Balestra

aa

,

ac

,

J. Barth

d

,

G. Baum

a

,

R. Beck

c

,

Y. Bedfer

v

,

A. Berlin

b

,

J. Bernhard

m

,

K. Bicker

j

,

q

,

E.R. Bielert

j

,

J. Bieling

d

,

R. Birsa

y

,

J. Bisplinghoff

c

,

M. Bodlak

s

,

M. Boer

v

,

P. Bordalo

l

,

1

,

F. Bradamante

x

,

y

,

C. Braun

h

,

A. Bressan

x

,

y

,

∗

,

M. Büchele

i

,

E. Burtin

v

,

L. Capozza

v

,

M. Chiosso

aa

,

ac

,

S.U. Chung

q

,

2

,

A. Cicuttin

z

,

y

,

M.L. Crespo

z

,

y

,

Q. Curiel

v

,

S. Dalla Torre

y

,

S.S. Dasgupta

f

,

S. Dasgupta

x

,

y

,

O.Yu. Denisov

ac

,

S.V. Donskov

u

,

N. Doshita

ag

,

V. Duic

x

,

W. Dünnweber

p

,

M. Dziewiecki

af

,

A. Efremov

g

,

C. Elia

x

,

y

,

P.D. Eversheim

c

,

W. Eyrich

h

,

M. Faessler

p

,

A. Ferrero

v

,

M. Finger

s

,

M. Finger Jr.

s

,

H. Fischer

i

,

C. Franco

l

,

N. du Fresne von Hohenesche

m

,

j

,

J.M. Friedrich

q

,

V. Frolov

j

,

F. Gautheron

b

,

O.P. Gavrichtchouk

g

,

S. Gerassimov

o

,

q

,

R. Geyer

p

,

I. Gnesi

aa

,

ac

,

B. Gobbo

y

,

S. Goertz

d

,

M. Gorzellik

i

,

S. Grabmüller

q

,

A. Grasso

aa

,

ac

,

B. Grube

q

,

T. Grussenmeyer

i

,

A. Guskov

g

,

F. Haas

q

,

D. von Harrach

m

,

D. Hahne

d

,

R. Hashimoto

ag

,

F.H. Heinsius

i

,

F. Herrmann

i

,

F. Hinterberger

c

,

Ch. Höppner

q

,

N. Horikawa

r

,

4

,

N. d’Hose

v

,

S. Huber

q

,

S. Ishimoto

ag

,

5

,

A. Ivanov

g

,

Yu. Ivanshin

g

,

T. Iwata

ag

,

R. Jahn

c

,

V. Jary

t

,

P. Jasinski

m

,

P. Jörg

i

,

R. Joosten

c

,

E. Kabuß

m

,

B. Ketzer

q

,

6

_,

_{G.V. Khaustov}

u

_,

_{Yu.A. Khokhlov}

u

,

7

_,

_{Yu. Kisselev}

g

_,

_{F. Klein}

d

_,

K. Klimaszewski

ad

,

J.H. Koivuniemi

b

,

V.N. Kolosov

u

,

K. Kondo

ag

,

K. Königsmann

i

,

I. Konorov

o

,

q

,

V.F. Konstantinov

u

,

A.M. Kotzinian

aa

,

ac

,

O. Kouznetsov

g

,

M. Krämer

q

,

Z.V. Kroumchtein

g

,

N. Kuchinski

g

,

F. Kunne

v

,

∗∗

,

K. Kurek

ad

,

R.P. Kurjata

af

,

A.A. Lednev

u

,

A. Lehmann

h

,

M. Levillain

v

,

S. Levorato

y

,

J. Lichtenstadt

w

,

A. Maggiora

ac

,

A. Magnon

v

,

N. Makke

x

,

y

,

G.K. Mallot

j

,

C. Marchand

v

,

A. Martin

x

,

y

,

∗∗

,

J. Marzec

af

,

J. Matousek

s

,

H. Matsuda

ag

,

T. Matsuda

n

,

G. Meshcheryakov

g

,

W. Meyer

b

,

T. Michigami

ag

,

Yu.V. Mikhailov

u

,

Y. Miyachi

ag

,

A. Nagaytsev

g

,

T. Nagel

q

,

F. Nerling

m

,

S. Neubert

q

,

D. Neyret

v

,

J. Novy

t

,

W.-D. Nowak

i

,

A.S. Nunes

l

,

A.G. Olshevsky

g

,

I. Orlov

g

,

M. Ostrick

m

,

R. Panknin

d

,

D. Panzieri

ab

,

ac

,

B. Parsamyan

aa

,

ac

,

S. Paul

q

,

G. Pesaro

x

,

y

,

D.V. Peshekhonov

g

,

S. Platchkov

v

,

J. Pochodzalla

m

,

V.A. Polyakov

u

,

J. Pretz

d

,

8

,

M. Quaresma

l

,

C. Quintans

l

,

S. Ramos

l

,

1

,

C. Regali

i

,

G. Reicherz

b

,

E. Rocco

j

,

N.S. Rossiyskaya

g

,

D.I. Ryabchikov

u

,

A. Rychter

af

,

V.D. Samoylenko

u

,

A. Sandacz

ad

,

S. Sarkar

f

,

I.A. Savin

g

,

G. Sbrizzai

x

,

y

,

P. Schiavon

x

,

y

,

C. Schill

i

,

T. Schlüter

p

,

K. Schmidt

i

,

3

,

H. Schmieden

d

,

K. Schönning

j

,

S. Schopferer

i

,

M. Schott

j

,

O.Yu. Shevchenko

g

,

19

_,

_{L. Silva}

l

_,

_{L. Sinha}

f

_,

_{S. Sirtl}

i

_,

M. Slunecka

g

,

S. Sosio

aa

,

ac

,

F. Sozzi

y

,

A. Srnka

e

,

L. Steiger

y

,

M. Stolarski

l

,

M. Sulc

k

,

R. Sulej

ad

,

H. Suzuki

ag

,

4

,

A. Szabelski

ad

,

T. Szameitat

i

,

3

,

P. Sznajder

ad

,

S. Takekawa

aa

,

ac

