Femtoscopy of pp collisions at sqrt{s}=0.9 and 7 TeV at the LHC with two-pion Bose-Einstein correlations

0.81 MB·English

by  ALICE Collaboration

Femtoscopyof pp collisionsat√s=0.9and7 TeV atthe LHC withtwo-pionBose-Einstein
correlations
(ALICE)
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M.Zhalov,47X.Zhang,65,a D.Zhou,65X.Zhu,65 A.Zichichi,15,ll G.Zinovjev,16Y.Zoccarato,68andM.Zynovyev16
1Department of Physics and Technology, University of Bergen, Bergen, Norway
2Centrode Aplicaciones Tecnolo´gicas y Desarrollo Nuclear (CEADEN),Havana, Cuba
3NuclearPhysicsInstitute, AcademyofSciencesoftheCzechRepublic, Rˇezˇ uPrahy, CzechRepublic
4Yale University, New Haven, Connecticut, United States
5Physics Department, Panjab University, Chandigarh, India
6European Organization for Nuclear Research (CERN), Geneva, Switzerland
7KFKIResearchInstituteforParticleandNuclearPhysics,HungarianAcademyofSciences,Budapest,Hungary
8Institutode F´ısica, Universidad Nacional Auto´noma de Me´xico, Mexico City, Mexico
9Variable Energy Cyclotron Centre, Kolkata, India
10Department of Physics Aligarh Muslim University, Aligarh, India
11Gangneung-Wonju National University, Gangneung, South Korea
12Institute for Theoretical and Experimental Physics, Moscow, Russia
13Russian Research Centre Kurchatov Institute, Moscow, Russia
14Sezione INFN, Turin, Italy
15Dipartimento di Fisica dell’Universita` and Sezione INFN, Bologna, Italy
16Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine
17FrankfurtInstituteforAdvancedStudies,JohannWolfgangGoethe-Universita¨tFrankfurt,Frankfurt,Germany
18Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy
19Research Division and ExtreMe Matter Institute EMMI,
GSI Helmholtzzentrum fu¨r Schwerionenforschung, Darmstadt, Germany
20V. FockInstitute for Physics, St. Petersburg State University, St. Petersburg, Russia
21National Institute for Physics and Nuclear Engineering, Bucharest, Romania
22Kirchhoff-Institut fu¨rPhysik, Ruprecht-Karls-Universita¨t Heidelberg, Heidelberg, Germany
23Department of Physics, Ohio State University, Columbus, Ohio, United States
24Rudjer Bosˇkovic´ Institute, Zagreb, Croatia
25Dipartimento di Fisica dell’Universita` and Sezione INFN, Padova, Italy
26Sezione INFN, Bologna, Italy
27SUBATECH,EcoledesMinesdeNantes, Universite´ deNantes, CNRS-IN2P3, Nantes, France
28Institutfu¨rKernphysik, Johann Wolfgang Goethe-Universita¨t Frankfurt, Frankfurt, Germany
29Laboratoire de PhysiqueSubatomique et deCosmologie (LPSC),Universite´ Joseph Fourier,
CNRS-IN2P3, Institut Polytechnique de Grenoble, Grenoble, France
30DepartamentodeF´ısicadePart´ıculasandIGFAE,UniversidaddeSantiagodeCompostela,SantiagodeCompostela,Spain
31Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
32Helsinki Institute of Physics (HIP) and University of Jyva¨skyla¨, Jyva¨skyla¨, Finland
33Sezione INFN, Catania, Italy
34Dipartimento di FisicaSperimentale dell’Universita` and Sezione INFN,Turin, Italy
35CentroFermi–CentroStudieRicercheeMuseoStoricodellaFisica“EnricoFermi”,Rome, Italy
36Commissariat a` l’Energie Atomique, IRFU, Saclay, France
37Laboratoire de Physique Corpusculaire (LPC), Clermont Universite´,
Universite´ Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France
38Institute of Experimental Physics, Slovak Academy of Sciences, Kosˇice, Slovakia
39Dipartimento di FisicaeAstronomia dell’Universita` and Sezione INFN,Catania, Italy
40School of Physicsand Astronomy, Universityof Birmingham, Birmingham, UnitedKingdom
41TheHenrykNiewodniczanski InstituteofNuclearPhysics,PolishAcademyofSciences, Cracow, Poland
42Institut fu¨rKernphysik, Westfa¨lische Wilhelms-Universita¨t Mu¨nster, Mu¨nster, Germany
43Joint Institute for Nuclear Research (JINR), Dubna, Russia
44Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
45InstitutPluridisciplinaireHubertCurien(IPHC),Universite´ deStrasbourg, CNRS-IN2P3,Strasbourg, France
4
46Wayne State University, Detroit, Michigan, United States
47Petersburg Nuclear Physics Institute, Gatchina, Russia
48Physics Department, University of Jammu, Jammu, India
49Laboratori Nazionali di Frascati, INFN, Frascati, Italy
50Faculty of Nuclear Sciences and Physical Engineering,
Czech Technical University in Prague, Prague, Czech Republic
51Nikhef, National Institute for Subatomic Physics, Amsterdam, Netherlands
52CentrodeInvestigaciones Energe´ticasMedioambientales yTecnolo´gicas(CIEMAT),Madrid, Spain
53University of Houston, Houston, Texas, United States
54Moscow Engineering Physics Institute, Moscow, Russia
55Institute for High Energy Physics, Protvino, Russia
56Faculty of Science, P.J. Sˇafa´rik University, Kosˇice, Slovakia
57Saha Institute of Nuclear Physics, Kolkata, India
58InstitutdePhysiqueNucle´aired’Orsay(IPNO),Universite´ Paris-Sud, CNRS-IN2P3,Orsay, France
59Department of Physics, University of Oslo, Oslo, Norway
60Dipartimento di Fisica dell’Universita` and Sezione INFN, Trieste, Italy
