A high-statistics measurement of transverse spin effects in dihadron production from muon-proton semi-inclusive deep-inelastic scattering

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Physics Letters B

www.elsevier.com/locate/physletb

A high-statistics measurement of transverse spin effects in dihadron production from muon–proton semi-inclusive deep-inelastic scattering

C. Adolph

^h

, R. Akhunzyanov

^g

, M.G. Alekseev

^x

, Yu. Alexandrov

^o,18

, G.D. Alexeev

^g

, A. Amoroso

^aa,ab

, V. Andrieux

^v

, V. Anosov

^g

, A. Austregesilo

^j,q

, B. Badełek

^ae

,

F. Balestra

^aa,ab

, J. Barth

^d

, G. Baum

^a

, R. Beck

^c

, Y. Bedfer

^v

, A. Berlin

^b

, J. Bernhard

^m

, R. Bertini

^aa,ab

, K. Bicker

^j,q

, J. Bieling

^d

, R. Birsa

^x

, J. Bisplinghoff

^c

, M. Bodlak

^s

, M. Boer

^v

, P. Bordalo

^l,1

, F. Bradamante

^y,j

, C. Braun

^h

, A. Bravar

^x

, A. Bressan

^y,x,∗

, M. Büchele

ⁱ

, E. Burtin

^v

, L. Capozza

^v

, M. Chiosso

^aa,ab

, S.U. Chung

^q,2

, A. Cicuttin

^z,x

, M.L. Crespo

^z,x

, Q. Curiel

^v

, S. Dalla Torre

^x

, S.S. Dasgupta

^f

, S. Dasgupta

^x

, O.Yu. Denisov

^ab

, S.V. Donskov

^u

, N. Doshita

^ag

, V. Duic

^y

, W. Dünnweber

^p

, M. Dziewiecki

^af

, A. Efremov

^g

, C. Elia

^y,x

,

P.D. Eversheim

^c

, W. Eyrich

^h

, M. Faessler

^p

, A. Ferrero

^v

, A. Filin

^u

, 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

, R. Garfagnini

^aa,ab

, F. Gautheron

^b

, O.P. Gavrichtchouk

^g

, S. Gerassimov

^o,q

, R. Geyer

^p

, M. Giorgi

^y,x

, I. Gnesi

^aa,ab

, B. Gobbo

^x

, S. Goertz

^d

, M. Gorzellik

ⁱ

,

S. Grabmüller

^q

, A. Grasso

^aa,ab

, B. Grube

^q

, A. Guskov

^g

, T. Guthörl

^i,3

, 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. Joerg

ⁱ

, R. Joosten

^c

, E. Kabuß

^m

, D. Kang

^m

, B. Ketzer

^q

, G.V. Khaustov

^u

, Yu.A. Khokhlov

^u,6

, 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,ab

, O. Kouznetsov

^g

, Z. Kral

^t

, 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

, S. Levorato

^x

, J. Lichtenstadt

^w

, A. Maggiora

^ab

,

*

Correspondingauthors.

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

1 AlsoatInstitutoSuperiorTécnico,UniversidadedeLisboa,Lisbon,Portugal.

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

3 SupportedbytheDFGResearchTrainingGroupProgramme1102“PhysicsatHadronAccelerators”.

4 AlsoatChubuUniversity,Kasugai,Aichi,487-8501,Japan.

5 AlsoatKEK,1-1Oho,Tsukuba,Ibaraki,305-0801,Japan.

6 AlsoatMoscowInstituteofPhysicsandTechnology,MoscowRegion,141700,Russia.

7 Presentaddress:RWTHAachenUniversity,III.PhysikalischesInstitut,52056Aachen,Germany.

8 SupportedbytheGermanBundesministeriumfürBildungundForschung.

9 SupportedbyCzechRepublicMEYSGrantsME492andLA242.

10 SupportedbySAIL(CSR),Govt.ofIndia.

11 SupportedbyCERN-RFBRGrants08-02-91009and12-02-91500.

12 Supported by the Portuguese FCT – Fundação para a Ciência e Tecnologia, COMPETE and QREN, Grants CERN/FP/109323/2009, CERN/FP/116376/2010 and CERN/FP/123600/2011.

13 SupportedbytheMEXTandtheJSPSundertheGrantsNo.18002006,No.20540299andNo.18540281;DaikoFoundationandYamadaFoundation.

14 SupportedbytheDFGclusterofexcellence‘OriginandStructureoftheUniverse’(www.universe-cluster.de).

15 SupportedbyEUFP7(HadronPhysics3,GrantAgreementnumber283286).

16 SupportedbytheIsraelScienceFoundation,foundedbytheIsraelAcademyofSciencesandHumanities.

17 SupportedbythePolishNCNGrantDEC-2011/01/M/ST2/02350.

18 Deceased.

http://dx.doi.org/10.1016/j.physletb.2014.06.080

0370-2693/©^{2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/3.0/).Fundedby SCOAP³.

