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https://www.sciencedirect.com/science/article/pii/S0370269318309924
DOI: 10.1016/j.physletb.2018.11.063
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DIRETORIA DE TRATAMENTO DA INFORMAÇÃO Cidade Universitária Zeferino Vaz Barão Geraldo
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Physics
Letters
B
www.elsevier.com/locate/physletb
Non-Gaussian
elliptic-flow
fluctuations
in
PbPb
collisions
at
√
s
NN=
5
.
02
TeV
.TheCMS Collaboration CERN, Switzerland a r t i c l e i n f o a b s t ra c t Article history: Received15November2017Receivedinrevisedform18November2018 Accepted23November2018
Availableonline2January2019 Editor: M.Doser
Keywords:
Event-by-eventellipticflow Non-Gaussianflowfluctuations Unfolding
Event-by-eventfluctuationsintheelliptic-flow coefficientv2 arestudiedinPbPbcollisionsat√sNN= 5.02 TeV usingtheCMSdetectorattheCERNLHC.Elliptic-flowprobabilitydistributionsp(v2)forcharged particleswithtransversemomentum0.3<pT<3.0 GeV/c andpseudorapidity|η|<1.0 aredetermined fordifferentcollisioncentralityclasses.Themomentsofthep(v2)distributionsareusedtocalculatethe
v2 coefficientsbasedoncumulantorders2,4,6,and8.Arankorderingofthehigher-ordercumulant results and nonzero standardized skewness values obtainedfor the p(v2) distributions indicate non-Gaussian initial-statefluctuations.Bessel–Gaussian andelliptic powerfits tothe flowdistributionsare studiedtocharacterizetheinitial-statespatialanisotropy.
©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
Ultrarelativisticheavy ioncollisions atboth theBNL Relativis-tic Heavy Ion Collider (RHIC) and the CERN Large Hadron Col-lider (LHC) create a hot and dense state of matter that consists ofstronglyinteracting quarksandgluons, the“quark–gluon plas-ma”(QGP)[1–7].Measurementsofazimuthal particlecorrelations resulting from these collisions reveal properties of the QGP, but alsoofthe initial state ofa heavy-ioncollision. Inparticular, the overall shape and fluctuations in the initial-state transverse en-ergy density transformed by the hydrodynamic evolution of the medium intoanisotropies inthe final-statemomentum spacefor theemittedparticles[8–10],asreflectedintheazimuthal charged-particle density. The early RHIC measurements of the azimuthal correlationsshowedthat theQGPcould bedescribed wellby hy-drodynamicmodels[11],withashearviscositytoentropydensity ratio(η/s)that isofthe orderofthe lowestpossible value fora quantumfluid[12,13].
Theazimuthalcharged-particledensitycanbecharacterizedby aFourierexpansion,with
dNch dφ ∝1+2 ∞ n=1 vncos[n(φ− n)]. (1)
Here,thenth-orderflowvectorforagiveneventis vn≡ (vncosn, vnsinn),where n is the angle ofthe intrinsicnth-order flow
E-mail address:cms-publication-committee-chair@cern.ch.
symmetry plane, as determined by the geometry of the partici-pantnucleons. Theexperimentally accessible“eventplane”angle, obsn ,isbasedonthedirectionofmaximumoutgoingparticle den-sityandis,onaverage,inthesamedirectionasn,butfluctuates
aboutn becauseofresolutioneffectsduetofiniteparticle
multi-plicities.
By calculating the flow coefficients over a large number of events,theunderlyingprobabilitydistributionfunctionsof individ-ualFouriercoefficientscanbedetermined.Whilethemeanvalues ofthe vn distributions canbe relatedto theoverall shapeofthe
interactionregion,thehigherordermomentscanbeusedto con-strain the origin and the nature of the initial-state fluctuations andhelp disentangletheinitial-stateeffectsfromthe subsequent evolution of themedium [14,15]. Here, an event-by-event analy-sis is performedwhere it is possibleto reduce the sensitivity of the results to nonflow correlations [16] and to clearly establish higher-ordermomentsofthen =2 (elliptic)distributionfunction. The mean ofthis distribution,v2, islargely determined by the lenticularshapeofthecollisionoverlapregion.