61Facultyof Mathematics, Physicsand Informatics, ComeniusUniversity, Bratislava, Slovakia
62Russian Federal Nuclear Center (VNIIEF), Sarov, Russia
63Physikalisches Institut, Ruprecht-Karls-Universita¨t Heidelberg, Heidelberg, Germany
64PhysicsDepartment, University of Cape Town, iThemba LABS,CapeTown, South Africa
65Hua-Zhong Normal University, Wuhan, China
66Seccio´nF´ısica, DepartamentodeCiencias, PontificiaUniversidad Cato´licadel Peru´, Lima, Peru
67Physics Department, Creighton University, Omaha, Nebraska, United States
68Universite´ de Lyon, Universite´ Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, France
69Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
70Nikhef,NationalInstituteforSubatomicPhysicsandInstituteforSubatomicPhysicsofUtrechtUniversity,Utrecht,Netherlands
71Division of Experimental High Energy Physics, University of Lund, Lund, Sweden
72University of Tsukuba, Tsukuba, Japan
73Sezione INFN, Cagliari, Italy
74CentrodeInvestigacio´nydeEstudiosAvanzados(CINVESTAV),MexicoCityandMe´rida, Mexico
75Beneme´rita Universidad Auto´noma de Puebla, Puebla, Mexico
76DipartimentodiScienzeeTecnologieAvanzatedell’Universita` delPiemonteOrientaleandGruppoCollegatoINFN,Alessandria,Italy
77InstitutodeCienciasNucleares, Universidad NacionalAuto´nomadeMe´xico, MexicoCity, Mexico
78Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy
79Institute of Space Sciences (ISS), Bucharest, Romania
80Institute of Physics, Bhubaneswar, India
81Universidade de Sa˜o Paulo (USP), Sa˜o Paulo, Brazil
82DipartimentodiFisica‘E.R.Caianiello’dell’Universita` andGruppoCollegatoINFN,Salerno, Italy
83Sezione INFN, Bari, Italy
84Dipartimento di Fisica dell’Universita` and Sezione INFN, Cagliari, Italy
85Soltan Institute for Nuclear Studies, Warsaw, Poland
86Sezione INFN, Rome, Italy
87Faculty of Engineering, Bergen University College, Bergen, Norway
88Sezione INFN, Padova, Italy
89Institute for Nuclear Research, Academy of Sciences, Moscow, Russia
90Sezione INFN, Trieste, Italy
91Physics Department, University of Athens, Athens, Greece
92Warsaw University of Technology, Warsaw, Poland
93Universidad Auto´noma de Sinaloa, Culiaca´n, Mexico
94Technical University of Split FESB, Split, Croatia
95Yerevan Physics Institute, Yerevan, Armenia
96University of Tokyo, Tokyo, Japan
97Department of Physics, Sejong University, Seoul, South Korea
98Lawrence Berkeley National Laboratory, Berkeley, California, United States
99Indian Institute of Technology, Mumbai, India
100Institut fu¨r Kernphysik, Technische Universita¨t Darmstadt, Darmstadt, Germany
101Yonsei University, Seoul, South Korea
102Zentrumfu¨rTechnologietransferundTelekommunikation(ZTT),FachhochschuleWorms,Worms,Germany
103California Polytechnic State University, San LuisObispo, California, United States
104China Institute of Atomic Energy, Beijing, China
105Instituteof Physics, Academyof Sciences of the CzechRepublic, Prague, CzechRepublic
106University of Tennessee, Knoxville, Tennessee, United States
107Dipartimento di Fisicadell’Universita` ‘LaSapienza’ and Sezione INFN,Rome, Italy
108Hiroshima University, Hiroshima, Japan
5
109Lawrence Livermore National Laboratory, Livermore, California, United States
110Budker Institute for Nuclear Physics, Novosibirsk, Russia
111Physics Department, University of Rajasthan, Jaipur, India
112Purdue University, West Lafayette, Indiana, United States
113Centre de Calcul de l’IN2P3, Villeurbanne, France
114Pusan National University, Pusan, South Korea
(Dated:January20,2011)
We report on the high statistics two-pion correlation functions from pp collisions at √s=0.9 TeV and
√s=7TeV,measuredbytheALICEexperiment attheLargeHadronCollider. Thecorrelationfunctionsas
wellastheextractedsourceradiiscalewitheventmultiplicityandpairmomentum.Whenanalyzedinthesame
multiplicityandpairtransversemomentumrange,thecorrelationissimilaratthetwocollisionenergies.Athree-
dimensionalfemtoscopicanalysisshowsanincreaseoftheemissionzonewithincreasingeventmultiplicityas
well as decreasing homogeneity lengths with increasing transverse momentum. The latter trend gets more
pronouncedasmultiplicityincreases. Thissuggeststhedevelopmentofspace-momentumcorrelations,atleast
for collisions producing a high multiplicityof particles. Weconsider thesetrends in thecontext of previous
femtoscopicstudies inhigh-energy hadron andheavy-ion collisions, anddiscuss possibleunderlying physics
mechanisms. Detailedanalysisofthecorrelationrevealsanexponentialshapeintheoutwardandlongitudinal
directions,whilethesidewardremainsaGaussian. Thisisinterpretedasaresultofasignificantcontribution
of strongly decaying resonances to the emission region shape. Significant non-femtoscopic correlations are
observed,andarearguedtobetheconsequenceof“mini-jet”-likestructuresextendingtolowp .Theyarewell
T
reproducedbytheMonte-Carlogeneratorsandseenalsoinp +p correlations.