,

J. ter Wolbeek

i

,

3

,

S. Tessaro

y

,

F. Tessarotto

y

,

F. Thibaud

v

,

S. Uhl

q

,

I. Uman

p

,

M. Virius

t

,

L. Wang

b

,

T. Weisrock

m

,

M. Wilfert

m

,

R. Windmolders

d

,

H. Wollny

v

,

K. Zaremba

af

,

M. Zavertyaev

o

,

E. Zemlyanichkina

g

,

M. Ziembicki

af

,

A. Zink

h

*

Correspondingauthorat:DepartmentofPhysics,UniversityofTrieste,viaA.Valerio2,34127Trieste,ITALY.

**

Correspondingauthors.

http://dx.doi.org/10.1016/j.physletb.2015.03.056

a_{UniversitätBielefeld,FakultätfürPhysik,33501Bielefeld,Germany}9

b_{UniversitätBochum,InstitutfürExperimentalphysik,44780Bochum,Germany}9,16 c_{UniversitätBonn,Helmholtz-InstitutfürStrahlen- undKernphysik,53115Bonn,Germany}9 d_{UniversitätBonn,PhysikalischesInstitut,53115Bonn,Germany}9

e_{InstituteofScientificInstruments,ASCR,61264Brno,CzechRepublic}10

f_{MatrivaniInstituteofExperimentalResearch&Education,Calcutta-700030,India}11 g_{JointInstituteforNuclearResearch,141980Dubna,MoscowRegion,Russia}12 h_{UniversitätErlangen–Nürnberg,PhysikalischesInstitut,91054Erlangen,Germany}9 i_{UniversitätFreiburg,PhysikalischesInstitut,79104Freiburg,Germany}9,16 j_{CERN,1211Geneva23,Switzerland}

k_{TechnicalUniversityinLiberec,46117Liberec,CzechRepublic}10 l_{LIP,1000-149Lisbon,Portugal}13

m_{UniversitätMainz,InstitutfürKernphysik,55099Mainz,Germany}9 n_{UniversityofMiyazaki,Miyazaki889-2192,Japan}14

o_{LebedevPhysicalInstitute,119991Moscow,Russia}

p_{Ludwig-Maximilians-UniversitätMünchen,DepartmentfürPhysik,80799Munich,Germany}9,15 q_{TechnischeUniversitätMünchen,PhysikDepartment,85748Garching,Germany}9,15

r_{NagoyaUniversity,464Nagoya,Japan}14 s

CharlesUniversityinPrague,FacultyofMathematicsandPhysics,18000Prague,CzechRepublic10 t_{CzechTechnicalUniversityinPrague,16636Prague,CzechRepublic}10

u_{StateScientificCenterInstituteforHighEnergyPhysicsofNationalResearchCenter‘KurchatovInstitute’,142281Protvino,Russia} v_{CEAIRFU/SPhNSaclay,91191Gif-sur-Yvette,France}16

w_{TelAvivUniversity,SchoolofPhysicsandAstronomy,69978TelAviv,Israel}17 x_{UniversityofTrieste,DepartmentofPhysics,34127Trieste,Italy}

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

aa_{UniversityofTurin,DepartmentofPhysics,10125Turin,Italy} ab_{UniversityofEasternPiedmont,15100Alessandria,Italy} ac_{TorinoSectionofINFN,10125Turin,Italy}

ad_{NationalCentreforNuclearResearch,00-681Warsaw,Poland}18 ae_{UniversityofWarsaw,FacultyofPhysics,02-093Warsaw,Poland}18

af_{WarsawUniversityofTechnology,InstituteofRadioelectronics,00-665Warsaw,Poland}18 ag_{YamagataUniversity,Yamagata,992-8510,Japan}14

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received21August2014

Receivedinrevisedform24March2015 Accepted26March2015

Availableonline1April2015 Editor:M.Doser

MeasurementsoftheCollinsand Siversasymmetriesforchargedpionsand chargedandneutralkaons produced in semi-inclusive deep-inelastic scattering of high energy muons off transversely polarised protonsare presented.The resultswereobtainedusingall theavailableCOMPASSproton data,which weretakenintheyears2007and 2010.TheCollinsasymmetriesexhibitinthevalenceregiona non-zerosignalforpionsandtherearehintsofnon-zerosignalalsoforkaons.TheSiversasymmetriesare foundtobepositiveforpositivepionsandkaonsandcompatiblewithzerootherwise.

©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

E-mailaddresses:Andrea.Bressan@cern.ch(A. Bressan),Fabienne.Kunne@cern.ch

(F. Kunne),Anna.Martin@ts.infn.it(A. Martin).

1 _{AlsoatInstitutoSuperiorTécnico,UniversidadedeLisboa,Lisbon,Portugal.} 2 _{AlsoatDepartmentofPhysics,PusanNationalUniversity,Busan609-735,}

Re-publicofKoreaandatPhysicsDepartment,BrookhavenNationalLaboratory,Upton, NY11973,USA.