A. Magnon

^v

, N. Makke

^y,x

, G.K. Mallot

^j

, C. Marchand

^v

, A. Martin

^y,x

, 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

ⁱ

, S. Neubert

^q

, D. Neyret

^v

, V.I. Nikolaenko

^u

, J. Novy

^t

, W.-D. Nowak

ⁱ

, A.S. Nunes

^l

,

I. Orlov

^g

, A.G. Olshevsky

^g

, M. Ostrick

^m

, R. Panknin

^d

, D. Panzieri

^ac,ab

, B. Parsamyan

^aa,ab

, S. Paul

^q

, M. Pesek

^s

, D. Peshekhonov

^g

, G. Piragino

^aa,ab

, S. Platchkov

^v

, J. Pochodzalla

^m

, J. Polak

^k,x

, V.A. Polyakov

^u

, J. Pretz

^d,7

, M. Quaresma

^l

, C. Quintans

^l

, S. Ramos

^l,1

, G. Reicherz

^b

, E. Rocco

^j

, V. Rodionov

^g

, E. Rondio

^ad

, A. Rychter

^af

, N.S. Rossiyskaya

^g

, D.I. Ryabchikov

^u

, V.D. Samoylenko

^u

, A. Sandacz

^ad

, S. Sarkar

^f

, I.A. Savin

^g

, G. Sbrizzai

^y,x

, P. Schiavon

^y,x

, C. Schill

ⁱ

, T. Schlüter

^p

, A. Schmidt

^h

, K. Schmidt

^i,3

, H. Schmieden

^c

,

K. Schönning

^j

, S. Schopferer

ⁱ

, M. Schott

^j

, O.Yu. Shevchenko

^g

, L. Silva

^l

, L. Sinha

^f

, S. Sirtl

ⁱ

, M. Slunecka

^g

, S. Sosio

^aa,ab

, F. Sozzi

^x

, A. Srnka

^e

, L. Steiger

^x

, M. Stolarski

^l

, M. Sulc

^k

, R. Sulej

^ad

, H. Suzuki

^ag,4

, A. Szabelski

^ad

, T. Szameitat

ⁱ

, P. Sznajder

^ad

, S. Takekawa

^ab

, J. ter Wolbeek

^i,3

, S. Tessaro

^x

, F. Tessarotto

^x

, F. Thibaud

^v

, S. Uhl

^q

, I. Uman

^p

,

M. Vandenbroucke

^v

, M. Virius

^t

, J. Vondra

^t

, L. Wang

^b

, T. Weisrock

^m

, M. Wilfert

^m

, R. Windmolders

^d

, W. Wi´slicki

^ad

, H. Wollny

^v

, K. Zaremba

^af

, M. Zavertyaev

^o

, E. Zemlyanichkina

^g

, M. Ziembicki

^af

aUniversitätBielefeld,FakultätfürPhysik,33501Bielefeld,Germany⁸

bUniversitätBochum,InstitutfürExperimentalphysik,44780Bochum,Germany^8,15 cUniversitätBonn,Helmholtz-InstitutfürStrahlen- undKernphysik,53115Bonn,Germany⁸ dUniversitätBonn,PhysikalischesInstitut,53115Bonn,Germany⁸

eInstituteofScientificInstruments,ASCR,61264Brno,CzechRepublic⁹

fMatrivaniInstituteofExperimentalResearch&Education,Calcutta700030,India¹⁰ gJointInstituteforNuclearResearch,141980Dubna,Moscowregion,Russia¹¹ hUniversitätErlangen–Nürnberg,PhysikalischesInstitut,91054Erlangen,Germany⁸ iUniversitätFreiburg,PhysikalischesInstitut,79104Freiburg,Germany^8,15 jCERN,1211Geneva23,Switzerland

kTechnicalUniversityinLiberec,46117Liberec,CzechRepublic⁹ lLIP,1000-149Lisbon,Portugal¹²

mUniversitätMainz,InstitutfürKernphysik,55099Mainz,Germany⁸ nUniversityofMiyazaki,Miyazaki889-2192,Japan¹³

oLebedevPhysicalInstitute,119991Moscow,Russia

pLudwig-Maximilians-UniversitätMünchen,DepartmentfürPhysik,80799Munich,Germany^8,14 qTechnischeUniversitätMünchen,PhysikDepartment,85748Garching,Germany^8,14

rNagoyaUniversity,464Nagoya,Japan¹³

sCharlesUniversityinPrague,FacultyofMathematicsandPhysics,18000Prague,CzechRepublic⁹ tCzechTechnicalUniversityinPrague,16636Prague,CzechRepublic⁹