Whilethefinal-stateparticledistributionischaracterizedbythe
vncoefficients,theinitial-statespatialanisotropycanbe
character-ized bya harmonicexpansion interms ofeccentricityvectorsεn
[17–20].Fora givenimpact parameter,fluctuationsinthe initial-state transverseenergydensitylead toevent-by-eventdifferences in the orientation and magnitudeof the εn vectorswith respect
totheexperimentallyinaccessible“reactionplane,”definedbythe collisionimpactparameterandbeamdirections.Thepresenceofa nonzeroviscositywilldegradethecorrespondencebetween initial-https://doi.org/10.1016/j.physletb.2018.11.063
0370-2693/©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
andfinal-stateanisotropies [11,21]. Still, an almost linear depen-denceis expected forthe lowest order n =2 [22–26] and n =3 [9,18] harmonics,with vn=kn εn [19].Here, vn≡ |vn|, εn≡ | εn|,
andkn is the flow response coefficient. The probability
distribu-tionfunctionsofthe magnitudesofthe εn vectors, p(εn), canbe
relatedtothecorresponding p(vn)distributionassuming a linear
response,accordingto:
p(vn)= dεn dvn p(εn)= 1 kn p vn kn , (2)
where the kn term is expected to depend on the hydrodynamic
evolutionofthemedium[27,28].
Theelliptic-flow p(v2)distribution canbe characterized using the experimentally determined multiparticle cumulant flow har-monics v2{m} [29,30], where m is the cumulant order. Alterna-tively, the distribution can be determined directly, as shown by theATLASCollaboration[16] andasdonehere,byremoving finite-multiplicityresolutioneffectsinthemeasured p(vobs
2 )distribution throughan unfoldingtechnique. The cumulantharmonicsare ex-pressedintermsofthemomentsofthe p(v2)distribution[31,32]:
v2{2}2≡E(v22), v2{4}4≡ −E(v24)+2E(v22)2, v2{6}6≡ E(v62)−9E(vn4)E(v22)+12E(v22)3 /4, v2{8}8≡−(E(v82)−16E(v62)E(v22)−18E(v42)2 +144E(v42)E(v22)2−144E(v22)4)/33, (3) whereE(vk 2) ≡ vk
2p(v2)dv2.The unitlessstandardized skewness ofaprobabilitydistributionisameasureoftheasymmetry about its mean.Forthe caseofellipticflow, thestandardized skewness withrespecttothereactionplanecanbeestimatedusingthe cu-mulantflowharmonicsasinRef. [33]:
γ1exp≡ −6√2v2{4}2
v2{4} −v2{6}
v2{2}2−v2{4}2
3/2. (4)
Hydrodynamiccalculationsfindthisestimatetobeingood agree-ment with the actual skewness except for the most peripheral events[33].
The standardized skewness estimate vanishes for fluctuations that arise from an isotropic Gaussian transverse initial-state en-ergy densityprofile. In thiscase, the p(v2) distribution is found by taking an integral over the azimuthal dependence of the two-dimensional Gaussian function [31,34]. The resultant, one-dimensional distributionhas a Bessel–Gaussian shape, wherethe evencumulantcoefficientsv2{m}withm ≥4 aredegenerate[31]. The observation for PbPb collisions that v2{4} ≈v2{6} ≈ v2{8} [35–37], wherethe approximate equalities are within a few per-cent,suggeststhatthe v2 fluctuationscanbewelldescribed bya two-dimensionalGaussianfunction[31].