−
PACSnumbers:25.75.-q,25.75.Gz,25.70.Pq
I. INTRODUCTION
Proton-protoncollisionsat√s=0.9TeVand√s=7TeV
havebeenrecordedbyALargeIonColliderExperiment(AL-
aAlsoatLaboratoiredePhysiqueCorpusculaire (LPC),ClermontUniver-
ICE)at theLargeHadronCollider(LHC) atCERN in2010.
site´,Universite´BlaisePascal,CNRS–IN2P3,Clermont-Ferrand,France
bNow at Centro Fermi – Centro Studi e Ricerche e Museo Storico della ThesecollisionsprovideauniqueopportunitytoprobeQuan-
Fisica “Enrico Fermi”, Rome, Italy; Now at European Organization for tumChromodynamics(QCD)inthenewenergyregime. The
NuclearResearch(CERN),Geneva,Switzerland distinguishingfeatureofQCDisthemechanismofcolorcon-
cAlso at European Organization for Nuclear Research (CERN), Geneva,
finement, the physics of which is not fully understood, due,
Switzerland
dNow at Physikalisches Institut, Ruprecht-Karls-Universita¨t Heidelberg,
Heidelberg, Germany; Nowat Frankfurt Institute forAdvanced Studies,
JohannWolfgangGoethe-Universita¨tFrankfurt,Frankfurt,Germany
eNowatSezioneINFN,Turin,Italy Goethe-Universita¨tFrankfurt,Frankfurt,Germany
fNowatUniversityofHouston,Houston,Texas,UnitedStates vNow at Research Division and ExtreMe Matter Institute EMMI, GSI
gAlsoatDipartimento diFisicaSperimentale dell’Universita` andSezione Helmholtzzentrumfu¨rSchwerionenforschung,Darmstadt,Germany
wAlsoatFachhochschuleKo¨ln,Ko¨ln,Germany
INFN,Turin,Italy
xAlsoatInstitute ofExperimental Physics, Slovak AcademyofSciences,
hAlsoatDipartimentodiFisicadell’Universita´,Udine,Italy
Kosˇice,Slovakia
iNowatSUBATECH,EcoledesMines deNantes, Universite´ deNantes, yNowatInstitutodeCienciasNucleares,UniversidadNacionalAuto´noma
CNRS-IN2P3,Nantes,France
deMe´xico,MexicoCity,Mexico
jNow at Centro de Investigacio´n y de Estudios Avanzados (CINVES- zAlsoatM.V.LomonosovMoscowStateUniversity,D.V.SkobeltsynInsti-
TAV),MexicoCityandMe´rida,Mexico;NowatBeneme´ritaUniversidad tuteofNuclearPhysics,Moscow,Russia
Auto´nomadePuebla,Puebla,Mexico aaAlsoatLaboratoiredePhysiqueSubatomiqueetdeCosmologie(LPSC),
kNowatLaboratoiredePhysiqueSubatomiqueetdeCosmologie(LPSC), Universite´JosephFourier,CNRS-IN2P3,InstitutPolytechniquedeGreno-
Universite´JosephFourier,CNRS-IN2P3,InstitutPolytechniquedeGreno- ble,Grenoble,France
ble,Grenoble,France bbAlsoat”Vincˇa”InstituteofNuclearSciences,Belgrade,Serbia
lNow at Institut Pluridisciplinaire Hubert Curien (IPHC), Universite´ de ccAlso at Dipartimento di Fisica ‘E.R. Caianiello’ dell’Universita` and
Strasbourg,CNRS-IN2P3,Strasbourg,France GruppoCollegatoINFN,Salerno,Italy
mNowatSezioneINFN,Padova,Italy ddAlsoatInstitutodeCienciasNucleares,UniversidadNacionalAuto´noma
nDeceased deMe´xico,MexicoCity,Mexico
oAlsoatDivisionofExperimentalHighEnergyPhysics,UniversityofLund, eeAlsoatUniversityofHouston,Houston,Texas,UnitedStates
Lund,Sweden ffAlsoatDepartmentofPhysics,UniversityofOslo,Oslo,Norway
pAlsoatUniversityofTechnologyandAustrianAcademyofSciences,Vi- ggAlsoatVariableEnergyCyclotronCentre,Kolkata,India
enna,Austria hhNowatDepartmentofPhysics,UniversityofOslo,Oslo,Norway
qNow at Oak Ridge National Laboratory, Oak Ridge, Tennessee, United iiAlsoatDipartimentoInterateneodiFisica‘M.Merlin’andSezioneINFN,
States
Bari,Italy
rNow at European Organization for Nuclear Research (CERN), Geneva,
jjNowatNikhef,NationalInstituteforSubatomicPhysicsandInstitutefor
Switzerland
sAlsoatWayneStateUniversity,Detroit,Michigan,UnitedStates SubatomicPhysicsofUtrechtUniversity,Utrecht,Netherlands
tAlsoatFrankfurtInstituteforAdvancedStudies,JohannWolfgangGoethe- kkAlsoatHua-ZhongNormalUniversity,Wuhan,China
Universita¨tFrankfurt,Frankfurt,Germany llAlso at Centro Fermi – Centro Studi e Ricerche e Museo Storico della
uNow at Frankfurt Institute for Advanced Studies, Johann Wolfgang Fisica“EnricoFermi”,Rome,Italy
6
in part, to its theoretical intractability [1]. The confinement theALICEexperimentalsetupanddatatakingconditionsfor
mechanismhasaphysicalscaleoftheorderoftheprotonra- thesampleusedinthiswork.InSectionIIIwepresentthecor-
diusandisespeciallyimportantatlowmomentum.Thestudy relation measurement and characterize the correlation func-
presentedinthisworkaimstomeasurethespace-timeextent tionsthemselves.InSectionIVAweshowthemainresultsof
ofthesourceonthisscale. thiswork:thethree-dimensionalradiiextractedfromthedata.