3 _{SupportedbytheDFGResearchTrainingGroup Programme1102“Physicsat}

HadronAccelerators”.

4 _{AlsoatChubuUniversity,Kasugai,Aichi487-8501,Japan.Seefootnote14.} 5 _{AlsoatKEK,1-1Oho,Tsukuba,Ibaraki305-0801,Japan.}

6 _{Presentaddress:UniversitätBonn,Helmholtz-InstitutfürStrahlen- und}

Kern-physik,53115Bonn,Germany.

7 _{AlsoatMoscowInstituteofPhysicsandTechnology,MoscowRegion,141700,}

Russia.

8 _{Presentaddress: RWTH Aachen University,III. PhysikalischesInstitut, 52056}

Aachen,Germany.

9 _{SupportedbytheGermanBundesministeriumfürBildungundForschung.} 10 _{SupportedbyCzechRepublicMEYSGrantsME492andLA242.}

11 _{SupportedbySAIL(CSR),Govt.ofIndia.}

12 _{SupportedbyCERN-RFBRGrants08-02-91009and12-02-91500.}

13 _{Supported by the Portuguese FCT – Fundação para a Ciência e}

Tecnolo-gia,COMPETEandQREN,GrantsCERN/FP/109323/2009,CERN/FP/116376/2010and CERN/FP/123600/2011.

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

No. 20540299andNo. 18540281;DaikoFoundationandYamadaFoundation.

15 _{SupportedbytheDFG clusterofexcellence‘OriginandStructureofthe}

Uni-verse’(www.universe-cluster.de).

1. Introduction

Thedescriptionofthenucleonspinstructureisstilloneofthe open issuesinhadronphysics.In thelastdecadesmajor progress inthisfield hasbeen madeby an interplaybetweennew experi-mentalresultsandthedevelopmentofnon-collinearQCD.Thefirst informationon transversespin andtransversemomentum effects havebecomeavailablerecently.Presently,thecompletedescription ofquarksinthenucleonincludesallpossiblecorrelationsbetween quark spin, quark transverse momentum and nucleon spin [1,2]. At leading twist, thesecorrelations are described for each quark

flavour by eight transverse momentum dependent (TMD) parton

distributionfunctions(PDFs).Afterintegrationovertransverse mo-mentum,onlythreeofthemsurvive,namelythenumberdensity, the helicity andthe transversity PDFs. One wayto access

exper-imentally these TMD PDFs is via semi-inclusive lepton–nucleon

deep inelastic scattering (SIDIS), i.e. by studying deep-inelastic

16 _{SupportedbyEUFP7(HadronPhysics3,GrantAgreementnumber283286).} 17 _{SupportedbytheIsraelScienceFoundation,foundedbytheIsraelAcademyof}

SciencesandHumanities.

scattering (DIS) with detection of at least one of the produced hadrons. When the target nucleon is transversely polarised, the SIDIScrosssectionexhibitsdifferentazimuthalmodulations[3]in different combinations of the two angles

φ

S and

φ

h. These are the azimuthal angles of the initial nucleon transverse spin vec-torandoftheproducedhadronmomentuminareferencesystem, in which the z-axis is the virtual photon direction andthe x–z

plane is the lepton plane according to Ref. [4]. The amplitudes of themodulations inthe cross section (the so-calledtransverse spin asymmetries) are proportional to convolutionsofTMD PDFs withTMDfragmentationfunctions.Thetwomostthoroughly stud-iedtransverse spinasymmetries arethe Collins andSivers asym-metries.The Collins asymmetriesallow accesstothe transversity PDFscoupledtotheCollinsfragmentationfunctions[5].TheSivers asymmetries give access to the Sivers PDFs [6], which describe

the correlations between quark transverse momentum and

nu-cleonspin. A Sivers PDF always appears in combination withan ‘ordinary’(unpolarised) fragmentationfunctionthat describesthe fragmentationofaquarkintoahadron.

Inthispaper,wepresentresultsontheCollinsandSivers asym-metries for pions and kaons produced on transversely polarised

protons in a NH3 target. Such measurements are in line with

the set ofmeasurements done by the COMPASS Collaboration in

the last years. Results on polarised deuterons were obtained for unidentified hadrons [7], pions and kaons [8], and on polarised protonsforcharged unidentifiedhadrons[9–11].The results pre-sentedinthisLetterareextractedfromallavailableCOMPASSdata takenin2007and2010usingtransversely polarisedprotons. For themeasurementsin2007and2010, asimilarspectrometer con-figurationwas used.Ascomparedtothe measurementson trans-verselypolariseddeuterons,themeasurementsontransversely po-larisedprotonsbenefitfromamajorupgradeoftheapparatus per-formedin2005.Ofparticularrelevanceforthesemeasurementsis theupgradeoftheRICH detector[12],whichledtoimproved ef-ficiencyandpurityforthesamplesofidentifiedparticles,andthe useofanewtargetsolenoidmagnetwithapolarangleacceptance of180mradascomparedtothe70mradofthemagnetuseduntil

2005.MeasurementsoftheseasymmetriesbytheHERMES

exper-imentexist[13,14] inadifferentkinematicrange (measurements in a limited x range also exist on neutron targets, see [15–17]). Comparisonwiththeseresultsarealsopresentedinthepaper.