uStateResearchCenteroftheRussianFederation,InstituteforHighEnergyPhysics,142281Protvino,Russia vCEAIRFU/SPhNSaclay,91191Gif-sur-Yvette,France¹⁵

wTelAvivUniversity,SchoolofPhysicsandAstronomy,69978TelAviv,Israel¹⁶ xTriesteSectionofINFN,34127Trieste,Italy

yUniversityofTrieste,DepartmentofPhysics,34127Trieste,Italy zAbdusSalamICTP,34151Trieste,Italy

aaUniversityofTurin,DepartmentofPhysics,10125Turin,Italy abTorinoSectionofINFN,10125Turin,Italy

acUniversityofEasternPiedmont,15100Alessandria,Italy adNationalCentreforNuclearResearch,00-681Warsaw,Poland¹⁷ aeUniversityofWarsaw,FacultyofPhysics,00-681Warsaw,Poland¹⁷

afWarsawUniversityofTechnology,InstituteofRadioelectronics,00-665Warsaw,Poland¹⁷ agYamagataUniversity,Yamagata,992-8510Japan¹³

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received30January2014

Receivedinrevisedform24June2014 Accepted30June2014

Availableonline4July2014 Editor: M.Doser

Ameasurementoftheazimuthalasymmetryindihadronproductionindeep-inelasticscatteringofmuons on transversely polarised proton (NH3) targets is presented.They provide independent access to the transversitydistributionfunctionsthroughthemeasurementoftheCollinsasymmetryinsinglehadron production.Thedata weretakenintheyear2010 withtheCOMPASSspectrometerusinga160 GeV/c muon beamofthe CERN SPS, increasingby afactorof about fourthe overall statistics with respect tothepreviouslypublisheddatatakenintheyear2007.Themeasuredsizeableasymmetryisingood agreementwiththepublisheddata.AnapproximateequalityoftheCollinsasymmetryandthedihadron asymmetryisobserved,suggestingacommonphysicalmechanismintheunderlyingfragmentation.

©^{2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/3.0/).FundedbySCOAP³.

1. Introduction

Thequarkstructureofthenucleoncanbecharacterisedbypar- tondistributionfunctions(PDFs)foreach quark flavour[1].Ifthe quark intrinsictransverse momentumkT isintegratedover,there remain at twist-two level three PDFs depending on the Bjorken scalingvariablexandthenegative squareofthefour-momentum transfer Q²,whichexhausttheinformationonthepartonicstruc- ture of the nucleon [2–5]. The spin-independent distribution f₁^q andthehelicitydistributiong^q₁havebeenmeasuredwithgoodac- curacy. However, up to ten years ago nothing was known about the transversespin distribution h^q₁, oftenreferred to astransver- sity,which describesthe probabilitydifference offindinga quark qpolarisedparallelorantiparalleltothespinofatransverselypo- larised nucleon. This distribution is difficult to measure, since it is relatedto soft processescorrelating quarks with opposite chi- rality,makingitachiral-oddfunction[1].As aresult,transversity canonlybeaccessedthroughobservablesinwhichitappearscou- pled to a second chiral-oddobject inorder to conserve chirality.

Thus it doesnot contribute to inclusive deep-inelastic scattering (DIS) at leading twist. In semi-inclusive deep-inelastic scattering (SIDIS)reactionsthechiral-oddpartnersofthetransversitydistri- butionfunction arefragmentationfunctions(FFs), whichdescribe thespin-dependenthadronisationofatransverselypolarisedquark qintohadrons.ForarecentreviewseeRef.[6].Uptonow,mostof theinformationontransversitycamefromtheCollinsasymmetry measuredinsinglehadronasymmetries[7–10]andusedinglobal analyses(e.g.[11]).

A complementary approach is to measure dihadron produc- tioninleptoproductioninSIDISontransverselypolarisednucleon, lN^↑→^{lh+h−X withbothhadronsproducedinthecurrentfrag-} mentationregion [12–15].In thisreactiona newchiral-oddfrag- mentationfunctionappears,the dihadronFragmentationFunction (DiFF) H₁,which describesthe spin-dependent part ofthe frag- mentation of a transversely polarised quark into a pair ofunpo- larised hadrons describing a correlation ofquark transverse spin withnormal pseudo-vector to the dihadron momenta plane (the handedness) [16]. The transverse polarisation of the fragment- ing quark is correlated with the relative momentum of the two hadrons, which gives rise to a transverse, target-spin-dependent azimuthalasymmetryaroundthevirtual-photondirection,withre- specttotheleptonscatteringplane.Inthiscase,thesumoftheto- taltransversemomentaofthefinalstatehadronscanbeintegrated over,leavingonlytherelativemomentumofthetwohadrons.This avoids the complexity of transverse-momentum-dependent con- volution integrals asin the analysisof single hadron production utilisingthe Collins effectandtheanalysiscan be performedus- ingcollinearfactorisation[17,18].Here,theevolutionequationsare known at next-to-leading order [19], so that results from e⁺e⁻ scattering andSIDIS can be connected, making it a theoretically cleanwaytoextracttransversityusingexisting facilities[17].The properties of the DiFFs are described in detail in Refs. [12–15, 20–23].