Two-pioncorrelationsatlowrelativemomentumwerefirst Wediscussvariousobservedfeaturesandcomparetheresults
showntobesensitivetothespatialscaleoftheemittingsource to other experiments. In Section V we show, for complete-
in p¯+p collisions by G. Goldhaber, S. Goldhaber, W. Lee ness,theone-dimensionalRinvanalysis. FinallyinSectionVI
and A. Pais 50 years ago [2]. Since then, they were stud- we summarize our results. All the numerical values can be
iedine++e [3],hadron-andlepton-hadron[4],andheavy obtainedfromtheDurhamReactionDatabase[15].
−
ion [5] collisions. Especially in the latter case, two-particle
femtoscopyhasbeendevelopedintoaprecisiontooltoprobe
thedynamically-generatedgeometrystructureoftheemitting II. ALICEDATATAKING
system. In particular, a sharp phase transition between the
color-deconfinedandconfinedstateswasprecludedbytheob-
In this study we report on the analysis of pp collisions
servation of short timescales, and femtoscopic measurement
recordedbytheALICEexperimentduringthe2010runofthe
ofbulkcollectiveflowprovedthata stronglyself-interacting
LHC. Approximately 8 million events, triggered by a mini-
systemwascreatedinthecollision[6,7].
mumbiastriggerattheinjectionenergyof√s=0.9TeV,and
Femtoscopyinheavy-ioncollisionsisbelievedtobeunder- 100millioneventswithsimilartriggeratthemaximumLHC
stoodinsomedetail,seee.g.[5]. Thespatialscalesgrownat- energytodate,√s=7TeV,wereanalyzedinthiswork.
urallywiththemultiplicityoftheevent.Stronghydrodynami- TheALICETimeProjectionChamber(TPC)[16]wasused
calcollectiveflowinthelongitudinalandtransversedirections to recordchargedparticle tracks as they left ionizationtrails
isrevealedbydynamicaldependenciesoffemtoscopicscales. in the Ne CO gas. The ionization drifts up to 2.5 m
2
The main puzzling aspect of the data is the relative energy fromthece−ntralelectrodetotheend-capstobemeasuredon
independenceoftheresultsofthemeasurements. 159 padrows, which are grouped into 18 sectors; the posi-
To some extent, Bose-Einstein correlations in particle tion at which the track crossed the padrow was determined
physics were initially of interest only as a source of sys- withresolutionsof2mmand3mminthedriftandtransverse
tematic uncertainty in the determination of the W boson directions, respectively. The momentum resolution is 1%
mass [8]. But overviews [3, 4, 9] of femtoscopic measure- for pions with p =0.5 GeV/c. The ALICE Inner Tra∼cking
T
mentsinhadron-andlepton-inducedcollisionsrevealsystem- System(ITS)wasalsousedfortracking.Itconsistsofsixsili-
aticssurprisinglysimilartothosementionedaboveforheavy- conlayers,twoinnermostSiliconPixelDetector(SPD)layers,
ioncollisions.Moreover,inthefirstdirectcomparisonoffem- two Silicon Drift Detector (SDD) layers, and two outer Sili-
toscopyinheavy-ioncollisionsatRelativisticHeavy-IonCol- conStripDetector(SSD)layers,whichprovideuptosixspace
lider (RHIC) and proton collisions in the same apparatus an points for each track. The tracks used in this analysis were
essentiallyidenticalmultiplicity-andmomentum-dependence reconstructed using the information from both the TPC and
wasreportedinthetwosystems[10]. However,themultiplic- theITS,suchtrackswerealsousedtoreconstructtheprimary
itiesatwhichthefemtoscopicmeasurementinppcollisionsat vertexofthecollision.Fordetailsofthisprocedureanditsef-
RHICwasmadewerestillsignificantlysmallerthanthosein ficiencysee [17]. The forwardscintillator detectorsVZERO
eventhemostperipheralheavy-ioncollisions.Inthisworkwe areplacedalongthebeamlineat+3mand 0.9mfromthe
are,forthefirsttime,abletocomparefemtoscopicradiimea- nominalinteractionpoint. Theycoveraregio−n2.8<h <5.1
suredinppandheavy-ioncollisionsatcomparableeventmul- and 3.7<h < 1.7 respectively. They were used in the
tiplicities. At these multiplicities the observed correlations mini−mumbiastrig−gerandtheirtimingsignalwasusedtore-
maybeinfluencedbyjets[11]whileotherstudiessuggestthat jectthebeam–gasandbeam-halocollisions.
asystembehavingcollectivelymaybecreated[12]. Theminimumbiastriggerrequiredasignalineitherofthe
In our previous work [13] we reported that a multiplicity twoVZEROcountersoroneofthetwoinnerlayersoftheSil-
integrated measurement does not show any pair momentum icon Pixel Detector (SPD). Within this sample, we selected
dependenceoftheRinvradiusmeasuredinthePairRestFrame events based on the measured charged-particle multiplicity
(PRF).SimilaranalysisfromtheCMScollaboration[14]also within the pseudorapidity range h <1.2. Events were re-
| |
mentionsthatnomomentumdependencewasobserved.How- quiredtohaveaprimaryvertexwithin1mmofthebeamline,
evertheanalysisintwomultiplicityrangessuggestedthatmo- and10 cm of the centerof the 5 m-longTPC. Thisprovides
mentumdependencemay changewith multiplicity, although almost uniform acceptance for particles with h <1 for all
anystrongconclusionswereprecludedbylimitedstatistics. In eventsinthesample. Itdecreasesfor1.0< h |<| 1.2. Inad-
| |
thisworkweexplorethisdependencebyusinghighstatistics dition,werequireeventstohaveatleastonechargedparticle
dataandmoremultiplicityranges.Itenabledustoperformthe reconstructedwithin h <1.2.