2. Apparatusanddataselection

The COMPASS spectrometer [18] is in operation in the North

Area of CERN since 2002. The

μ

+ beam provided by the M2

beamlinehad a momentumof 160 GeV

/c,

a momentum spread

p/p

= ±

5%, anda longitudinalpolarisationof

−

80% that origi-natedfromthe

π

-decaymechanism.Themeanbeamintensitywas about2

.

3

×

107

μ

+

/

s and4

×

107

μ

+

/

s withspilllengthsof4.8 s and10 sin2007and2010,respectively.

Thetargetconsistedofthreecylindricalcellsof4 cmdiameter, eachseparatedbygapsof5 cm.Thelengthofthecentralcellwas

60 cmand that of the two outer ones 30 cm. For the

measure-mentoftransverse spin effects,thetarget materialwas polarised alongthe verticaldirection. Inorderto reduce systematiceffects, neighbouringcellswerepolarisedinoppositedirections,which al-lowsforsimultaneousdatatakingwithbothtargetspindirections. Tofurtherminimisesystematiceffects,thepolarisationofeachcell wasreversedevery4–5days.Duringthe2007datataking,atotal amountof12

×

109 events(440 TB)wasrecorded insixperiods, each consisting of two sub-periods of data taking with opposite polarisation. In 2010 about 37

×

109 events (1.9 PB)of raw data wererecordedovertwelveperiods.

Only events with a photon virtuality Q2

_>

₁

₍

_GeV

_/c)

2 _{and a} massofthehadronicfinalstate W

>

5 GeV

/c

2 havebeenusedto ensure the kinematicregion of DIS. Theupper limit on the frac-tional energy of the virtual photon ( y) was set to 0.9to reduce uncertaintiesduetoelectromagneticradiativecorrectionsand

con-tamination from pion decay. A lower limit on y is required to

ensure a good resolution in thisvariable. In the standard analy-sis this limit has been setto 0.1. A complementary sample with 0

.

05

<

y

<

0

.

1 wasalsostudied,mainlytoaddressthe Q2 depen-denceoftheasymmetries.TheBjorkenvariablex coverstherange from0.003 to0.7.A minimumvalueof0

.

1 GeV

/c for

the hadron transverse momentum ph_T withrespect to the virtual photon di-rection was required to ensure good resolution in the measured

azimuthal angle. A minimum value for the relative hadron

en-ergy z with respect to the virtual photon energy is needed to

select hadronsfromthe current fragmentationregion. Thisvalue hasbeensetto0.2forthestandardsample,whilea complemen-tarylower-z region

(

0

.

1

<

z

<

0

.

2

)

wasalsostudied.

The stability of the apparatus during data taking is crucial. Therefore,varioustestswereperformedusingthe2007and2010 data, asdescribed in[9–11]. As aresultfrom thesequalitytests, only fourperiods ofdatatakingin 2007were usedforthe anal-ysis of the Sivers asymmetries, while for the Collins asymmetry all six periods were used. This can be understood as the Sivers asymmetryisverysensitivetoinstabilitiesinthespectrometer ac-ceptance, because it represents the amplitudeof the modulation thatdependsontheazimuthalangleofthehadrontransverse mo-mentum withrespect to the target spin vector, whichis aligned alongafixeddirection.Duetoimproveddetectorstability,all peri-odsof2010couldbeusedfortheextractionofbothasymmetries.

3. Particleidentification

3.1. Chargedpionsandkaons

The RICH detector information was used to identify charged

hadrons as kaons and pions in the momentum range between

the Cherenkovthreshold(about 2

.

6 GeV

/c for

pions, 9 GeV

/c for

kaons)and50 GeV

/c.

The detectoraftertheupgradeof2005and theparticleidentification(PID)procedurearedescribedinRef.[19]

and only the relevant details of the likelihood PID method are givenhere.

The pattern of the detected photons in each event is anal-ysedtakingintoaccountthepredictedpathofthechargedparticle to compute likelihood values for each reconstructed track enter-ing the RICH acceptance. The likelihoodvalues are computedfor different masshypotheses (

L

M, with M

=

π

,

K

,

p,e)and forthe hypothesis ofabsence ofsignal,namely theso-calledbackground hypothesis(

L

back).A massvalueisattributedtoatrackifthe like-lihood for the corresponding mass hypothesis is the largest. In addition, cuts on the ratioof the largest likelihood value to the second largest one are applied to minimise the misidentification probability.A specificcutontheratio

L

K

/

L

back isappliedtokeep thecontaminationofprotonsinthekaonsampleatafewpercent inthemomentumrangebetweenthekaonandtheproton thresh-oldsone (about18 GeV

/c).

Thecutshavebeentuned toimprove theparticleidentificationefficiencyandthesamplepurity(defined as the fraction of K (

π

) inside the identified K (

π)

sample) in order to maximisetheir product which isthe figure ofmerit for particleidentification.Thetuninghasbeenperformedonthedata collected in2007and,thankstothehighstability ofthedetector, thesamecutshavebeenappliedforthe2010data.

The particle identification efficiencies and misidentification probabilitiesweredeterminedusingsamplesofpionsfromthe K0

Fig. 1. Purity of the identified positive and negative kaons as a function of x, z, ph T.

Fig. 2. Momentump (left),relativeenergyz (centre),Q2_{(right)distributionoftheunidentifiedchargedhadrons(white),pions(lightgrey)andkaons(darkgrey).Thesame}

codeforparticles,withslightlylightergraytonesisusedforthe0.1<z<0.2 kinematicinterval;thestandardselectionisusedforthekinematicdistributionsinx andQ2_.