First evidenceforan azimuthal asymmetry in leptoproduction of

π

⁺

π

⁻ pairs was published by HERMES, using a transversely polarised hydrogentarget [24].The DiFFs were firstmeasured in e⁺e⁻reactionsbyBelle[25]andBaBar[26].Thesemeasurements indicate a sizeable u quark transversity distribution – as already knownfromthemeasurements oftheCollins asymmetry [9,27,7]

–andnon-vanishingDiFFs[28,7].

Recently, COMPASS published results on dihadron asymme- try obtainedfromthe data collected usingtransversely polarised deuteron(⁶LiD)andproton(NH3)targetsintheyears2002–2004 and 2007, respectively [29]. Due to the large acceptance of the COMPASS spectrometer and the large muon momentum of

160 GeV/c, results with high statistics were obtainedcovering a large kinematic rangein xand M_h+h⁻,the invariant mass ofthe dihadron.Sizeableasymmetriesweremeasuredontheprotontar- get while on the deuteron target only small asymmetries were observed. These results indicate non-vanishing u quark transver- sityandDiFFs, aswellasa cancellationofthecontributions ofu andd quark transversities inthe deuteron.Using thesedata sets in conjunctionwith theBelle data, afirst parametrisation of the u anddquark transversities was performedbased ona collinear framework [30]. The sameprocedure was applied to directlyex- tract u andd quark transversities in thesame x bins asused to obtaintheCOMPASSprotonanddeuteronresults[31].InthisLet- ter,thedihadron azimuthalasymmetriesmeasured fromthedata collectedin2010 withatransverselypolarisedprotontarget(NH₃, asin2007) arepresented.Thestatistics accumulatedinthisdata takingperiodincreasesthetotalavailablestatisticsonprotonbya factoroffour.

2. Theoreticalframework

Here, only a short summary of the theoretical framework is given. For a more detailed view, we recommend the references givenaboveandourrecentpaper[29]onthesametopic.

Atleadingtwistandafterintegrationovertotaltransversemo- menta, the cross section of semi-inclusivedihadron leptoproduc- tion on a transversely polarised target is given as a sum of a spin-independentandaspin-dependentpart[21,22]:

d⁷

σ

U U

dcos

θ

dM²_h+h−d

φ

Rdz dx dy d

φ

S

= α

²

2

π

Q²y

1

−

y

+

^y2 2

×

q

e²_qf₁^q

(

x

)

D_1,q

z

,

M²_h+h−

,

cos

θ

,

(1)

d⁷

σ

U T

dcos

θ

dM²_h+h−d

φ

Rdz dx dy d

φ

S

= α

²

2

π

Q²yS_⊥

(

1

−

^y

)

×

q

e²_q

|

^p1

−

^p2

|

2M_h+h⁻

sin

θ

sin

φ

R Sh^q₁

(

x

)

H_1,q

z

,

M_h²_+h−

,

cos

θ .

(2) Here, the sums run over all quark and antiquark flavours q, p₁ and p₂ denotethethree-momenta ofthetwo hadronsofthedi- hadron,wherethesubscript1 alwaysreferstothepositivehadron in this analysis. The first subscript (U) indicates an unpolarised beam andthe second (U or T), an unpolarised and transversely polarised target, respectively. Note that the contribution from a longitudinally polarisedbeamanda transverselypolarised target,

σ

LT, isneglected inthis analysissince it exhibitsa different az- imuthalangleandissuppressedbyafactorof1/Q [22].Thefine- structure constantisdenotedby

α

, y isthefractionofthemuon energy transferred to the virtual photon, D_1,q(z,M_h²_+h−,cosθ ) is thespin-independentdihadronfragmentationfunctionforaquark offlavour q, H_1,q(z,M_h²_+h−,cosθ ) isthespin-dependent DiFFand z₁, z₂ are the fractions of the virtual-photon energy carried by these twohadrons withz=^z1+^z2.The symbol S_⊥ denotes the componentofthetargetspinvectorS perpendiculartothevirtual- photondirection,andθ isthepolarangleofoneofthehadrons – commonly the positive one – in the dihadron rest frame with

Fig. 1.SchematicviewoftheazimuthalanglesφRandφSfordihadronproduction indeep-inelasticscattering,wherel,l,qand piarethethree-momentaofbeam, scatteredmuon,virtualphotonandhadronsrespectively,intheγ^∗-nucleonsystem.