| |
three-dimensionalanalysis in the LongitudinallyCo-Moving The minimum number of clusters associated to the track
System (LCMS), where the pair momentum along the beam in the TPC is 70 (out of the maximum of 159) and 2 in the
vanishes. ITS (out of the maximum of 6). The quality of the track is
Thepaperisorganizedasfollows:inSectionIIwedescribe determined by the c 2/N value for the Kalman fit to the re-
7
constructedpositionoftheTPCclusters(N is thenumberof
TABLE I. Multiplicity selection for the analyzed sample. Uncor-
clustersattachedtothetrack);thetrackisrejectedifthevalue
is larger than 4.0 (2 degreesof freedomper cluster). Tracks rneucmtebdeNrcohfienv|ehn|ts<a1n.d2,nhudmNbche/rdohfii|dNechn≥ti1ca(slepeiotenxtpfaoirrsthinedeaecfihnirtaionng)e,
with h <1.2aretakenfortheanalysis. The p ofaccepted
T aregiven.
| |
particleshasalowerlimitof0.13GeV/c,becausetrackswith
lower pT donotcrossenoughpadrowsin theTPC. Theeffi- Bin Nch hdNch/dh i|Nch≥1 No.events×106 No.pairs×106
ciency of particle reconstructionis about 50% at this lowest √s=0.9TeV
limitandthenquicklyincreasesandreachesastablevalueof 1 1–11 2.7 3.1 8.8
approximately80%forp >0.2GeV/c.Inordertoreducethe
T 2 12–16 7.0 0.685 8.6
numberof secondaryparticlesin our sample, we requirethe
3 17–22 9.7 0.388 9.5
tracktoprojectbackto theprimaryinteractionvertexwithin
0.018+0.035p−T1.01cminthetransverseplaneand0.3cmin 4 23–80 14.6 0.237 12.9
the longitudinaldirection (so-calledDistance of Closest Ap- √s=7TeV
proachorDCAselection). 1 1–11 3.2 31.4 48.7
ALICEprovidesanexcellentparticleidentificationcapabil- 2 12–16 7.4 9.2 65.0
ity, throughthe combinationof the measurementof the spe- 3 17–22 10.4 7.4 105.7
cificionization(dE/dx)intheTPCandtheITSandthetiming
4 23–29 13.6 4.8 120.5
signalsintheALICETimeOfFlight(TOF).Inthemomentum
5 30–36 17.1 3.0 116.3
rangecoveredhere(0.13GeV/cto0.7GeV/c)pionsconstitute
6 37–44 20.2 2.0 115.6
themajorityofparticles. We useonlytheTPCmeasurement
forParticleIDentification(PID)inthiswork,astheotherde- 7 45–57 24.2 1.3 114.5
tectors offer significant improvementat higher p than used 8 58–149 31.1 0.72 108.8
T
here. ThisPIDprocedureresultsinasmallcontaminationof
thepionsamplebyelectronsat pT<0.2GeV/candkaonsat |q |<0.16 GeV/c
side,long
pT >0.65 GeV/c. Allowing other particles into our sample 1.51.5 ALICE pp @ 7 TeV
hasonlyaminoreffectofloweringthestrengthofthecorrela- )ut
tion(thel parameter),whileitdoesnotaffectthefemtoscopic qo
(
radius, so we do not correctfor it explicitly. The amountof C
electroncontaminationislessthan5%. 1
1
0 0.5 |q |<0.16 1GeV/c
out,long
1.5 N 1-11 k (0.2, 0.3)
1.5 ch T
III. CORRELATIONFUNCTIONMEASUREMENT )side NNcchh 3107--3262 kkTT ((00..22,, 00..33))
q
Experimentally,thetwo-particlecorrelationfunctionisde- (
C
fined as the ratio C(q) = A(q)/B(q), where A(q) is the 1
1
measuredtwo-piondistributionofpairmomentumdifference
0 0.5 |q |<0.16 G1 eV/c
iqng=ppa2ir−sopf1p,aarntdicBle(sqf)roimsadsifimfeirleanrtdeivsetrnibtsu[t1io8n].formedbyus- 1.51.5 out,side
)
The size of the data sample used for this analysis al- ng
o
lowed for a highlydifferentialmeasurement. In order to ad- ql
(
dress the physics topics mentioned in the introduction, the C
1
analysis was performed simultaneously as a function of the 1
total event multiplicity N and pair transverse momentum 0.00 00..55 1.10
ch
q (GeV/c)
k = ~p +~p /2. For the multiplicity determination we
T T,1 T,2 out,side,long
| |
counted the tracks reconstructed simultaneously in the ITS
and the TPC, plus the tracks reconstructed only in the ITS FIG.1. Projectionsofthe3DCartesianrepresentationsofthecorre-
in case the track was outside of the TPC h acceptance. The lation functions onto the qout, qside, and qlong axes for pairs with
total number of events accepted after applying the selection 0.2<kT <0.3 GeV/c, for three multiplicity ranges. To project
criteria in the √s=7 TeV sample was 60 106 and in the onto one q-component, the others are integrated over the range
√s=0.9TeVsampleitwas4.42 106. We×dividedthefull 0 0.16GeV/c.