Fig. 3. Meanvaluesofthetransversemomentumph

T (left),relativeenergyz (centre),Q2(right)oftheunidentifiedpositivehadrons(circles),pions(squares)andkaons

(triangles).Themeanvaluesfornegativeparticlesareessentiallyidentical. 97%forpionsand94%forkaons.Thesevaluesstarttodecreasefor momenta about30 GeV

/c and

reach values of 60% in the larger momentumregion.Inorder toachieve highvaluesofthe sample purity,themisidentificationprobabilitiesbetweenpionsandkaons

were kept aslow as a few percent even at the largest

momen-tumvalues,by adjustingthe value ofthe cut onthe ratioofthe largestlikelihood valueto the second largestone. Thepurity de-pendsalsoontherelativepopulationofthevariousparticletypes and is evaluated from the particle identification efficiencies and misidentificationprobabilitiesandthenumberofidentifiedkaons

andpions for every bin in which the asymmetry are measured.

The protoncontribution is very smallasalready mentioned, and wasneglectedforthepuritycalculation.Theaveragepurityvalues forpionsareabove99%.Thekaonpurityinthedifferentx,z,and

ph

T binsisshowninFig. 1.Itisabout94%withamostly mild de-pendenceonthevariables.The strongestdependenceisvisiblein thelarge z region forthe negative kaonsample, whichis dueto theincreasingratioofpionstokaons.Boththesamplepurityand theidentificationefficiencyhavebeenmeasured andfoundto be

compatibleinthetwodatatakingyearsaswellasinthedifferent periodsofeachyear.Effectsduetothehadronidentificationusing theRICHhavebeenevaluatedandfoundtobe smallwithrespect tothestatisticaluncertainties(lessthanhalfofthestatistical un-certaintiesintheworstcase,namelythelastz bin).Nocorrection hasbeenappliedtothefinalresultsandtheestimatesofthe pos-sible effects havebeen included in the systematicpoint-to-point uncertainties.

In Fig. 2 the distributions in momentum p, z and Q2 for

identified pionsandkaons areshownandcompared tothose for

unidentifiedhadrons.Theclearlyvisibledifferencesinthe p andz

distributionsareduetothedifferentmomentumcutsrequiredby the particleidentification. The mean valuesofthe ph_T, z and Q2

distributions asafunction ofx areshowninFig. 3.The different

x dependence ofthe meanvalues of z for the differentparticles

is due to the different cuts inmomentum combined withthe x

dependence of the kinematic correlation between z and p. The

Fig. 4. Left:Armenteros–Podolanskyplotofthehadronpair.Right:DifferenceoftheinvariantmassofthehadronpairandthePDGvalueoftheK0_{mass.Themassrange}

usedfortheanalysisisshaded.

Table 1

Finalstatisticsfor2007and2010foridentifiedchargedpionsandkaonsandneutral kaons.

Year Number of particles (×10−6₎

π+ π− K+ K− K0

2007 (Collins) 10.77 9.41 1.79 1.10 0.37

2007 (Sivers) 6.84 5.97 1.12 0.69 0.25

2010 27.26 23.72 4.48 2.71 1.00

3.2. K0_{identification}

The K0 identification isbased on the detection oftwo oppo-sitely charged tracks coming froma secondary vertex, for which the 2-pioninvariant mass lies inthe window m_K0

±

20 MeV

/c

2.

A separation between the primary and the secondary vertex of

atleast10 cmwas required.Furthermore,the anglebetweenthe reconstructedmomentum vector ofthe trackpairand thevector connectingtheprimaryandsecondaryverticeswasrequiredtobe smallerthan10 mrad.Ontheleft sideofFig. 4,theArmenteros– Podolanskyplotofthehadron pairisshown, inwhichthe

trans-verse momentum pT of one hadron with respect to the sum of

hadron momentais shownasa function ofthe difference ofthe longitudinal momenta over their sum,

(p

L1

−

pL2

)/(p

L1

+

pL2

)

. The K0 _{band is clearly visibleaswell as the}

_

_and

¯

_bands.In order to exclude the contamination by the

/ ¯



signal, the pT regionbetween80 MeV

/c and

110 MeV

/c was

excluded.The back-ground from e+e− pairs was suppressed by a lower cut on pT at40 MeV

/c.

Forthe detected K0_{s, thedifference betweentheir} mass value and the PDG [20] value is shown in the right panel ofFig. 4,wheretheverticallinesat

±

20 MeV

/c

2 enclosethe K0s usedforfurther analysis. Theasymmetry in thebackground visi-bleintheplotisaconsequenceofthepT cutusedtosuppressthe

/ ¯



contaminationwhichreducestheratio‘backgroundtototal’ intheselectedmassrangefrom0.07 to0.02.The transversespin asymmetriesofthebackgroundhavebeencheckedtobe compati-blewithzeroandtheoveralleffectonthefinalresultshavebeen evaluatedtobe completelynegligibleascomparedtothe statisti-caluncertainties.Thesamecutsonz andph_T asforthecharged

π

andK sampleswereappliedtotheneutralkaons.Themeanvalue

oftherelevantkinematicvariables areverycloseto thosefor pi-ons givenin Fig. 3 andthefinal statisticsfor the K0 _{sample are} giveninTable 1.

4. Results

In order to extract the transverse spin asymmetries fromthe data,the sameprocedure asdescribed in Refs. [10,11]was used.