Notethattheazimuthalplaneisdefinedbythedirectionsoftherelativehadron momentumandthevirtualphoton.

respecttothedihadronboostaxis.TheazimuthalangleφR S isde- finedas

φ

R S

= φ

R

− φ

S

= φ

R

+ φ

S

− π ,

(3) whereφS istheazimuthalangleoftheinitialnucleonspinandφS istheazimuthalangleofthespinvectorofthefragmentingquark withφ_S=

π

−φS (Fig. 1).TheazimuthalangleφR isdefinedby

φ

R

= (

q

×

^l

) ·

^R

|(

^q

×

^l

) ·

^R

|

^arccos

(

q

×

^l

) · (

q

×

^R

)

|

^q

×

^l

||

^q

×

^R

|

,

(4)

wherel isthe incominglepton momentum,q the virtual-photon momentum and R the relative hadron momentum [13,32] given by

R

=

^z2p1

−

z1p₂

z₁

+

^z2

=: ξ

2p₁

− ξ

1p₂

.

(5) The number N_h+h⁻ of pairs of oppositely charged hadrons pro- ducedonatransverselypolarisedtargetcanbewrittenas N_h+h⁻

x

,

y

,

z

,

M_h²_+h−

,

cos

θ, φ

R S

∝ σ

U U

1

+

f

(

x

,

y

)

PTDnn

(

y

)

A^sin_{U T}^{φR S}sin

θ

sin

φ

R S

,

(6)

omittingluminosityanddetectoracceptance.Here,PT isthetrans- verse polarisation of the target protons and Dnn(y)= _1−y¹⁻_+y^y2/2 thetransverse-spin-transfercoefficient,while f(x,y) isthetarget polarisationdilutionfactorcalculated forsemi-inclusive reactions depending on kinematics.It is given by the abundance-weighted ratioofthetotalcrosssectionforscatteringonpolarisableprotons tothat forscatteringon all nucleiinthe target. Thedependence ofthedilutionfactoronthehadron transversemomenta appears to be weak in the kinematic range ofthe COMPASS experiment.

Dilutionduetoradiativeeventsistakenintoaccountbytheratio oftheone-photonexchangecrosssectiontothetotalcrosssection.

For¹⁴NH₃, f containscorrectionsforthepolarisationofthespin-1 14Nnucleus.

Theasymmetry

A^sin_{U T}^{φR S}

= |

^p1

−

^p2

|

2M_h+h⁻

qe²_q

·

h^q₁

(

x

) ·

H_1,q

(

z

,

M²_h+h−

,

cos

θ )

qe²_q

·

^f₁^q

(

x

) ·

^D1,q

(

z

,

M²_h+h−

,

cos

θ )

⁽⁷⁾

isthenproportionaltotheproductofthetransversitydistribution functionandthespin-dependentdihadronfragmentationfunction, summedoverthequarkandantiquarkflavours.

Fig. 2. Invariant mass distributions of the final samples. The cut Mh+h−<

1.5 GeV/c²isindicated.TheK⁰,ρand f1resonancesarevisible.

3. Experimentaldataandanalysis

The analysis presented in this Letter is performed using data taken in the year 2010 with the COMPASS spectrometer [33], which was obtained by scattering positive muons of 160 GeV/c produced fromthe M2 beamline ofCERNs SPS off atransversely polarisedsolid-stateNH3 target.Detailsondatataking,dataqual- ity,eventselectionandanalysiscanbefoundinRefs.[27,29].

Thebeammuonsarenaturallypolarisedwithanaveragelongi- tudinalpolarisationofabout0.8 witharelativeuncertaintyof 5%.

The average dilution factor for NH₃ is ^f∼⁰.15 and the aver- age transverse polarisation is ^PT∼⁰.8. The same target as in theyear2007 wasused.Itconsistedofthreecylindricalcellswith differentorientations ofthe polarisationvector. In orderto com- pensateforacceptanceeffectsthepolarisationwasdestroyed and builtupinoppositedirectioneveryfourtofivedays,foratotalof 12 data-takingsub-periods.

For the analysis, events with incoming and outgoing muons and at least two reconstructed hadrons from the reaction ver- tex inside the target cells are selected. Equal flux through the whole targetisobtainedby requiringthat theextrapolatedbeam track crossesall three cells. In order to select events in the DIS regime, cutsare appliedonthesquaredfour-momentumtransfer, Q²>1(GeV/c)²,andontheinvariantmassofthefinalhadronic state, W>5 GeV/c². Furthermore,the fractional energy transfer tothevirtual photonisrequiredto be y>0.1 and y<0.9 tore- moveeventswithpoorly reconstructedvirtualphotonenergyand eventswithlargeradiativecorrections,respectively.