Still,non-Gaussianfluctuationsare expectedintheinitial-state energydensity[33],whichshouldleadtodifferencesinthehigher order cumulantcoefficients. Such differenceshave been reported by theATLAS Collaboration[16] ina similarmeasurement of pe-ripheralPbPbcollisionstothatreportedhere.Theprecisionofthe LHCmeasurements allows forthesedifferencestobe explored in detail,givinganewmethodtoinvestigatetheinitial-state behav-ior.Theellipticpowerfunctionhasbeensuggestedtodescribethe asymmetric behaviorof the p(εn) distributions [14,15,38], noting
that the Bessel–Gaussian distribution reproduces neither Glauber
Monte Carlo nor IP-Glasma results other than for very central events[14].Thisfunctionisbasedontheassumptionthatthe ini-tialenergydensityprofileofthe collisionisa superpositionofN point-like,independentsources.Intermsoftheharmonic-flow co-efficientsandassumingalinearresponse,
p(vn)= 2αvn πk2 n (1−ε02)α+1/2 π 0 (1−v2 n/k2n)α−1dφ (1−ε0vncosφ/kn)2α+1 , (5)
where ε0 is approximatelyequal to the meaneccentricityin the reaction plane and α, which is approximately proportional to N, describes the size of the eccentricity fluctuations. The ellip-tic power distributionreduces to aGaussian, Bessel–Gaussian, or power distribution form withthe appropriate choice of parame-ters[39] andhastheadvantageofnaturallyincorporatingtheunit constraintoneccentricity,where | n| <1.
In this Letter, the p(v2) distributions for charged particles in the pseudorapidityrange |η| <1.0 andwithtransverse momenta 0.3<pT<3.0 GeV/c are presentedforPbPbcollisions at√sNN= 5.02 TeV collected withthe CMSdetectoratthe LHC.The results are shown in bins of centrality, defined as fractions of the to-tal inelastic hadroniccross section, where 0% corresponds to the eventswiththegreatesthadronicactivityintheforwarddirection (|η| >3.0). The elliptic-flow harmonicvalues fordifferent cumu-lant orders are determined based on the moments of the p(v2) distributions, with these results used to estimate the standard-izedskewness oftheflowdistribution.EllipticpowerandBessel– Gaussianfitstotheflowdistributionsarepresentedtogainfurther insightintotheinitial-stateanditsfluctuations.
2. TheCMSdetector
The central feature of the CMS apparatus is a superconduct-ing solenoid of6 m internal diameter, providing a magneticfield of 3.8 T. Withinthe solenoidvolume are asilicon pixeland strip tracker,aleadtungstatecrystalelectromagneticcalorimeter,anda brass andscintillatorhadroncalorimeter,eachcomposedofa bar-relandtwoendcapsections.Muonsaredetectedingas-ionization chambers embedded in the steel flux-return yoke outside the solenoid.
Thebarrelandendcapdetectorsprovidecoverageintherange
|η| <3.0, with Hadron Forward calorimeters (HF) extending the pseudorapidity coverage to 3.0<|η| <5.2. The HF detectors are used both to selectevents forthe analysisandto determine the collisioncentrality.TheHFcalorimetersareazimuthallysubdivided into20◦ modularwedgesandfurthersegmentedtoform0.175× 10◦ ( η× φ) towers.The silicon trackermeasures charged par-ticles within the range|η| <2.5. It consistsof1440silicon pixel and 15 148 silicon strip detector modules. At midrapidity, there are 3 pixel detector layers and 10 strip detector layers. At the outer edge of the tracker acceptance, there are 2 pixel detector layers and 12 strip detector layers. For nonisolated particles of 1<pT<10 GeV/c and |η| <1.4,thetrackresolutionsaretypically 1.5%inpTand25–90(45–150) μminthetransverse(longitudinal) distance ofclosest approach[40].A more detaileddescription of theCMSdetector,togetherwithadefinitionofthecoordinate sys-tem used andthe relevant kinematic variables, can be found in Ref. [41].
3. Eventandtrackselection
This analysisisbased on aPbPb minimum biasdata setwith
√
sNN=5.02 TeV and corresponding to an integrated luminosity of26 μb−1,collected in2015. Theminimum-biastrigger used re-quires coincident signals in the HF calorimeters atboth ends of
theCMSdetectorwithenergydepositsaboveapredefinedenergy threshold of approximately 1 GeV and the presence of both col-lidingbunchesattheinteractionpointasdetermined usingbeam pickuptimingmonitors.Byrequiringcollidingbunches,eventsdue tonoise(e.g.,cosmicraysandbeambackgrounds)arelargely sup-pressed. Events are further selected offline by requiring at least threetowers with an energyabove 3 GeV in each ofthe two HF calorimeters.The primary vertexfor each eventis chosen asthe reconstructedvertexwiththelargestnumberofassociatedtracks. Primaryverticesarerequiredtohaveatleasttwoassociatedtracks andtobelocatedwithin15 (0.2) cmofthenominalcollisionpoint alongthelongitudinal(transverse)direction.Tosuppress contam-ination from events with multiple collisions in the same bunch crossing (pileup), the procedure outlined in Ref. [6] is followed. Here,compatibility scores basedon the numberof pixelclusters withwidthscompatible withparticles originatingfromeach pri-maryvertexaredeterminedandeventswithprimaryverticeswith compatibilityscoresbelowa predefinedthresholdare rejectedas pileup.Afterapplyingtheselectioncriteria,theaveragenumberof collisions per bunch crossing is less than ≈0.001 for the events usedinthisanalysis,withapileupfraction<0.05%.
