Measurement of azimuthal hadron asymmetries in semi-inclusive deep inelastic scattering off unpolarised nucleons

0.54 MB·

by  C. Adolph

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
COMPASS
CERN-PH-EP-2014–009
January23,2014
Measurement of azimuthal hadron asymmetries in semi-inclusive deep
inelastic scattering off unpolarised nucleons
TheCOMPASScollaboration
4
1
0 Abstract
2
Spin-averagedasymmetriesintheazimuthaldistributionsofpositiveandnegativehadronsproduced
n
a in deep inelastic scattering were measured using the CERN SPS muon beam at 160 GeV/c and a
J 6LiD target. The amplitudes of the three azimuthal modulations cosφ , cos2φ and sinφ were
h h h

4 obtainedbinningthedataseparatelyineachoftherelevantkinematicvariablesx,z orph andbin-
T
2 ninginathree-dimensionalgridofthesethreevariables. Theamplitudesofthecosφ andcos2φ
h h

modulationsshowstrongkinematicdependenciesbothforpositiveandnegativehadrons.
]
x
e
-
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e
h
[

1
v
4
8
2
6
.
1
0
4
1
:
v
i (tobesubmittedtoNucl.Phys.B)
X
r
a
TheCOMPASSCollaboration
C.Adolph8,R.Akhunzyanov7,M.G.Alekseev24,Yu.Alexandrov15,*,G.D.Alexeev7,A.Amoroso27,28,
V.Andrieux22,V.Anosov7,A.Austregesilo10,17,B.Badełek31,F.Balestra27,28,J.Barth4,G.Baum1,
R.Beck3,Y.Bedfer22,A.Berlin2,J.Bernhard13,R.Bertini27,28,K.Bicker10,17,J.Bieling4,R.Birsa24,
J.Bisplinghoff3,M.Bodlak19,M.Boer22,P.Bordalo12,a,F.Bradamante25,10,C.Braun8,A.Bravar24,
A.Bressan25,24,M.Büchele9,E.Burtin22,L.Capozza22,M.Chiosso27,28,S.U.Chung17,b,
A.Cicuttin26,24,M.L.Crespo26,24,Q.Curiel22,S.DallaTorre24,S.S.Dasgupta6,S.Dasgupta24,
O.Yu.Denisov28,S.V.Donskov21,N.Doshita33,V.Duic25,W.Dünnweber16,M.Dziewiecki32,
A.Efremov7,C.Elia25,24,P.D.Eversheim3,W.Eyrich8,M.Faessler16,A.Ferrero22,A.Filin21,
M.Finger19,M.Fingerjr.19,H.Fischer9,C.Franco12,N.duFresnevonHohenesche13,10,
J.M.Friedrich17,V.Frolov10,R.Garfagnini27,28,F.Gautheron2,O.P.Gavrichtchouk7,
S.Gerassimov15,17,R.Geyer16,M.Giorgi25,24,I.Gnesi27,28,B.Gobbo24,S.Goertz4,M.Gorzellik9,
S.Grabmüller17,A.Grasso27,28,B.Grube17,A.Guskov7,T.Guthörl9,c,F.Haas17,D.vonHarrach13,
D.Hahne4,R.Hashimoto33,F.H.Heinsius9,F.Herrmann9,F.Hinterberger3,Ch.Höppner17,
N.Horikawa18,d,N.d’Hose22,S.Huber17,S.Ishimoto33,e,A.Ivanov7,Yu.Ivanshin7,T.Iwata33,
R.Jahn3,V.Jary20,P.Jasinski13,P.Joerg9,R.Joosten3,E.Kabuß13,D.Kang13,B.Ketzer17,
G.V.Khaustov21,Yu.A.Khokhlov21,f,Yu.Kisselev7,F.Klein4,K.Klimaszewski30,J.H.Koivuniemi2,
V.N.Kolosov21,K.Kondo33,K.Königsmann9,I.Konorov15,17,V.F.Konstantinov21,
A.M.Kotzinian27,28,O.Kouznetsov7,Z.Kral20,M.Krämer17,Z.V.Kroumchtein7,N.Kuchinski7,
F.Kunne22,K.Kurek30,R.P.Kurjata32,A.A.Lednev21,A.Lehmann8,S.Levorato24,J.Lichtenstadt23,
A.Maggiora28,A.Magnon22,N.Makke25,24,G.K.Mallot10,C.Marchand22,A.Martin25,24,
J.Marzec32,J.Matousek19,H.Matsuda33,T.Matsuda14,G.Meshcheryakov7,W.Meyer2,
T.Michigami33,Yu.V.Mikhailov21,Y.Miyachi33,A.Nagaytsev7,T.Nagel17,F.Nerling9,S.Neubert17,
D.Neyret22,V.I.Nikolaenko21,J.Novy20,W.-D.Nowak9,A.S.Nunes12,I.Orlov7,A.G.Olshevsky7,
M.Ostrick13,R.Panknin4,D.Panzieri29,28,B.Parsamyan27,28,S.Paul17,M.Pesek19,D.Peshekhonov7,