Thedihadronsampleconsistsofallcombinationsofoppositely chargedhadronsoriginatingfromthereactionvertex.Hadronspro- ducedin the currentfragmentation region are selected requiring z>0.1 for the fractional energy and xF >0.1 of each hadron.

Exclusivedihadronproductionissuppressedbyrequiringthemiss- ingenergyEmiss=((P+^q−^p1−^p2)²−^m2P)/(2mP)tobegreater than3.0 GeV,where P isthetarget protonsfour-momentumand m_P itsmass. Asthe azimuthal angleφR is onlydefinedfornon- collinear vectors R and q, a minimum value is required on the componentof R perpendicular to q,|^R⊥|>0.07 GeV/c.Afterall cuts,3.5×^107h+h−combinationsremain.Fig. 2showstheinvari- ant mass distributions of the dihadron system, always assuming the pion mass for each hadron. A cut of M_h+h⁻<1.5 GeV/c² is applied in order to allow for the analysisof the data suggested by[21],whereboththespin-dependentandspin-independentdi- hadronfragmentationfunctionsareexpandedintermsofLegendre polynomialsofcosθ.Whileremovingonlyanegligiblepartofthe

Fig. 3.Protonasymmetry,integratedovertheangleθ,asafunctionofx,zand Mh+h−,forthedatatakenwiththeproton(NH3)targetintheyear2010.Thegreybands indicatethesystematicuncertainties.ThelastbininMh⁺h⁻containseventswhichwereremovedfromthesampleusedforresultsshownasafunctionofxandz.

Fig. 4.Comparison of the asymmetry obtained from the data taken in the years 2007 and 2010, integrated over the angleθ, as a function ofx,zandMh⁺h⁻, respectively.

data,thiscutallowsforaconvenientrestrictiontorelative s- and p-wavesinthisanalysis.

In the analysiswe extract the product A= ^Asin_{U T}^{φR Ssin}θ^{, in-} tegrated over the angle θ. For a detailed discussion we refer to Ref.[29].ItisimportanttostressthatintheCOMPASSacceptance the openingangle θ peaksclose to

π

/2 with ^sinθ=⁰.94 and thecosθ distributionissymmetricaroundzero.Inordertoallow foradetailedconsiderationoftheexpansionmentionedabove,the mean values of all three relevant distributions (sinθ, cosθ and cos²θ) for the individual kinematic bins can be found on HEP- DATA[34].The asymmetry isevaluated in kinematicbins of x, z or M_h+h⁻, whilealways integratingover theother two variables.

Asestimatortheextendedunbinnedmaximumlikelihoodfunction inφR andφS isused,alreadydescribedinRef.[29].

In order to avoidfalse asymmetries,care was taken to select only such data for the analysis for which the spectrometer per- formance was stable in consecutive periods of data taking. This was ensured by extensive data quality tests described in detail inRef. [27].The remaining datasample was carefullyscrutinised for a possible systematic bias in the final asymmetry. Here, the two main sources for uncertainties are false asymmetries,which can be evaluated by combining data samples with same target spin orientation, and effects of acceptance,which can be evalu- atedby comparingsub-samplescorresponding todifferentranges intheazimuthal angleofthe scatteredmuon.No significantsys- tematic bias could be found and the results from all 12 sub- periodsofdatatakingproved tobecompatible. Therefore,anup- per limit was estimated comparing the results of the systematic studies to expected statistical fluctuations. The resulting system- aticuncertaintyforeachdata pointamountsto about75% ofthe statisticaluncertainty.An additionalscaleuncertainty of2.2% ac- counts for uncertainties in the determination of target polarisa- tion andtarget dilution factorcalculated for semi-inclusivereac- tions[35].

4. Results

The obtained asymmetry is shown in Fig. 3 as a function of x, z and M_h+h⁻. Large negative asymmetry amplitudes are ob- servedinthehighxregion,whichimpliesthatboth,thetransver- sity distributionsandthespin-dependent dihadronfragmentation functions do not vanish. Over the measured range ofthe invari- ant mass M_h+h⁻ and z,theasymmetry isnegative andshowsno strong dependence on these variables. Fig. 4 shows the compar- ison of thepresent resultsto the previously published COMPASS results ontheprotontarget from2007 data [29].The resultsob- tained fromthe dataof2010 havesignificantly smallerstatistical uncertainties then theprevious resultsfrom 2007 data and both are in good agreement (CL of 25%). Fig. 5 (top) shows the final result obtained by combining both data sets together with pre- dictions from modelcalculations [36,37]. The bottom plotshows thesamedatawithacutonthequark valenceregion(x>0.032) enhancing the observed signal as a function of z and M_h+h⁻. In comparison tothe published HERMES results[24],theresults on the proton target presented in this work have higher statistics and cover a larger kinematic range in x and M_h+h⁻. In the the- oreticalapproach[21–23],alldihadronfragmentationfunctionsfor di-pion productionwerecalculatedintheframework ofa specta- tor model forthe fragmentationprocess. Predictions were made fortheDiFF H₁ aswellasforthes- and p-wavecontributionsto thespin-independentfragmentationfunctionsD1 andinRef.[23]