Track reconstruction [40,42] is performedin two iterations to easethecomputationalloadforhigh-multiplicitycentralPbPb col-lisions.The firstiteration reconstructs tracksfromsignals(“hits”) inthesiliconpixelandstripdetectorscompatiblewithatrajectory of pT>0.9 GeV/c. These tracks are requiredto have consistency withoriginatingfromtheprimaryvertex,havingalongitudinal as-sociationsignificance(dz/σdz) anda distance ofclosest approach
significance(d0/σd0) eachlessthan 3.Inaddition,the pT
resolu-tion[40,42] foreachtrack, σpT/pT,isrequiredtobelessthan10%
andtracks are required to have at least11 out of the 14 possi-ble hitsalong their trajectory in the pixel and strip trackers. To reducethenumberofmisidentifiedtracks,whichcanoccurwhen thehitpatternisconsistentwithmorethanonepossibletrack so-lution,the chi-squaredper degreeoffreedom, χ2/dof,associated with fitting the track trajectory through the different pixel and striplayersmustbe lessthan0.15timesthetotalnumberof lay-erswithhitsalongthetrajectoryofthetrack.Theseconditeration reconstructstrackscompatiblewithatrajectoryof pT>0.2 GeV/c usingsolely thepixel detector.These tracksare required tohave longitudinal association significance dz/σdz<8 and a fit χ
2/dof valuelessthan12timesthenumberoflayerswithhitsalongthe trajectory of the track. In the final analysis, first iteration tracks with pT>1.0 GeV/c are used together with pixel-detector-only tracks with pT<2.4 GeV/c after removing duplicates. Track re-construction for the merged iterations has a combined geomet-ric acceptance and efficiency exceeding 60% for pT≈1.0 GeV/c and |η| <1.0. When the track pT is below 1 GeV/c, the accep-tanceandefficiencysteadilydrops,reachingapproximately40%at pT≈0.3 GeV/c.
4. Analysistechnique
Analysesofflowharmonicsusingmultiparticlecumulantswere initially introduced as a way to minimize nonflow effects [30]. These analyses have been based on either the generating func-tion formalism [30] or, more recently, through direct calculation [43]. The unfolding procedure employed here, as introduced by theATLAS collaboration[16],isexpectedtogivesimilarresultsto amultiparticlecumulantanalysis, butwithreducedsensitivityto multiplicityfluctuationsandnonfloweffects[44].
Theevent-by-eventv2 coefficientsandphasesinEq. (1) canbe estimatedwith
vobs2,x= |v2obs|cos(2obs2 )= cos(2φ) =
iwicos(2φi)
iwi ,
vobs2,y= |v2obs|sin(2obs2 )= sin(2φ) = iw isin(2φi) iwi , |vobs2 | = vobs2,x 2 +vobs2,y 2 , (6)
where φi is the azimuthal angle of the track, obs2 is the event
planeangleforthe2ndharmonic,theangularbracketsdenotean efficiencyweighted averageover all particles in a givenrange of phase space for an event, and wi=1/εi is the inverse of the
tracking efficiency εi(pT,η) of the ith track. The analysis does not require the explicit calculation of the event plane angle for eachevent.Intheabsenceofparticlecorrelationsunrelatedtothe hydrodynamic flow behavior (“nonflow”), the observed event-by-event flow vectors of Eq. (6) will approach the true underlying flow vectors as the particle multiplicity becomes large. In addi-tiontothe efficiencyweighting, astandardrecentering procedure [45], where the eventaverage x- and y-components of the flow vector are required to equal zero, is applied to further suppress acceptancebiases.