The asymmetries were evaluated in bins of the kinematic

vari-ables x, z, or ph

T, using the same binning as in our previous analyses [8]. Allthe numericalresults are available on HEPDATA. The (

φ

S,

φ

h)distributions fromthe differenttarget cells and

sub-periods were fitted using an extended maximum likelihood

es-timator [9], and the eight transverse spin asymmetries expected in the SIDIS process were extracted simultaneously. It has been checked that including in the fit possible additional terms due to the longitudinal components of the target polarisation [21], the changes in the resulting Sivers and Collins asymmetry val-uesare negligibleascompared tothestatisticaluncertainty.Note

that the asymmetry reported here (one dimensional projection,

integrated over theother kinematicsvariables) havein principle, the instrumentalacceptancefolded in.Theyarenot correctedfor it since in all our simulations the corrections turned out to be negligible.

The resulting sin

(φ

h

+ φ

s

)

andsin

(φ

h

− φ

s

)

modulations yield the Collins andSiversasymmetries, respectively,after division by

i)thetargetmaterialdilutionfactor f ,ii)theaveragetargetproton polarisation,andfortheCollinsasymmetryiii)thetransversespin transfercoefficient.Inadditiontoammoniathetargetcellscontain small amounts of other materials. The dilution factor takes into account that the selected sample does not only include scatter-ingonthepolarisedprotonsbutalsoonothernuclei(i.e.different isotopes of He and N), whose content inside the solid state tar-get containers is knownbetter than % level. As forall the other COMPASSresultsonspindependentobservables(seef.i.[22]),the dilution factor f isexpressed in termsof thenumbernA of nu-cleiwithmassnumberA andthecorrespondingspin-independent cross sections

σ

tot

A per nucleon (corrected for radiative effects) for all the elements involved f

=

nH

·

σ

_Htot

/(

AnA

·

σ

Atot

)

. The to-tal cross section ratios,

σ

tot

A

/

σ

tot

H , are obtained from the struc-ture function ratios, Fn₂

(x,

y)/Fp₂

(x,

y) and FA₂

(x,

y)/F₂d

(x,

y) [23, 24]. Theoriginal procedureleading fromthemeasuredcross sec-tionratios

σ

tot

A

/

σ

Htottothepublishedstructurefunctionratioswas inverted stepbystep involvingthecorrectionstoaccount forthe non-isoscalar content of the target and the radiative corrections. For unmeasured nuclei the cross section ratios are obtained in the same way from a parameterisation of F₂A

(x,

y)/F₂d

(x,

y) as a function of A.In thepresentanalysis, thedilutionfactoris mod-ifiedby acorrectionfactor

ρ

=

σ

p1γ

/

σ

ptot accountingforthe dilu-tionduetoradiativeeventsonunpolarisedprotons[25].Moreover a correction for polarisation of the admixture of 15_{N to} 14_{N is} also applied. The dilution factor iscalculated in any bin andfor

every event using x and y. Its dependence on other kinematic

dilu-Fig. 5. Left:comparisonbetweentheCollinsasymmetriesforpionsasafunctionofx,extractedfrom2007and2010datataking.Right:thesamecomparisonfortheSivers asymmetries.

Fig. 6. The Collins asymmetries for charged pions (top), charged kaons (middle) and neutral kaons (bottom) on proton as a function of x, z and ph T.

tion factor increases with x from about 0.14 to 0.17. As a

func-tion of z and ph_T it is almost constant with an average value

of 0.15.

A non-flat azimuthal acceptance introduces correlations be-tweenthevariousmodulations resultingfromthefit.The correla-tioncoefficientsforCollinsvs.Siversasymmetriesarefoundtobe smallandbelow0.2forallbins.Moreover,theasymmetries mea-suredalongdifferentprojectionsofthe(x,z, ph

T)phasespaceare statisticallycorrelated,becausetheoverallsampleofeventsisthe same.InthecaseofCOMPASS,thesecorrelationcoefficientsforthe CollinsandfortheSivers asymmetriesare all smallerthanabout

0.3, butnon-negligible,sothat theyshouldbe takenintoaccount in any globalfit. They are slightly different for kaons and pions duetothedifferentkinematiccoverageofthetwosamples.

Inorder toestimate thesystematicuncertainties, severaltests

were performed based on our previous work for the charged

Fig. 7. TheCollinsasymmetriesforpions(top)andkaons(bottom)asafunctionof z andph

T,requiringx>0.032.

compatibilityofthe results was checked.No such false asymme-trywasobservedwithintheaccuracyofthemeasurementandthe point-to-pointsystematicuncertaintieswereevaluatedfromthese tests asa fractionof the statisticalerror. For 2010, this fraction is 0.6 and for 2007 it ranges between 0.5 and 0.7. The system-aticuncertaintyduetoparticlemisidentificationisverysmalland included in these fractions. All results are subject to a 5% scale uncertaintythatresultsfromtheuncertaintiesinthetarget polar-isationanddilutionfactor.

For both years of data taking, the asymmetries were evalu-ated in each period andtheir compatibility was checked. While

for 2010 this test shows good agreement among the results of

the differentperiods, for2007 itintroduces an additionalsource ofsystematicuncertaintiesfortheSiversasymmetries.Verymuch like in the case of unidentified hadrons, an additional absolute uncertainty of

±

0

.

012 was assigned to the

π

+ Sivers asymme-try. No such time dependencewas observed either forthe other hadronsorfortheCollins asymmetries.Thisvalue istaken tobe half of the difference between the mean asymmetries evaluated usingthe datafromthebeginning andthe endofthe2007data taking. Fig. 5 shows the Collins and Sivers asymmetries for

pi-ons asa function of x from the two data taking years,obtained

as weighted mean of the asymmetries from the different

peri-ods. Thetwo measurements arein goodagreementforthe pions

andforthenotshownkaons.The substantialimprovementofthe statistical precision of the 2010 data with respect to the 2007 data amounts to a factor of 1

.