× −
multiplicityrangeintoeightandfourrangesforthetwoener-
giesrespectivelyinsuchawaythatthelike-chargepionpair
multiplicityineachofthemwascomparable.TableIgives(a) lmeainstedo.neWcehagrigveedthpeiodnNicdhe/ndthifiveadl1ueasndinitTsamb.oImfeonrtuthmisdeevteenr-t
valuesfor the rangeof raw chargedparticle multiplicity that
wasusedtocategorizetheevent,(b)thecorrespondingmean
charge particle density dNch/dh as well as (c) number of 1Infactthecorrelationsignalisconstructedfromeventshavingatleasttwo
h i
eventsand(d)thenumberofidenticalpionpairsineachrange. same-chargepions(apair).Theone-pioneventsdocontributetothemixed
The femtoscopicmeasurementrequiresthe eventsto have at background.
8
sample. We denotethisvalueas dN /dh ;itstypical ALICE pp @ 7 TeV
uncertainty is 10%. We note thaht fochr theit|hNech≥lo1west multi- 1.15.5
plicity this charged particle density is biased towards higher
00
valueswithrespecttothefullsampleofinelasticevents. C
The pair momentum k ranges used in the analysis
T
were (0.13,0.2), (0.2,0.3), (0.3,0.4), (0.4,0.5), (0.5,0.6), 11
(0.6,0.7)GeV/c.
0.01.10 pp0++.5 pp ++ NNch 117-1-122 1 kkT ((00..22,, 00..33))
p + p + Nch 30-36 kT (0.2, 0.3)
ch T
A. Correlationfunctionrepresentations 0C2 00
Thecorrelationsaremeasuredasafunctionofpairrelative
-0-.01.1
momentumfour-vectorq. Wedealwithpions,sothemasses
of the particles are fixed - in this case q reduces to a vec- 0.01.10 0.5 1
tor:~q. Theone-dimensionalanalysisisperformedversusthe
magnitude of the invariant momentum difference qinv =|~q|, 2C2 00
in PRF. The large available statistics for this work allowed
us to perform a detailed analysis also for the 3D functions.
In forming them, we calculate the momentum difference in -0-.01.1
LCMS and decomposethis~qLCMS accordingto the Bertsch– 0.00 00..55 1.10
Pratt [19, 20] “out-side-long” (sometimes indicated by o, s, q (GeV/c)
and l subscripts) parametrization. Here, q is parallel to LCMS
long
the beam, q is parallel to the pair transverse momentum,
out FIG.2. MomentsoftheSHdecompositionofthecorrelationfunc-
and q is perpendicularto q and q . If one wishes to
side long out tions for pairs with 0.2<kT <0.3 GeV/c, for three multiplicity
compare the radii measured in LCMS to R one needs to
inv ranges.
multiplyone of the transverse radiiin LCMS (the one along
thepairtransversemomentum)bytheLorentzg correspond-
ingtothepairtransversevelocity,andthenaveragethethree analyzedinthiswork.
radii.ThereforeanRinvconstantwithmomentumisconsistent The C0 is the angle-averaged component. It captures the
0
withtheradiiinLCMSdecreasingwithmomentum.Figure1 generalshapeof the correlation. The widthof the peaknear
showsone-dimensionalprojectionsofthe3-dimensionalcor- q=0isinverselyproportionaltotheoverallfemtoscopicsize
relation functionC(qout,qside,qlong) onto the qout, qside, and ofthesystem. TheC0 componentisthecorrelationweighed
qlongaxes,forp +pairsfromoneofthemultiplicity/kTranges withthecos2(q ). Ifit2differsfrom0,itsignifiesthatthelongi-
fromthe√s=7TeVsample.Thefunctionisnormalizedwith
tudinalandtransversesizesoftheemissionregiondiffer.The
a factorthatisa resultofthefit(thedetailsoftheprocedure C2 isweighedwithcos2(f ). Ifitdiffersfrom0,itsignalsthat
2
aredescribedinSec.IIID);unitymeansnocorrelation.
the outward and sideward sizes differ. The correlationfunc-
The 1-dimensional projections, shown in Fig. 1, present
tion is normalized to the number of pairs in the background
a limited view of the 3-dimensionalstructure of the correla-
dividedbythenumberofpairsinthesignal.