G.Piragino27,28,S.Platchkov22,J.Pochodzalla13,J.Polak11,24,V.A.Polyakov21,J.Pretz4,h,
M.Quaresma12,C.Quintans12,S.Ramos12,a,G.Reicherz2,E.Rocco10,V.Rodionov7,E.Rondio30,
A.Rychter32,N.S.Rossiyskaya7,D.I.Ryabchikov21,V.D.Samoylenko21,A.Sandacz30,S.Sarkar6,
I.A.Savin7,G.Sbrizzai25,24,P.Schiavon25,24,C.Schill9,T.Schlüter16,A.Schmidt8,K.Schmidt9,c,
H.Schmieden3,K.Schönning10,S.Schopferer9,M.Schott10,O.Yu.Shevchenko7,L.Silva12,
L.Sinha6,S.Sirtl9,M.Slunecka7,S.Sosio27,28,F.Sozzi24,A.Srnka5,L.Steiger24,M.Stolarski12,
M.Sulc11,R.Sulej30,H.Suzuki33,d,A.Szabeleski30,T.Szameitat9,P.Sznajder30,S.Takekawa28,
J.terWolbeek9,c,S.Tessaro24,F.Tessarotto24,F.Thibaud22,S.Uhl17,I.Uman16,M.Vandenbroucke22,
M.Virius20,J.Vondra20 L.Wang2,T.Weisrock13,M.Wilfert13,R.Windmolders4,W.Wis´licki30,
H.Wollny22,K.Zaremba32,M.Zavertyaev15,E.Zemlyanichkina7,andM.Ziembicki32
1 UniversitätBielefeld,FakultätfürPhysik,33501Bielefeld,Germanyj
2 UniversitätBochum,InstitutfürExperimentalphysik,44780Bochum,Germanyjq
3 UniversitätBonn,Helmholtz-InstitutfürStrahlen-undKernphysik,53115Bonn,Germanyj
4 UniversitätBonn,PhysikalischesInstitut,53115Bonn,Germanyj
5 InstituteofScientificInstruments,ASCR,61264Brno,CzechRepublick
6 MatrivaniInstituteofExperimentalResearch&Education,Calcutta-700030,Indial
7 JointInstituteforNuclearResearch,141980Dubna,Moscowregion,Russiam
8 UniversitätErlangen–Nürnberg,PhysikalischesInstitut,91054Erlangen,Germanyj
9 UniversitätFreiburg,PhysikalischesInstitut,79104Freiburg,Germanyjq
10 CERN,1211Geneva23,Switzerland
11 TechnicalUniversityinLiberec,46117Liberec,CzechRepublick
12 LIP,1000-149Lisbon,Portugaln
13 UniversitätMainz,InstitutfürKernphysik,55099Mainz,Germanyj
14 UniversityofMiyazaki,Miyazaki889-2192,Japano
15 LebedevPhysicalInstitute,119991Moscow,Russia
16 Ludwig-Maximilians-UniversitätMünchen,DepartmentfürPhysik,80799Munich,Germanyjp
17 TechnischeUniversitätMünchen,PhysikDepartment,85748Garching,Germanyjp
18 NagoyaUniversity,464Nagoya,Japano
19 CharlesUniversityinPrague,FacultyofMathematicsandPhysics,18000Prague,CzechRepublick
20 CzechTechnicalUniversityinPrague,16636Prague,CzechRepublick
21 StateResearchCenteroftheRussianFederation,InstituteforHighEnergyPhysics,142281Protvino,
Russia
22 CEAIRFU/SPhNSaclay,91191Gif-sur-Yvette,Franceq
23 TelAvivUniversity,SchoolofPhysicsandAstronomy,69978TelAviv,Israelr
24 TriesteSectionofINFN,34127Trieste,Italy
25 UniversityofTrieste,DepartmentofPhysics,34127Trieste,Italy
26 AbdusSalamICTP,34151Trieste,Italy
27 UniversityofTurin,DepartmentofPhysics,10125Turin,Italy
28 TorinoSectionofINFN,10125Turin,Italy
29 UniversityofEasternPiedmont,15100Alessandria,Italy
30 NationalCentreforNuclearResearch,00-681Warsaw,Polands
31 UniversityofWarsaw,FacultyofPhysics,00-681Warsaw,Polands
32 WarsawUniversityofTechnology,InstituteofRadioelectronics,00-665Warsaw,Polands
33 YamagataUniversity,Yamagata,992-8510Japano
a AlsoatInstitutoSuperiorTécnico,UniversidadedeLisboa,Lisbon,Portugal
b AlsoatDepartmentofPhysics,PusanNationalUniversity,Busan609-735,RepublicofKoreaand
atPhysicsDepartment,BrookhavenNationalLaboratory,Upton,NY11973,U.S.A.