Eventsaresortedintodifferentcentralityclasses,asdetermined bythetransverseenergydepositedintheHFcalorimeters[6],and themagnitudesoftheestimatedflowvectorsareusedtoconstruct the “observed” p(vobs2 ) distributions foreach class.Finite particle multiplicitiesresultinastatisticalfluctuationofthe vobs2 estimate foragiveneventaboutthetrueunderlyingv2valuebyaresponse function p(vobs2 |v2).This,inturn,resultsina p(vobs2 ) distribution that isbroaderthantheunderlying p(v2) behavior.The observed distribution can be expressed asa convolution of the underlying flowbehaviorandtheresponsefunction
p(vobs2 )=p(v2obs|v2)∗p(v2). (7) A data-based technique, first introduced by the ATLAS Collabo-ration [16], was used to build the response function in Eq. (7). This technique divides thefull event sample into two symmetric subevents (a andb)basedon pseudorapidity.Giventhat v2(η) is symmetric about η=0 on average for the symmetric PbPb sys-tem, the physical flow signal cancels in the distribution of flow vector differences from each subevent p(van− vbn). The resulting distributioncontainsresidualeffectsfrommultiplicity-related fluc-tuationsandnonfloweffects[44] andprovidesabasisforbuilding theresponsefunction.Theabilityoftheanalysisprocedureto sup-press nonflow effects was studied by introducing a v2 signal on topof hijing 1.383 [46] simulatedevents,whichcontainnonflow. TheEbyEanalysisisfoundtorecoverthe“truth”towithin0.1%.
To unfold the effects of multiplicity-related fluctuations, the D’Agostini iterative method with early stopping (regularization) [47–49] was used to obtain a maximum likelihood estimate of the underlying p(v2) behavior. The analysis was done usingthe RooUnfold[50] packageofthe root dataanalysisframework[51]. Theunfoldingprocedurebecomesincreasinglysensitiveto statisti-calfluctuationswhenthenumberofiterationsisallowedtorunto large values,resulting inunphysical oscillations inthe low event count tails of the unfolded distribution. The regularization crite-rion usedto suppress theseoscillations is to apply the response functiontoeachunfoldingiteration(“refolding”)andcomparethe resulting distribution tothe observed one. Iterationsare stopped whenthe χ2/dof betweentherefoldedandobserveddistribution isapproximatelyequaltoone.Afterthisfinalunfoldingiterationis reached, theresultingdistribution istruncatedabove v2 +4σv2
to further suppress any residual artifacts in the tails that result from the unfolding procedure. Representative final unfolded dis-tributions are shown in Fig. 1. In addition, p(vobs
Fig. 1. Representativefinalunfolded p(v2)distributions(closedblackcircles)inthreecentralitybins(15–20%,30–35%,and 55–60%)obtainedusingD’Agostiniiteration unfolding.Respectiveobserved p(vobs2 )distributions(openblacksquares)areshowntoillustratethestatisticalresolutionpresentineachcentralitybinpriortounfolding. Systematicuncertaintiesfromtheunfoldingprocedurearepresentedasshadedbands.DistributionsarefittedwithBessel–Gaussian(dashedbluelines)andellipticpower (solidredlines)functionstoinferinformationontheunderlying p(ε2)distributions.Theverticalbluearrowsindicatethev2+4σv2cutoffdiscussedinthetext.
are plotted for each centrality to illustrate the statistical resolu-tioneffectspresentpriortounfolding.ThefitsshowninFig.1are discussedinSection6.