tionfunction. Itisincreasinglycommontorepresentcorrela-
tionfunctionsinaharmonicanalysis[21–23];thisprovidesa
more complete representationof the 3-dimensionalstructure
B. Measuredcorrelations
ofthecorrelation,abetterdiagnosticofnon-femtoscopiccor-
relations [22], and a more direct relation to the shape of the
In Figs. 1 and 2 we show selected correlations to illus-
source [24]. The moments of the Spherical Harmonic (SH)
trate how they depend on multiplicity. This is done for k
decompositionaregivenby T
of (0.2,0.3) GeV/c; the behavior in other k ranges and at
T
thelowercollisionenergyisqualitativelythesame. Thenar-
1 rowingofthecorrelationpeakwithincreasingmultiplicityis
Am(~q) df d(cosq )C(~q,q ,f )Ym(q ,f ). (1)
l | | ≡ √4p Z | | l apparent,correspondingtotheincreaseofthesizeoftheemit-
tingregion.Thebehaviorofthecorrelationfunctionatlargeq
Here,theout-side-longspaceismappedontoEuleranglesin isalsochanging,thelowmultiplicitybaselineisnotflat,goes
which q = ~q cosq and q = ~q sinq cosf . For pairs of below1.0aroundq=1 GeV/c and thenrises againatlarger
long out
| | | |
identicalparticlesincolliderexperimentsdonewithsymmet- q,forhighermultiplicitiesthebackgroundbecomesflatterat
ricalbeams,includingtheanalysisinthiswork,theoddland largeq.InCartesianrepresentationshowninFig.1,areaswith
theimaginaryandoddm componentsforevenl vanish. The no data points (acceptance holes) are seen in q projection
out
firstthreenon-vanishingmoments, whichcaptureessentially nearq=0.5GeV/candinq above0.6GeV/c. Sinceq
long long
all of the 3-dimensional structure, are then C0, C0, and C2. isproportionaltothedifferenceoflongitudinalmomenta,its
0 2 2
These are shown in Fig. 2. The components for l 4 rep- valueislimitedduetoh acceptance. Intheout directionthe
≥
resentthefine detailsof the correlationstructureand arenot holeappearsduetoacombinationoflower p cut-offandthe
T
9
ALICE pp @ 7 TeV |q |<0.16 GeV/c
side,long
1.5
1.15.5 1.5 ALICE pp @ 7 TeV
)
0C0 qout
(
C
11 11
0.01.10 pp0++.5 pp ++ NNch 1177--2222 1 kkT ((00..24,, 00..35)) 1.50 |qout,long|<00..51N6 G 1e7V-2/c2 k (01.2, 0.3)
p + p + Nch 17-22 kT (0.6, 0.7) 1.5 Nch 17-22 kT (0.4, 0.5)
0C2 00 ch T )side Ncchh 17-22 kTT (0.6, 0.7)
q
(
C
-0-.01.1 11
0.01.10 0.5 1 0 |qout,side|<00..516 GeV/c 1
1.5
1.5
)
2C2 00 ong
ql
(
C
-0-.01.1 11
0.00 00..55 1.10 0.00 00..55 1.10
q (GeV/c) q (GeV/c)
LCMS out,side,long
FIG.3. MomentsoftheSHdecompositionofthecorrelationfunc- FIG.4. Projectionsofthe3DCartesianrepresentationsofthecorre-
tionsforeventswith17 Nch 22,forthreekTranges. lationfunctionsontotheqout,qside,andqlong axes, foreventswith
≤ ≤
17 N 22,forthreek ranges.Toprojectontooneq-component,
ch T
≤ ≤
theothersareintegratedovertherange0 0.16GeV/c.
−
selectedk range.Itcanbesimplyunderstoodasfollows:For
T
theprojectionintheupperpanelofFig.1, wetakethevalue ALICE p + p +
of q and q small. The value of q is proportional pp @ 0.9 TeV
side long side
to the azimuthalangledifference,while q is proportional 1.51.5 pp @ 7 TeV
long
to polar angle difference. For qside,qlong =0, qout is simply 0C0
p p andk is(p +p )/2,where p isnolongera
T,2 T,1 T T,1 T,2 T
−
2-vector,butjustascalar.Theparticlesareeitherfullyaligned
11
(both p ’s are positive or both are negative)or back-to-back
T
(one p is positive, the other negative). When we combine 0.10 N0 .512-16 1
T 0.1 ch
k (0.3, 0.4)
the lower pT cut-off pT >0.13 GeV/c and the kT selection T
| |
0.2 k 0.3, it can be shown that some range of the q
valu≤es iTs≤excluded. This range will depend on the k seleocu-t 0C2 00
T
tion.
ThekT dependenceofthecorrelationfunctionisshownin -0.-10.1
Fotihges.r3maunldtip4l,icfoitrymraunltgiepslicaintyd1a7t l≤owNecrhe≤ne2r2g.yTihseqbueahliatavtiiovreilny 0.01.10 0.5 1
similar (except the lowest multiplicity bin where the behav-
ior is more complicated- see the discussion of the extracted 2C2 00
radiiinSec.IIIDfordetails). Wesee astrongchangeofthe
correlationwithk , withtwoapparenteffects. Atlowk the
T T -0.1
-0.1
correlationappearstobedominatedbythefemtoscopiceffect
atq<0.3GeV/c,andisflatatlargerq. Ask grows,thefem- 0.00 00..55 1.10
T
q (GeV/c)
toscopicpeakbroadens(correspondingtoadecreaseinsizeof
LCMS
theemittingregion). Inaddition,awidestructure,extending
up to 1.0 GeV/c in q for the highest k range, appears. We FIG.5. MomentsoftheSHdecompositionofthecorrelationfunc-
T
analyzethis structurein furtherdetaillater in this work. We tionsforeventswith12 Nch 16,pairswith0.3<kT<0.4GeV/c.
≤ ≤
alsoseethat,accordingtoexpectations,theacceptanceholes Opensymbolsarefor√s=0.9TeVcollisions, closedsymbolsfor
intheoutandlongregionmoveaswechangethek range. √s=7TeVcollisions.
T
Figure5showstheexampleofthecorrelationfunction,for
the same multiplicity/k range, for pp collisions at two col-
T
lision energies. We note a similarity between the two func- tiplicity ranges. The similarity is not trivial: changing the
tions; the same is seen for other k ’s and overlapping mul- multiplicity by 50%, as seen in Fig. 2 or k by 30% as seen
T T
10
ALICE p + p + ingthesamemultiplicityandk ranges. TheMCcalculation
T
Pythia Perugia-0
1.51.5 pp @ 7 TeV doesnotincludethe wave-functionsymmetrizationfor iden-
ticalparticles; hence,theabsenceofthefemtoscopicpeakat
00
C lowqisexpected.Intheangle-averagedC0 componentasig-
0
nificant correlation structure is seen, up to 1 GeV/c, with a
11 slope similar to the data outside of the peak at low q. Sim-
ilarly, in theC0 componenta weak and wide correlationdip
0.10 N0 .512-16 1 1.5 2
0.1 kc h(0.3, 0.4) isseenaroundq=0.5GeV/c,whichisalsoseeninthedata.