c Supported by the DFG Research Training Group Programme 1102 “Physics at Hadron Accelera-
tors”
d AlsoatChubuUniversity,Kasugai,Aichi,487-8501Japano
e AlsoatKEK,1-1Oho,Tsukuba,Ibaraki,305-0801Japan
f AlsoatMoscowInstituteofPhysicsandTechnology,MoscowRegion,141700,Russia
g present address: National Science Foundation, 4201 Wilson Boulevard, Arlington, VA 22230,
UnitedStates
h presentaddress: RWTHAachenUniversity,III.PhysikalischesInstitut,52056Aachen,Germany
i AlsoatGSImbH,Planckstr.1,D-64291Darmstadt,Germany
j SupportedbytheGermanBundesministeriumfürBildungundForschung
k SupportedbyCzechRepublicMEYSGrantsME492andLA242
l SupportedbySAIL(CSR),Govt.ofIndia
m SupportedbyCERN-RFBRGrants08-02-91009and12-02-91500
n SupportedbythePortugueseFCT-FundaçãoparaaCiênciaeTecnologia,COMPETEandQREN,
GrantsCERN/FP/109323/2009,CERN/FP/116376/2010andCERN/FP/123600/2011
o SupportedbytheMEXTandtheJSPSundertheGrantsNo.18002006,No.20540299andNo.18540281;
DaikoFoundationandYamadaFoundation
p SupportedbytheDFGclusterofexcellence‘OriginandStructureoftheUniverse’(www.universe-
cluster.de)
q SupportedbyEUFP7(HadronPhysics3,GrantAgreementnumber283286)
r SupportedbytheIsraelScienceFoundation,foundedbytheIsraelAcademyofSciencesandHu-
manities
s SupportedbythePolishNCNGrantDEC-2011/01/M/ST2/02350
*Deceased
Measurementofazimuthalhadronasymmetriesinsemi-inclusivedeepinelastic... 3
1 Introduction
In the quark-parton model the transverse degrees of freedom of the nucleon constituents are usually
integrated over, and the parton distribution functions (PDFs) as determined in lepton-nucleon deep in-
elastic scattering (DIS) depend only on the Bjorken scaling variable x and on Q2, the virtuality of the
exchanged photon. On the other hand it was soon realised [1, 2] that in semi-inclusive DIS (SIDIS)
processes,namelyinlepton-nucleonDISinwhichatleastonehadronfromthecurrentjetisdetected,a
possibleintrinsictransversemomentumofthetargetquarkwouldcausemeasurableeffectsinthecross-
section. IndeedtheSIDIScross-sectionisexpectedtoexhibitacosφ andacos2φ modulation,where
h h
φ is the angle between the lepton scattering plane and the plane defined by the hadron and the virtual
h
photon directions, as shown in Fig. 1. The coefficients of these modulations are predicted to vanish
asymptoticallyas1/Qand1/Q2,respectively[2]. Theearlymeasurementsinthe70showeverwerenot
accurateenoughtodetectsuchmodulations.
hadron plane
ph ph
T
h
y
x
z
q
lepton plane
Fig.1: SIDISintheγ∗N system: p(cid:126)h isthemomentumoftheproducedhadronandp(cid:126)h itstransversecomponent
T
withrespecttothevirtualphotondirection.