5. Systematicuncertainties
A numberof potential sources of systematicuncertainties for the v2{m}valuesextractedfromtheunfolded p(v2)distributions wereconsidered. Thesystematicuncertainties thatarise fromthe vertex z position were investigated by splitting the default ver-tex rangeinto two windows of |zvtx| <3.0 cm and3.0<|zvtx| < 15.0 cm andcomparing the resultsfrom the two ranges.The re-sultinguncertainties rangefrom5% forcentralevents,decreasing to0.5%formid-centralevents.Toestimatethebiasfrom misiden-tifiedtracks,thetrackqualitycriteriadescribedinSection3were varied. Two scenarios were considered, with one increasing and theotherdecreasingtheprobabilityofmisidentifyingatrack.The results of these two scenarios were compared to the values ob-tained in the default analysis. The resulting uncertainties range from2% for central events to 1% formid-central events.To esti-matethesystematicuncertaintyinthechoiceofresponsefunction, theunfolding procedurewas repeatedusing ananalytic response function obtainedfrom a Gaussian fit tothe data-driven statisti-cal resolutiondistribution[16].The resultinguncertainties are3% forcentraleventsanddecreaseto1%formid-centralevents.Other sources of potential systematicbias were explored and found to be negligible. To assess the potential bias from residual pileup events,thethresholdfordeterminingpileupeventswas raisedto decrease the probability of including events with multiple colli-sions in theanalysis. The bias fromunfolding regularization was studiedbymodifyingthe χ2/dof goodness-of-fitregularization cri-teriaandcomparingthecaseswhentherefolding χ2/dof cutoffis 2.0relativetowhenitis1.0.Totestthepotentialbiasthatmight resultfromthe 4σ truncationof thefinal unfolded distributions, thetruncationpointwasvariedbetween3.5σ and4.5σ.Toassess theuncertainty onthe choice oftheprior, the unfoldingwas re-peated usingpriorsthat were systematicallytransformed to have 10%largerandsmallermeansthanthedefaultprior.Nosignificant biaswasfoundwiththesevariationsoftheprior.Thetotal system-aticuncertainties were obtainedby addingthecontribution from each source in quadrature. The v2 values calculated for the dif-ferentcumulantordershavea totalsystematicuncertaintyofthe orderof 5% forcentral collisions, which decreases to 1% in mid-centralcollisions.
Fig. 2. Elliptic-flowcumulantharmonicswithvaluesobtainedfromthemomentsof theunfolded p(v2)distributions.Systematicuncertaintiesareshownasgraybands. Formostcentralities,theuncertaintiesaresmallerthanthesymbolsize.
Asallofthesystematicuncertaintiesareexpectedtobe corre-latedbetweenthe differentcumulantorders,withthe samedata usedinthecalculationofeachorder,alloftheabovestudieswere alsoperformedfortheratiosofdifferentordersandforthe skew-ness estimategivenbyEq. (4).Fortheratios,thetotalsystematic uncertaintyisfoundas1%forcentralcollisions,decreasingto0.1% formid-centralcollisions.Thestandardizedskewnessisvery sensi-tivetosmallfluctuationsinthecumulantflowharmonics,resulting in asystematicuncertainty of100%forcentral collisions that re-ducesto20%formid-centralcollisions.
6. Results
The cumulant elliptic-flow harmonics obtained from the mo-mentsoftheunfolded p(v2)distributionsusingEq. (3) areshown inFig.2forcumulantorders2,4,6,and8.Itwas notpossibleto obtain0–5%centralresultsfor v2{4}andv2{6}becausethe right-handsideofEq.(3) wasfoundtobenegativeforthesevalues.This behaviormightbeaconsequenceofvolumefluctuations dominat-ing the cumulantbehavior for thesecentral events,as discussed
Fig. 3. Ratiosofhigherordercumulantelliptic-flowharmonicswith valuesobtainedfromthemomentsoftheunfolded p(v2)distributions. Bothstatistical(lines)and systematic(graybands)uncertaintiesareshown.Hydrodynamicpredictionsfor2.76 TeV collisionsfromRef. [33] arepresentedasadarkcolorbandandarecomparedto themeasured v2{6}/v2{4}ratio.Inaddition,higherordercumulantratiosreportedbytheATLASCollaborationfor2.76 TeV collisions[37] with0.5<pT<20.0 GeV/c and
|η|<2.5 arecomparedtothe5.02 TeV measurement.TheerrorbarsontheATLASmeasurementrepresentthequadraticsumofstatisticalandsystematicuncertaintiesand pointsareoffsethorizontallyforclarity.