6 for the Collins asymmetry and of 1

.

9 forthe Sivers asymmetry. The final results were obtained combiningthetwosamples,takingintoaccountthedifferent sta-tistical andsystematicuncertainties.The resultingsystematic un-certainties areabout0.6ofthe statisticalonesforall theparticle types.

The Collinsasymmetriesasa functionofx,z,or ph

T measured

by COMPASS for pions and kaons on transversely polarised

pro-tons are shownin Fig. 6.The pion asymmetries are very similar to theunidentifiedhadron asymmetries [10]: atsmallx they are compatible withzero, while inthe valence region they show an increasing signal, which has opposite sign for

π

+ and

π

−. This naively indicates that the unfavoured and favoured Collins frag-mentation functions have opposite sign. The results for charged kaons,althoughwithlargerstatisticaluncertainties,showasimilar trend: inparticularthe K+ asymmetryhasa negativetrendwith increasing x, andthe K− one is positive on average. The Collins asymmetry forneutralkaonsshowsapositivetrendwith increas-ing z.Theaverageasymmetryispositivebutcompatiblewithzero within thestatistical uncertainty.In order to investigatein more detail the behaviour of the asymmetries as a function of z and ph_T,theasymmetriesforchargedhadronswere evaluatedina re-gion where the signal is different from zero, namely x

>

0

.

032. The results are showninFig. 7 for pionsandkaons. Theyare in

good agreementwiththe other existingmeasurements on a

pro-tontargetfromtheHERMESexperiment[13].Thisisanon-obvious result, asinthelast x binsthe COMPASS Q2 valuesarelarger by

afactor3–4thantheHERMESones.Theweak Q2 _dependenceof

theCollinsasymmetryisalsosupportedbyarecentglobalfit[26]

oftheHERMESpionresults,theCOMPASSpreliminarypion asym-metries from the 2010 data, and the Belle [27] e+e−

→

π

+

π

− asymmetries,whichisabletoprovideagooddescriptionofallthe datasets.Acomparisonbetweenthefinalresultsofthispaperand thefitisshowninFig. 8.

TheCollinsasymmetryforchargedhadronswasfurther investi-gatedbyextendingthestandardkinematicrangesinz andy. Com-paredtotheabovepresentedresults,theasymmetriesextracted in

Fig. 8. ComparisonbetweentheCollinsasymmetriesforpionsandoneofthefitsin[26](fitwithstandardparameterisationandfitofA12 Belleasymmetries[27]).The

Fig. 9. The Sivers asymmetries for charged pions (top), charged kaons (middle) and neutral kaons (bottom) as a function of x, z and ph T.

thelow-z region(0

.

1

<

z

<

0

.

2)gavenoindication fora

substan-tialz-dependence,neitherforpionsnorforkaons.Similarly,inthe

low-yregion(0

.

05

<

y

<

0

.

1)thepionasymmetriesdonotexhibit any special behaviour, while the kaon ones suffer fromtoo low statistics.

The Sivers asymmetries measured by COMPASS for pions and

kaonsontransversely polarisedprotons areshowninFig. 9. Also inthiscase,thepionasymmetriesareverysimilartothe unidenti-fiedhadronasymmetries[11].Theasymmetriesfornegativepions andkaons,aswellasforneutralkaons arecompatiblewithzero, while for positive pions and kaons there is a clear evidence for a positive signal extending over the full measured x region and increasing with z. Very intriguing is the fact that, as for HER-MES[14],theK+signalislargerthanthe

π

+one,whichindicates a possibly not negligible role of seaquarks [28–30]. This is well visible in Fig. 10, where the two asymmetries are directly com-pared, andfromthe meanvaluesin the x

>

0

.

032 region, which arerespectively0

.

027

±

0

.

005 and0

.

043

±

0

.

014.Unlikethecaseof

theCollins asymmetry,the Sivers asymmetry measured by

COM-PASSat large x for positive pions andkaons is smaller than the onefromHERMES [14].Thisdifference iswell visiblealso inthe

z and ph_T variables when selecting the x

>

0

.

032 region of the

COMPASS data, as shown in Fig. 11. Several fits, which include the recently revisited Q2 evolution, were performed using HER-MESasymmetries[14],COMPASSasymmetriesondeuteron[8]and for unidentified hadrons on proton [11], and JLab Hall A asym-metries on 3_{He [15,16]. In Fig. 12, the results of some of these} fits[31–33],whichemploy Q2 TMDevolutions,areshowntowell reproducetheCOMPASSresults.Itwillbeinterestingtoseethe

re-Fig. 10. The Sivers asymmetries for positive pions and kaons, as a function of x.

sultsofsuch fitswhentheresultspresentedinthisLetterwillbe included.

Moreinformationonthe Q2_{evolutionisprovidedbythestudy} ofthe Sivers asymmetriesin thelow- y region between0.05 and

0.1, performed only using the 2010 data (as already done for

chargedhadrons[10,11]).Thepionasymmetriesinthisregionare comparedintheleftpanelofFig. 13totheasymmetriesobtained in the standard y range. In the region of overlap the mean Q2 values of these two samples are respectively 3

.

5

(

GeV

/c)

2 and 1

.