Attheendofthe70s,interestinpossiblemodulationsoftheSIDIScross-sectioncamealsofromadiffer-
entdirection. Azimuthalasymmetriesinunpolarisedprocessesinquantumchromodynamics(QCD)are
generatedbygluonradiationandsplitting,andtheobservationoftheseasymmetrieswasinfactproposed
as a test of perturbative QCD (pQCD) [3]. Such a possibility however was immediately questioned by
R. Cahn [4]. Using simple kinematics the amplitudes of the azimuthal modulations expected from the
quark intrinsic transverse momentum could be computed and shown to be the dominant term as long
as both Q2 and the hadron transverse momentum are not too large [4]. Azimuthal modulations in the
SIDIS cross-section were indeed first observed by the EMC Collaboration [5, 6] and then at FNAL [7],
and at higher energies by the ZEUS experiment at HERA [8]. The present understanding is that pQCD
accountsfortheasymmetriesatlargevaluesofthefinal-statehadrontransversemomentumph,whileat
T
lowvalues(ph(cid:46)1GeV/c)itistheintrinsictransversemotionofthequarkswhichplaysthekeyrole[9].
T
Intrinsictransversemomentumhasrecentlyattractedmuchattentioninconnectionwiththegreatexper-
imental and theoretical effort to understand the origin of the nucleon spin and, in particular, the many
transverse spin effects in hadronic reactions observed since several decades. The PDFs of the nucleon
have been generalised to include this new degree of freedom, introducing the transverse-momentum-
dependent(TMD)distributions. Also,TMDfragmentationfunctions(FF)havebeenintroduced,thebest
knownbeingtheCollinsFF,whichdescribesacorrelationbetweenthetransversemomentump(cid:126)h ofeach
T
of the hadrons in a hadronic jet and the spin of the fragmenting quark in the hadronization process of
a transversely polarised quark. The knowledge of this new sector of hadronic physics is still at its be-
ginning, but several new important phenomena have been assessed [10] within a solid theoretical QCD
framework[11]. Withinthisframework,muchattentionhasbeenpayedtodistributionswhichareT-odd
4 TheCOMPASScollaboration
and for a long time were believed to be zero to preserve T-invariance. It was demonstrated afterwards
that either initial or final state interactions can result in non-zero T-odd distributions. One T-odd PDF,
the Sivers function, has already been shown to be definitely different from zero in SIDIS processes off
transverselypolarisedprotons,evenathighenergies[12,13]. AnotherT-oddTMDPDFistheso-called
Boer-Mulders(B-M)function,whichdescribesthecorrelationbetweenthequarktransversespinandits
transverse momentum in an unpolarised nucleon [14]. On top of the Cahn effect, the B-M TMD PDF
convoluted with the Collins FF is expected to contribute to the amplitudes of the cosφ and cos2φ
h h
modulations in unpolarised SIDIS processes and its extraction from the cross-section data is an impor-
tantgoalofthemorerecentinvestigationsatlowerenergiesbytheHERMESCollaboration[15]andby
theCLASCollaboration[16].
Inthispaper,firstresultsontheazimuthalmodulationsinunpolarisedSIDISobtainedbytheCOMPASS
experimentarepresented. Thepaperisorganisedasfollows. Section2summarisestheformalismforthe
SIDIScross-sectionintheone-photonexchangeapproximation. Ashortdescriptionoftheexperimental
apparatus during the 2004 run is given in Sect. 3. The data analysis, the method used to extract the
azimuthal asymmetries and the studies of the possible systematic effects are described in Sections 4, 5
and 6. Finally,theresultsaregiveninSect.7.
2 TheSIDIScross-section
The spin-averaged differential SIDIS cross-section for the production of a hadron h with transverse
momentumph andafractionz oftheavailableenergyisgivenintheone-photonexchangeapproxima-
T
tion[17]by:
dσ (cid:16)
= σ 1+(cid:15) AUU cosφ +
phdphdxdydzdφ 0 1 cosφh h
T T h
(cid:17)
+(cid:15) AUU cos2φ +λ(cid:15) ALU sinφ , (1)
2 cos2φh h 3 sinφh h
whereσ istheφ independentpartofthecross-section,λisthelongitudinalpolarisationoftheincident
0 h
lepton,y isthefractionalenergyofthevirtualphoton,andthequantities(cid:15) aregivenby:
i
√ √
2(2−y) 1−y 2(1−y) 2y 1−y
(cid:15) = , (cid:15) = , (cid:15) = . (2)
1 1+(1−y)2 2 1+(1−y)2 3 1+(1−y)2
The amplitudes AXU will be referred to as azimuthal asymmetries in the following. The superscripts
f(φ )
h
UU andLU refertounpolarisedbeamandtarget, andtolongitudinallypolarisedbeamandunpolarised
target,respectively.