inRef. [52].The cumulantresultsexhibitthepreviously observed v2{2} >v2{4} ≈v2{6} ≈v2{8} behavior. Thecentrality-dependent ratiosfortheelliptic-flowcoefficientsobtainedfordifferent cumu-lant orders are shown in Fig. 3. For most centrality ranges, the ratiosindicatea rankorderingofthe cumulants,withdifferences on the order of a few percent and with v2{4} >v2{6} >v2{8}, thatis qualitativelyinconsistent withapure Gaussian fluctuation modelofflowharmonics.Thedifferencesincreaseasthecollisions become more peripheral. The calculated v2{6}/v2{4} ratio based onanevent-by-eventhydrodynamiccalculationusingMonteCarlo Glauberinitial conditions[53] andan η/s value of0.08isshown bytheshaded band.Thissimulation isforpions with0.2<pT< 3.0 GeV/c inPbPb collisions at√sNN=2.76 TeV [33]. Alsoshown are resultsfrom the ATLAS Collaboration [37] forPbPb collisions at2.76 TeV and forcharged particles with0.5<pT<20.0 GeV/c and |η| <2.5.Thecalculation isconsistentwiththeexperimental resultsfoundatbothbeamenergies.Thesimilaritybetween exper-imentalresultswith2.76and5.02 TeV isconsistentwiththesmall changesin the initial-stateeccentricities expectedbetweenthese energies[54] andtheexpectationthatthecumulantflowharmonic ratiosfollowthoseofthecorrespondingeccentricityratios[33].
Fig. 4 shows the centrality dependence of the standardized skewness γ1exp.Finitevaluesarefoundforthestandardized skew-ness for collisions with centralities greater than ≈15%. The hy-drodynamicpredictions forthe γ1exp values forPbPbcollisions at 2.76 TeV from Ref. [33] are also shown and found to be consis-tent with the current measurements. Within the hydrodynamic modelandallowingforafiniteskewnessoftheevent-by-eventv2 distribution,thesmallsplittingbetweenthecumulantordersis ex-pectedtofollowtherelationship(v2{6} −v2{8})/(v2{4} −v2{6}) = 0.091 [33]. Experimentally, we find a value forthis splitting ra-tioof0.143±0.008(stat)±0.014(syst) for20–25%centralevents, withtheratioincreasingto0.185±0.005(stat)±0.012(syst) asthe centralityincreasesto55–60%.Theobservedvaluesmightsuggest higher order terms in a cumulant expansion of the v2 distribu-tion are required to account for the skewness. This relationship wasrecentlyexaminedbytheALICEcollaborationinRef. [55] us-ingaq-cumulantanalysis,withresultscomparabletothefindings inthispaperwhenconsideringsystematicuncertaintiesanda dif-ferentkinematicrangefortheALICEmeasurement.
BothellipticpowerandBessel–Gaussianparametrizationsused forfitssuchasshowninFig.1assumealinearresponsebetween eccentricityandflow,butonlytheellipticpowerlawallowsfora finiteskewness. Fora Bessel–Gaussian distribution, the skewness isequaltozero.Thisfeatureresultsintheellipticpowerfunction beinginbetter agreementwiththeobserved fluctuationbehavior
Fig. 4. Theskewnessestimatewithrespecttothereactionplanedeterminedusing theelliptic-flowharmonicbasedondifferentcumulantorders.Bothstatisticaland systematicuncertaintiesareshown,wherestatisticaluncertaintiesaresmallerthan thedatapoints.Hydrodynamicmodelpredictionsfor2.76 TeV PbPbcollisionsfrom Ref. [33] areshownasacoloredband.
than theBessel–Gaussianparametrization, yielding χ2/dof values onthe orderofunity. Toavoidbin-to-bincorrelationsintroduced by the unfolding procedure, goodness of fit values are obtained byrefoldingthefitteddistributionswiththeresponsematrixand comparingtothemeasureddistribution.Theellipticpower χ2/dof values vary between0.8 and 1.5 from central to peripheral col-lisions, while theBessel–Gaussian χ2/dof values varybetween 3 and9.Point-by-pointsystematicuncertaintiesontheunfolded dis-tributionsarecorrelatedandarethusnotconsideredinthefits.