the expected asymmetries for COMPASS were calculated assum- ing different models for the transversity distributions. Recently, these parametrisations of the dihadron fragmentation functions fromRef. [23] were also usedtogether withthe transversity dis- tributions extractedfrom single hadron production[11] to make predictionsforbothprotonanddeuterontargetsinthekinematic rangecoveredbyCOMPASS.Thecalculatedasymmetryisshownas solid bluelinesin Fig. 5(topandbottom).The latteradaptedfor thecutinx,showsagoodagreementofthesepredictionswithour

Fig. 5.Protonasymmetry,integratedovertheangleθ,asafunctionofx,zandMh⁺h⁻,forthecombineddatatakenwiththeproton(NH3)targetintheyears2007 and 2010 (topplot).Thegreybandsindicatethesystematicuncertainties.Thebottomplotshowsthesamedataforthevalencequarkregion(x≥0.032).Thecurvesintheupper plotsshowpredictions[36,37]madeusingthetransversityfunctionsextractedinRef.[11](solidlines)orapQCDbasedcountingruleanalysis(dottedlines).Thecurvesin thelowerplotsshowthepredictionsof[36]inthesamex≥⁰.032 region.Notethatthesignoftheoriginalpredictionswaschangedtoaccommodatethephaseπinthe definitionoftheangleφR SusedintheCOMPASSanalysis.

data.Significantasymmetryamplitudesarepredictedandthexde- pendentshapeiswelldescribed,aswellasforthedependenceon z inthecaseofthecalculationsbyBacchettaetal.Agoodagree- mentintermsoftheM_h+h⁻ dependenceisonlyinthemassregion ofthe

ρ

meson;nooptimizationofparameters inthecalculation ofthe dihadron fragmentation function to extendthe agreement over a larger M_h+h⁻ region (as e.g., the fractionof the

ω

to 3

π

decayinthes–pinterference)wasperformedby theauthors.The predictionofMa etal.[37] (dashedlines inFig. 5(top)) usesthe parametrisationsof [23] forthedihadron fragmentation, together withamodelforthe transversity distributions,based ona pQCD countingruleanalysis. Thispredictiondescribesthemaintrendof thedatabuttendstooverestimatethemeasuredasymmetry.

5. ComparingthedihadronasymmetryandtheCollins asymmetry

ThereisastrikingsimilarityamongtheCollins asymmetryfor positive and for negative hadrons [27] and the dihadron asym- metry as functions of x, as clearly shown in Fig. 6, where the combined results from the 2007 and 2010 COMPASS runs are presented.First, there is a mirror symmetry betweenthe Collins asymmetry forpositive andfor negative hadrons, the magnitude of the asymmetry being essentially identical and the sign being opposite. This symmetry has been phenomenologically described intermsofoppositesignsofu anddquark transversitydistribu- tionswithalmostequalmagnitudeandoppositesignforfavoured andunfavouredCollinsfragmentationfunctions[11].

Thenewresultsshowthatthevaluesofthedihadronasymme- tryareslightlylargerinmagnitude,butveryclosetothevaluesof theCollinsasymmetryforpositivehadronsandtothemeanofthe valuesoftheCollinsasymmetryforpositiveandnegativehadrons, afterchangingthesignoftheasymmetry ofthenegative hadrons.

Thehadronsamplesonwhichtheseasymmetriesareevaluatedare different[29,27]sinceatleastonehadronwithz>0.2 isrequired

Fig. 6.Comparisonoftheasymmetryvs. xobtainedintheanalysisofdihadronpro- ductiontothecorrespondingCollinsasymmetryforthecombined2007 and2010 data.

to evaluate theCollins asymmetry, whileall the combinations of positiveandnegativehadronswithz>0.1 areusedinthecaseof the dihadron asymmetry.It has beenchecked, however,that the similaritybetweenthe two differentasymmetriesstays thesame whenmeasuringtheasymmetriesforthecommonhadronsample, selected withtherequirementof atleasttwo oppositely charged hadronsproducedintheprimaryvertex.Thisgivesastrongindica- tionthattheanalysingpowersofthesingleanddihadronchannels arealmostthesame.

More work has been done to understand these similarities.