The cosφ and the cos2φ asymmetries are related to the Cahn effect and to the B-M TMD PDF. The
h h
CahneffectcontributionstoAUU andAUU originatefromkinematics,whentheintrinsictransverse
cosφh cos2φh
momenta(cid:126)k of quarks inside the nucleon is taken into accouunt, starting from the elastic quark-lepton
T
cross-section [4]. Also the B-M function contributes to both AUU and AUU , where it appears
cosφh cos2φh
convoluted with the Collins FF. The ALU asymmetry is due to higher-twist effects and has no clear
sinφh
interpretationintermsofthepartonmodel.
The amplitudes of the cosφ and cos2φ modulations have been measured in SIDIS on unpolarised
h h
proton and deuteron targets in a kinematic region similar to that of COMPASS by previous experi-
ments [5, 7] and at higher energies by the ZEUS experiment [8]. Results at lower energies have been
recentlypublishedbyHERMES[15]forpositiveandnegativehadronsseparatelyandbyCLAS[16]for
π+.
COMPASShaspresentedpreliminaryresultsforAUU ,AUU andALU onthedeuteronforpositive
cosφh cos2φh sinφh
and negative hadrons in 2008 [18]. A more refined analysis on a limited phase space as well as the
Measurementofazimuthalhadronasymmetriesinsemi-inclusivedeepinelastic... 5
removalofsomespecificproblemsrelatedtotheacceptancecorrectionhasleadthefinalresultspresented
here. Theyhavebeenobtainedfromthedatacollectedin2004withthetransverselypolarised6LiDtarget
tomeasuretheCollinsandSiversasymmetries[19].
3 Theexperimentalapparatus
A brief description of the 2004 COMPASS apparatus is given in this Section. More details on the
COMPASSspectrometercanbefoundinRef.[20].
The µ+ beam was naturally polarised by the π decay mechanism, and the beam polarisation λ was
about −80%. The beam intensity was 2·108 µ+ per spill of 4.8 s with a cycle time of 16.8 s. The µ+
momentum (∼160 GeV/c) was measured event by event in a Beam Momentum Station (BMS) with a
precision∆p/p(cid:46)1%.
Asthestudyofthenucleonspinwasthemainpurposeoftheexperiment,apolarisedtargetsystemwas
usedin2004. Itconsistedoftwocells, each60cmlong, filledwith6LiD,placedonthebeamline, and
housed in a cryostat positioned along the axis of a solenoidal magnet. The 6LiD grains were immersed
inamixtureofliquid3He/4He. Asmallcontaminationof7Lialmostexactlybalancestheprotonexcess
in3He,sothatthetargetcaneffectivelyberegardedtobeisoscalar. Thedatausedinthepresentanalysis
(25%ofthefull2004datasample)havebeentakenwiththetargettransverselypolarised,i.e.polarised
along the direction of the dipole field (0.42 T) provided by two additional saddle coils. The two target
cellswereoppositelypolarised,sodataweretakensimultaneouslyforthetwotargetpolarizationstates.
Inordertokeepsystematiceffectsundercontrol,theorientationofthepolarisationwasreversedevery4
to5days(referredtoasa“period”ofdatatakinginthefollowing).
Thespectrometerconsistsoftwomagneticstagesandcomprisesavarietyoftrackingdetectors,aRICH
detector, two hadron calorimeters, and thick absorbers providing muon identification. The first stage is
centredaroundthespectrometermagnetSM1,located4mdownstreamfromthetargetcentre,whichhas
abendingpowerof1Tmandalargeopeningangletocontainthehadronsofthecurrentjet. Thesecond
stageusesthespectrometermagnetSM2(operatedatabendingpowerof4.4Tm), located18mdown-
stream from the target, with an acceptance of ±50 and ±25 mrad in the horizontal and vertical planes,
respectively. Inordertomatchtheexpectedparticlefluxatvariouslocationsalongthespectrometer,var-
ioustrackingdetectorsareused. Thesmall-areatrackersconsistofseveralstationsofscintillatingfibres,
silicon detectors, micromegas chambers and gaseous chambers using the GEM technique. Large-area
trackingdevicesaremadefromgaseousdetectors(DriftChambers, StrawTubes, andMWPC’s)placed
aroundthetwospectrometermagnets.