T InMC, thecorrelationinC0 disappearsatlowerq,whilefor
2
0C200 the data it extends to much lower q, exactly where the fem-
toscopic peak is expectedand seen inC0. Our hypothesisis
0
thatboththelong-rangepeakinC0 andthedipinC0 areofa
-0.1 0 2
-0.1 “mini-jet”origin.Theyneedtobetakenintoaccountwhenfit-
0.10 0.5 1 1.5 tingthecorrelationfunctionfromdata,sothatthefemtoscopic
0.1
peakcanbeproperlyextractedandcharacterized. Thecalcu-
lations was also carried out with a second Monte-Carlo, the
2C200 PHOJET model[27,28], andgavesimilarresults. Thediffer-
encesbetweenthetwomodelsarereflectedinthesystematic
-0.1 error.
-0.1
0 0.0.55 1.10 1.5 In order to characterize the non-femtoscopic background
q (GeV/c) westudyindetailthecorrelationstructureintheMCgenera-
LCMS
tors,inexactlythesamemultiplicity/k rangesasusedfordata
T
analysis. Weseetrendsthatareconsistentwiththe“mini-jet”
FIG. 6. Moments of the SH decomposition of the correlation
functions for events with 12 Nch 16, pairs with 0.3<kT < hypothesis. The correlation is small or non-existent for low
0.4GeV/c.OpensymbolsareP≤YTHI≤AMCsimulations(Perugia-0 pT(firstkTrange)anditgrowsstronglywith pT. InFig.7we
tune),closedsymbolsareALICEdatafrom√s=7TeVcollisions. show this structure for selected multiplicity/kT at both ener-
gies. Atthehighestk theeffecthasthemagnitudeof0.3at
T
lowq,comparabletotheheightofthefemtoscopicpeak. The
in Fig. 3 hasa strongerinfluence on the correlationfunction appearanceofthesecorrelationsisthemainlimitingfactorin
thanchangingthecollisionenergybyanorderofmagnitude. the analysis of the k dependence. We tried to analyze the
T
Weconcludethatthemainscalingvariablesforthecorrelation correlationsatk higherthan0.7GeV/c butwewere unable
T
functionareglobaleventmultiplicityandtransversemomen- toobtainameaningfulfemtoscopicresult,becausethe“mini-
tumofthepair; thedependenceoncollisionenergyissmall. jet” structure was dominating the correlation. The strength
The energy independence of the emission region size is the ofthecorrelationdecreaseswithgrowingmultiplicity(asex-
firstimportantphysicsresultofthiswork. Weemphasizethat pected), slower than 1/M, so that it is still significant at the
it can be already drawn from the analysis of the correlation highest multiplicity. We studied other tunes of the PYTHIA
functionsthemselves,butwewillalsoperformmorequalita- modelandfoundthatthePerugia-0tunereproducesthe“mini-
tivechecksanddiscussionswhenwereportthefittedemission jet”correlationstructuresbest,whichiswhyitisourchoice.
regionsizesinSectionIV. Its limitation though is a relatively small multiplicity reach,
smaller than the one observed in data. As a result the MC
calculationforourhighestmultiplicityrangeislessreliable–
C. Non-femtoscopiccorrelationstructures thisisreflectedinthesystematicerror.
Analyzingtheshapeoftheunderlyingeventcorrelationfor
InFig.3wenotedtheappearanceoflong-rangestructures identical particle pairs in MC is important; however, it does
inthecorrelationfunctionsforlargek . Ifthesewereoffem- not ensure that the behavior of the correlation at very low q
T
toscopicorigin,theywouldcorrespondtoanunusuallysmall is reproduced well in MC. We compared the identical parti-
emissionregionsizeof0.2fm.Wereportedtheobservationof cleMCanddatainthelargeqregion,wherethefemtoscopic
thesestructuresinourpreviousanalysis[13]at√s=0.9TeV, effect is expected to disappear, and found them to be very
where they were interpretedas non-femtoscopiccorrelations similar in all multiplicity/k . However, if the “mini-jet” hy-
T
comingfrom“mini-jet”likestructuresatp <1GeV/c. Here pothesisiscorrect,thesamephenomenoncausessimilarcor-
T
wefurtheranalyzethishypothesis.InFig.6weshowthecom- relationstoappearfornon-identicalpions. Themagnitudeis
parisonofthecorrelationfunctionatmultiplicity12 N expected to be higher than for identical pions, because it is
ch
≤ ≤
16 in an intermediate k range, where the long-range corre- easiertoproduceanoppositely-chargedpairfromafragment-
T
lations are apparent, to the Monte-Carlo (MC) calculation. ing“mini-jet”thanit is to createan identically-chargedpair,
The simulation used the PYTHIA generator [25], Perugia-0 duetolocalchargeconservation. Moreover,thefemtoscopic
tune [26] as input and was propagated through the full sim- effectfornon-identicalpionscomesfromtheCoulombinter-
ulationoftheALICEdetector[16]. Thenitwasreconstructed actiononly. Itislimitedtoverylowq,below0.1GeV/c. Itis
and analyzed in exactly the same way as our real data, us- thereforepossibletotestthelow-qbehaviorofthe“mini-jet”