SincetheCollinsasymmetriesaretheamplitudesofthesinemod- ulations of the Collins angles φC^± =φh^± +φS −

π

, where φh^±

Fig. 7.Difference between the two dihadron anglesφRandφ2h.

are theazimuthal angles ofpositive andnegative hadronsinthe

γ

^∗-nucleon system, the mirror symmetry suggests that in the multi-hadronsfragmentationofthestruckquarkazimuthalangles of positive and negative hadrons created in the event differ by

≈

π

,namelythatwhena transverselypolarisedquark fragments, oppositelychargedhadronshaveantiparalleltransversemomenta.

Thisanti-correlationbetweenφ_h+ andφ_h− couldbeduetoalocal transverse momentumconservation inthe fragmentation, asitis presentintheLEPTO[38]generatorforspin-independentDIS.The relevantpointhereisthatsuchacorrelationshowsupalsointhe Collins fragmentationfunction that describesthe spin-dependent hadronisationofatransverselypolarisedquarkqintohadrons.

Ifthisis the case, asymmetriescorrelated withthe dihadrons can also be obtainedin a way differentfrom the one described above.Foreachpairofoppositelychargedhadrons,usingtheunit vectors oftheir transverse momenta, we haveevaluated the an- gleφ2h ofthevector RN= ˆ^pT,h⁺− ˆ^pT,h⁻ whichisthearithmetic meanoftheazimuthal anglesofthetwohadronsaftercorrecting for the discussed

π

phase difference between both angles. This azimuthal angle of the dihadron is strongly correlated with φR, ascanbe seeninFig. 7wherethedifferenceofthetwoanglesis shown.ThesamecorrelationispresentalsointheLEPTOgenerator forspin-independent DIS.Introducingtheangleφ2h,S=φ2h−φS, one simply obtains the mean of the Collins angle of the posi- tiveandnegativehadrons(againaftercorrectingforthediscussed

π

phase difference betweenthe two angles), i.e. a mean Collins typeangleofthedihadron.Theamplitudesofthemodulations of sinφ2h,S,whichcould thenbecalledtheCollinsasymmetryforthe dihadron,areshownasa functionof xinFig. 8 forall theh⁺h⁻ pairs with z>0.1 in the 2010 data, and comparedwith the di- hadronasymmetryalreadygiveninFig. 3,whereanadditionalcut ofp_T>0.1 GeV/c onthetransversemomentumoftheindividual hadronswas appliedforaprecisedeterminationoftheazimuthal angles.Theasymmetriesareveryclose,hintingatacommonphys- icaloriginfortheCollinsmechanismandthedihadronfragmenta- tionfunction,asoriginally suggestedinthe³P0 Lundmodel[39], intherecursive stringfragmentationmodel [32,40]andinrecent theoreticalwork[41].¹⁹

6. Conclusions

Inthispaperwepresenttheresultsofanewmeasurement of the transverse spin asymmetry indihadron production in DISof

19 Afterfinalizingthepresentpaper,anewpublicationappeared[42]reproducing withMonteCarlocalculationstheobservationsofthissection.

Fig. 8.Comparisonbetweenthedihadronasymmetry(blackpoints)andtheCollins- likeasymmetryforthedihadron(openbluepoints)asafunctionofxforthe2010 data.

160GeV/c muonsoffatransverselypolarisedproton(NH3)target.

The measured asymmetry amplitudesare in agreement withour previousmeasurementperformedwithdatacollectedin2007.The statistical and systematic uncertainties are considerably reduced.

The combined results show a clear signal in the x range of the valencequarksandareinagreementwitharecenttheoreticalcal- culation,usingasinputthetransversitydistributionobtainedfrom global fits to the Collins asymmetry.As expected, the results do notshow astrongzdependence.Clearstructuresareexhibitedas a function ofthe dihadrons’ invariant mass,withvaluescompat- ible withzero atabout 0.5 GeV/c² anda sharp fall to −^{0.05 at} the

ρ

mass.These newcombinedresults will allowa more pre- cise extractionof thetransversity distributions along thelines of the models recently developed.The high precision and the large kinematicrangeoftheCOMPASSprotondataallowsustocompare thedihadronasymmetry andtheCollins asymmetry.Inthepaper we underlinethestrikingsimilaritybetweenthemandgiveargu- ments infavour of a commonunderlying physics mechanism, as alreadysuggestedinthepastby severalauthors.Inparticularwe show that inour datatheangle commonlyusedinthe dihadron asymmetry analysisisveryclosetothemeanCollinsangleofthe two hadrons, andthat thus the asymmetriesevaluated using the twoanglesturnouttobeverysimilar.

Acknowledgements

This work was madepossible thanks to the financial support ofourfunding agencies.Wealsoacknowledgethe supportofthe CERNmanagementandstaff,aswellastheskillsandeffortsofthe techniciansofthecollaboratinginstitutes.

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