Muonsareidentifiedinlarge-areadetectorsusingdrift-tubesdownstreamofironorconcreteabsorbers.
Hadrons are detected by two large iron-scintillator sampling calorimeters, installed in front of the ab-
sorbers and shielded to avoid electromagnetic contamination. The charged particle identification relies
ontheRICHtechnology,butisnotusedinthisanalysiswhereresultsaregivenfornon-identifiedcharged
hadronsonly.
In most DIS events the scattered muon is identified by coincidence signals in the trigger hodoscopes
which measure the particle trajectory in the vertical (non-bending) plane and check its compatibility
with the target position. Several veto counters upstream of the target are used to avoid triggers due to
beamhalomuons. Inadditiontothisinclusivetriggermode,severalsemi-inclusivetriggersselectevents
fulfilling requirements based on the muon energy loss and on the presence of a hadron signal in the
calorimeters. TheacceptanceisfurtherextendedtowardhighQ2 valuesbytheadditionofastandalone
calorimetrictriggerinwhichnoconditionissetforthescatteredmuon.
6 TheCOMPASScollaboration
4 Eventselectionandkinematicdistributions
TheDISeventandhadronselectionsareperformedasinpreviousanalysesbasedonthesamedata[19],
andonlyashortdescriptionoftheprocedureisgivenhere.
A track reconstructed in the scintillating fibres and silicon detectors upstream of the target is assumed
tobeanincomingmuonifitsmomentumismeasuredintheBMS.Scatteredmuonsareselectedamong
the positively charged outgoing tracks with a momentum larger than 1 GeV/c, passing through SM1.
In order to be accepted as the scattered muon, a track is required to cross an amount of material in the
spectrometer corresponding to at least 30 radiation lengths and must be compatible with the hits in the
triggerhodoscopes. Onlyeventswithonescatteredmuoncandidateareaccepted. Themuoninteraction
point(theso-called“primaryvertex”)isdefinedbyonebeamparticleandthescatteredmuon. TheDIS
eventsareselectedrequiringQ2>1(GeV/c)2,0.1<y<0.9,andaninvariantmassofthehadronicfinal
statesystemW >5GeV/c2.
If the amount of material traversed in the spectrometer is less than 10 radiation lengths the outgoing
particlesareassumedtobehadrons. Inordertohaveagoodresolutionontheazimuthalanglethecharged
hadrons are required to have at least 0.1 GeV/c transverse momentum ph with respect to the virtual
T
photon direction. In order to reject hadrons from target fragmentation the hadrons are also required
to carry a fraction z >0.2 of the available energy while the contamination from hadrons produced in
exclusive reactions is reduced by requiring z to be smaller than 0.85. No attempt is made to further
suppressdiffractivemesonproduction,asdonee.g. inRef.[15].
In addition to these standard requirements, further cuts have been applied specific for this analysis be-
cause it requires acceptance corrected azimuthal distributions of the final state hadrons. An upper limit
on the transverse hadron momentum has been introduced (ph <1.0 GeV/c), both to ensure negligible
T
pQCDcorrectionsandtoobtainabetterdeterminedhadronacceptance. Inordertohaveaflatazimuthal
acceptance the cut θ lab <60 mrad is applied, where θ lab is the virtual photon polar angle calculated
γ∗ γ∗
withrespecttothenominalbeamdirectioninthelaboratorysystem. Thecutsy>0.2andx<0.13have
beenalsoappliedbecauseofthecorrelationofxandy withθlab.
γ∗
Thefinaleventandhadronselectionisthus:
Q2>1(GeV/c)2, W >5GeV/c2, 0.003<x<0.13, 0.2<y<0.9,
θlab<60mrad, 0.2<z<0.85 and 0.1GeV/c<ph <1.0GeV/c.