8

(

GeV

/c)

2. As forunidentified hadrons, there is an indication foranincreaseofthe

π

+ asymmetriesatlow- y. Thedependence of the Sivers asymmetries with z is further investigated

Fig. 11. TheSiversasymmetriesforpositivepions(top)andkaons(bottom)onprotonasafunctionofx,z andphT,requiringx>0.032.Theasymmetriesarecomparedto

HERMESresults[14].

Fig. 12. ComparisonbetweentheSiversasymmetriesforpionsandexistingglobalfits[31–33],inwhichtheCOMPASSresultsfortheunidentifiedhadronsonprotons[11]

areincluded.

showsmaller values.The comparisonofthepionasymmetries as afunction of x for the twoseparated z ranges areshown inthe rightpanel ofFig. 13.Fornegative pions,a positive signalshows up in the low-z region, which is not observed for larger values of z.

Insummary,usingthehighstatisticsdatacollectedin2007and 2010,COMPASShasmeasured theCollinsandSiversasymmetries

in muonproduction of charged pions and charged and

neu-tral kaons produced off transversely polarised protons. The high

energy muon beam allowed the measurement of a broad

kine-matic range in x and Q2_{. The x, z and p}

T dependences of

the asymmetries were studied. Further investigations extending

the range in z and y were also performed. The Collins

asym-metries are definitely different from zero for pions and there are hints of a non-zero signal also for kaons, although in this case the statistical significance is marginal. The Sivers asymme-tries are positive for positive pions and kaons, although differ-ent in size. This result is of particular interest since it can be used to access the sea quark Sivers PDFs.The results presented in this paper provide an important input for the global

anal-yses. Together with other measurements covering

complemen-tary kinematic ranges, they allow the study of the Q2 depen-denceof the asymmetries and the quantitative extraction of the Collins FF andof the transversity andSivers PDFs. This informa-tion is crucial for the predictions for future Drell–Yan

measure-ments and for measurements at future high-energy electron–ion

colliders.

Acknowledgements

Thiswork was made possible thanks to the financial support ofourfundingagencies.Wealsoacknowledge thesupportofthe CERNmanagementandstaff,aswellastheskillsandeffortsofthe techniciansofthecollaboratinginstitutes.

References

[1]A.Kotzinian,Nucl.Phys.B441(1995)234.

[2]P.J.Mulders,R.D.Tangerman,Nucl.Phys.B461(1996)197; P.J.Mulders,R.D.Tangerman,Nucl.Phys.B484(1997)538(Erratum).

[3]A.Bacchetta,etal.,J.HighEnergyPhys.0702(2007)093.

[4]A.Bacchetta,etal.,Phys.Rev.D70(2004)117504.

[5]J.C.Collins,Nucl.Phys.B396(1993)161.

[6]D.W.Sivers,Phys.Rev.D41(1990)83.

[7]E.S.Ageev,etal.,COMPASSCollaboration,Nucl.Phys.B765(2007)127.

[8]M.Alekseev,etal.,COMPASSCollaboration,Phys.Lett.B673(2009)127.

[9]M.Alekseev,etal.,COMPASSCollaboration,Phys.Lett.B692(2010)240.

[10]C.Adolph,etal.,COMPASSCollaboration,Phys.Lett.B717(2012)376.

[11]C.Adolph,etal.,COMPASSCollaboration,Phys.Lett.B717(2012)383.

[12]P.Abbon,etal.,Nucl.Instrum.MethodsSect.A616(2010)21.

[13]A.Airapetian,etal.,HERMESCollaboration,Phys.Lett.B693(2010)11.

[14]A.Airapetian,etal.,HERMESCollaboration,Phys.Rev.Lett.103(2009)152002.

[15]X.Qian,etal.,JeffersonLabHallACollaboration,Phys.Rev.Lett.107(2011) 072003.

[16]K. Allada,et al., JeffersonLab HallA Collaboration,Phys. Rev.C89 (2014) 042201.

[17]Y.X.Zhao,etal.,JeffersonLabHallACollaboration,Phys.Rev.C90 (5)(2014) 055201.

[18]P.Abbon,etal.,COMPASSCollaboration,Nucl.Instrum.MethodsSect.A577 (2007)455.

[19]P.Abbon,etal.,Nucl.Instrum.MethodsSect.A631(2011)26.

[20]J.Beringer,etal.,ParticleDataGroup,Phys.Rev.D86(2012)010001.

[21]M.Diehl,S.Sapeta,Eur.Phys.J.C41(2005)515,arXiv:hep-ph/0503023.

[22]M.G.Alekseev,etal.,COMPASSCollaboration,Phys.Lett.B690(2010)466.

[23]P.Amaudruz,etal.,NewMuonCollaboration,Nucl.Phys.B371(1992)3.

[24]J.Ashman,etal.,EuropeanMuonCollaboration,Z.Phys.C57(1993)211.

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

[26]M.Anselmino,etal.,Phys.Rev.D87(2013)094019.

[27]R.Seidl,etal.,BelleCollaboration,Phys.Rev.D86(2012)032011(E).

[28]A.V.Efremov,K.Goeke,P.Schweitzer,Eur.Phys.J.Spec.Top.162(2008)1.

[29]A.V.Efremov,K.Goeke,P.Schweitzer,Czechoslov.J.Phys.56(2006)F181.

[30]M.Anselmino,etal.,Eur.Phys.J.A39(2009)89.

[31]M.Anselmino,E.Boglione,S.Melis,Phys.Rev.D86(2012)014028.

[32]P.Sun,F.Yuan,Phys.Rev.D88(2013)114012.