γ∗ T
The statistics of the hadron sample after all cuts is given in Table 1 for each of the 4 periods of data
taken with the transversely polarised 6LiD target in 2004. The data with opposite polarisation have
beencombinedafternormalisingthemontherelativeincomingmuonflux. Thehadronstandardsample
consistsmainlyofpions[21],about70%forpositivehadrons,76%incaseofnegativehadrons. Positive
kaons and protons amount to about 15% each, negative kaons and antiprotons amount to 16% and 8%,
respectively,asevaluatedwithaLEPTOMonteCarloandcross-checkedwiththeRICHdetector.
The x distribution and the Q2 distribution for the final sample are shown in Fig. 2 together with the
hadron ph and z distributions. The mean values of y and Q2 with respect to x, z, and ph are shown in
T T
Fig.3.
5 Extractionoftheazimuthalasymmetries
5.1 Themethod
FromEq.(1),themeasuredazimuthaldistributionsareexpectedtobe:
N(φ ,(cid:126)v) = N ((cid:126)v)a(φ ,(cid:126)v)[1+(cid:15) AUU ((cid:126)v)cosφ +
h 0 h 1 cosφh h
Measurementofazimuthalhadronasymmetriesinsemi-inclusivedeepinelastic... 7
Table1: Finalstatisticsusedfortheazimuthalasymmetryevaluationforeachofthe4data-takingperiods.
period positivehadrons negativehadrons polarisation
1 3.9·105 3.4·105 +
2 3.4·105 2.9·105 −
3 5.8·105 5.0·105 +
4 3.6·105 3.1·105 −
×103
106
s s
nt nt 120
e 105 e
v v
e e 100
104
80
103
60
102
40
10
1 20
10−1
0 5 10 15 20 25 30 35 40 10−2 10−1
Q2 ((GeV/c)2) x
×103 ×103
s s
ron140 ron600
d d
a120 a
h h
100
400
80
60
200
40
20
0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1
ph (GeV/c) z
T
Fig. 2: Upper row: Q2 and x distributions of all the events in the final sample. Lower row: ph and z hadron
T
distributionsforthesamesampleofevents.
+(cid:15) AUU ((cid:126)v)cos2φ +(cid:15) λALU ((cid:126)v)sinφ ], (3)
2 cos2φh h 3 sinφh h
where a(φ ,(cid:126)v) is the apparatus acceptance and (cid:126)v indicates the generic set of kinematic variables (x,
h
z, ph, ...) on which the apparatus acceptance and the azimuthal asymmetries can depend. In order to
T
extracttheazimuthalasymmetriesitisnecessarytocorrectthemeasuredazimuthaldistributionsbythe
φ dependent part of the apparatus acceptance and to fit the corrected distribution with the appropriate
h
φ modulation.
h
The azimuthal asymmetries have been first extracted from the data binned in x, z or ph, and inte-
T
grated over the other two variables (“integrated asymmetries”). The bin widths have been chosen to
be larger than the experimental resolution estimated from Monte Carlo simulations. In each kinematic
bintheazimuthaldistributionsN(φ )areproducedseparatelyforpositiveandnegativehadrons, divid-
h
ing the (0,2π) φ range into 16 bins. The apparatus acceptance a(φ ) is calculated from Monte Carlo
h h
simulations for positive and negative hadrons for each bin of φ and for each kinematic bin, as will
h
be described in Sect. 5.2. The hadron azimuthal distributions corrected for the apparatus acceptance
8 TheCOMPASScollaboration
〉 1.5 15 )
〈y 〈y〉 2V/c)
e
1.0 〈Q2〉 10 (G
(
〉
2
Q
〈
0.5 5
0.0 10−2 10−1 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0
x z ph (GeV/c)
T
Fig.3: Q2andymeanvaluescalculatedinthebinsofx,ofzandofph.
T
N (φ ) = N(φ )/a(φ ) are then fitted with a four parameter function: F(φ ) = p ·(1+p ·
corr h h h h 0 cosφh
cosφ +p ·cos2φ +p ·sinφ ). The azimuthal asymmetries are then obtained by dividing
h cos2φh h sinφh h
thefittedparametersbytheappropriatequantities,i.e.:
p p p
AUU = cosφh, AUU = cos2φh, ALU = sinφh. (4)
cosφh (cid:104)(cid:15) (cid:105) cos2φh (cid:104)(cid:15) (cid:105) sinφh (cid:104)(cid:15) (cid:105)λ
1 2 3
The quantities (cid:104)(cid:15) (cid:105) are the mean values of (cid:15) defined in Eq. (2) and calculated for each kinematic bin.
i i
Thetwocentralbinsinφ havebeenexcludedfromthefitaswillbeexplainedinSect.6.2.
h
Thesameprocedureisusedtomeasuretheazimuthalasymmetriesforthehadronsbinnedsimultaneously
inx,z andph (“3dasymmetries”).
T
5.2 MonteCarloandacceptancecorrections
Ineachkinematicbinandforeachφ bintheazimuthalacceptancehasbeenevaluatedas:
h
a(φ ) = N (φ )/N (φ ), (5)
hi rec hi gen hi
where N (φ ) is the number of reconstructed hadrons obtained from the Monte Carlo simulation
rec hi
and N (φ ) is the corresponding number of generated hadrons. In order to obtain the number of
gen hi
reconstructed hadrons the same kinematic cuts, the same event reconstruction, and the same event and
hadron selection as for the real data have been applied. Only the kinematic cuts are applied to evaluate
thenumberofgeneratedhadrons.
ThesimulationinvolvesthefullCOMPASSMonteCarlochain,namely: thegenerationoftheDISevent,
thepropagationoftheeventinsidetheapparatus, andthereconstructionofparticletracks. TheLEPTO
generator[22]isusedforthefirststep. Theinteractionsbetweenparticlesandmaterialsandthedetectors
response are simulated using COMGEANT, a software based on GEANT3 [23] and developed inside
the Collaboration to describe the COMPASS set-up and which also includes trigger efficiencies,while
detector efficiencies are simulated at CORAL level. The package CORAL [24] is used to perform the
trackreconstructionanditisthesameprogramusedfortherealdata. Ithasbeencarefullycheckedthat
theMonteCarlosimulationgivesagooddescriptionoftheapparatus.
StartingfromthedistributionsobtainedusingthedefaultLEPTOsetting,differenttuningsoftheLEPTO
parameters and also different sets of PDFs, already tested in other COMPASS analysis [25], have been
used. The CTEQ5 [26] PDF set and the tuning of Ref. [25] have been adopted for the extraction of the
acceptances.
Measurementofazimuthalhadronasymmetriesinsemi-inclusivedeepinelastic... 9
TheratiosbetweenthedistributionsforrealandforMonteCarloeventsareshowninFig.4asafunction
of the DIS variables, and in Fig. 5 as a function of the hadron variables. The agreement is satisfac-
tory and gives confidence in the quality of the apparatus description used in the simulations. A typical
hadronazimuthaldistributionfromrawdataN(φ ),thecorrespondingacceptancefromtheMonteCarlo
h
simulationa(φ ),andthecorrecteddistributionN (φ )areshowninFig.6asafunctionofφ .
h corr h h
R R
1.5 1.5
1.0 1.0
0.5 0.5
10−2 10−1 0.2 0.4 0.6 0.8
x y
R R
1.5 1.5
1.0 1.0
0.5 0.5
1 10 10
Q2 ((GeV/c)2) W (GeV/c2)
Fig.4: RatioRbetweendataandMonteCarloeventsdistributionsforx,y,Q2andW.
Equation(3)showsthattherelevantpartoftheacceptanceistheonecontainingcosφ ,cos2φ andsinφ
h h h
modulations. Theamplitudesoftheseazimuthalmodulations,whichareessentiallythecorrectionsgiven
by the Monte Carlo, have been evaluated and their trend has been studied as a function of the various
kinematic variables. It has been found that the largest corrections, up to about 15%, have to be applied
to the cosφ modulations. The cos2φ corrections are of the order of a few percent and the sinφ
h h h
correctionsarenegligible.
Apriorytheacceptancefunctiona(φ ,(cid:126)v)evaluatedinaparticularbinofaspecificvariablexcouldstill
h
depend on some geometrical observable t like the azimuthal or polar angle of the scattered muon or on
someotherkinematicvariables. Ithasbeenverifiedthatthisisnotthecase. Whenextractinga(φ ,(cid:126)v,t)in
h
binsoft,theresultingazimuthalasymmetriesdifferonaveragefromthoseextractedthroughintegration
over t by less than one standard deviation of the statistical uncertainty, and also significantly less than
thefinalsystematicuncertainty.
6 Systematicstudies
Several possible systematic effects have been investigated. The most relevant studies are described in
thissection. Someeffectsturnedouttohaveanegligibleimpactontheresultsandthuswerenotincluded
intheevaluationofthefinalsystematicuncertainties.