Thefitparametersfortheellipticpowerfunctionareshownin Fig. 5forthe differentcentralitybins. As alsofound inRef. [15], thefits donot convergeforcentralcollisions wherethe distribu-tionsbecome veryclosetoaBessel–Gaussianform. Consequently, the parameters are shownfor centralities >15%.The experimen-tal k2 values show only a weak centrality dependence. Viscous hydrodynamic calculations indicate that deviations from thermal equilibriumshouldleadtoareducedcorrespondencebetweenthe initial-stategeometry andthe flow signal inperipheral collisions [27,28]. This effect is suggestedin Fig. 5 by the decrease in the k2 valuewithincreasingcentrality,althoughthesystematic
uncer-Fig. 5. Centralitydependenceoftheparametersextractedfromellipticpowerfunctionfitstotheunfolded p(v2)distributions.Bothstatistical(errorbars)andsystematic (shadedboxes)uncertaintiesareshown.Thesolidlinerepresentsatheoreticalcalculation[15] usingviscoushydrodynamicswithGlauberinitialconditionsandanη/s value
of0.19todeterminetheresponsecoefficient k2.Glauber(blueshadedband)andIP-Glasma(redshadedband)modelcalculationsfromRef. [15] areshownfortheαand ε0parameters.Thesystematicuncertaintiesaccountforthehighlycorrelatedparametersoftheellipticpowerfunctionfitandforthebin-to-bincorrelationsintheunfolded distributionsintroducedbytheunfoldingprocedure.
tainties are too large for this to be a definitive observation. The calculateddecreaseis greaterthan observed,although withinthe systematicuncertainties ofthemeasurement.The eccentricity pa-rameterofthepowerlawfit, ε0,isfoundtofirstincrease,andthen leveloffwithincreasingcentrality.Thelevelingoccursfor central-ities >40%, which is also where the v2 valuesstart to level off and then decrease. The α parameter, which reflects the number ofsources inthepower-lawfit,isfoundtosteadilydecreasewith increasingcentrality,asexpected.
Theoreticalpredictionsat2.76 TeV fromRef. [15] arecompared to the current analysis in Fig. 5. A viscous hydrodynamic calcu-lation with Glauber initial conditions and an η/s value of 0.19 isin agreement withtheexperimental k2 values. Thiscoefficient isexpected tohave onlya weak dependenceon theinitial state, withits centralitydependence largely determined by the viscos-ity of the medium [15]. Predictions obtained using Glauber and IP-Glasma [56,57] initial conditions, where the IP-Glasma model includesgluonsaturationeffects,are shownforthe ε0 and α pa-rameters. These latter two calculations qualitatively capture the observedbehaviorforthe α-parameter,butasignificantdifference isfound incomparingthe theoretical ε0 valueswithexperiment. Thisdifferencemightreflectanonlinearresponseterm,whichwill alter the magnitude of the flow response coefficient and conse-quentlythe ε0 and αparameters,assuggestedinRef. [15].
7. Summary
Insummary,anon-Gaussianbehaviorisobservedinthe event-by-event fluctuations of the elliptic flow v2 coefficients in PbPb collisions recorded by the CMSdetectorat √sNN=5.02 TeV. The probability distributions p(v2) for 5%-centrality bins between5% and 60% centrality are found by unfolding statistical resolution effectsfrommeasured flow distributions.The v2 coefficients cor-responding to different cumulant orders are calculated fromthe moments ofthe unfolded p(v2)distributions. Arank ordering of v2{4} >v2{6} >v2{8},withdifferencesontheorderofafew per-cent, is observed for noncentral events with centralities greater than ≈15%. Thestandardizedskewnessofeach p(v2)distribution is calculatedusing the cumulant results.In cases wherethere is adifferenceinthecumulantvalues,thestandardizedskewnessis found to be negative withan increasing magnitude as collisions becomelesscentral.Bessel–Gaussian andellipticpower functions are fitted to the unfolded p(v2) distributions. The two distribu-tions are similar for central collisions, though the elliptic power functionprovidesabetterdescriptionfornoncentralcollisions.
Based on the elliptic power function fits, the centrality de-pendence oftheflow responsecoefficient, whichrelatesthefinal state geometry to the initial state energydensity distribution, is found tobe consistentwithmodelcalculations.However, the ob-served eccentricities aresmallerthan predictionsbased oneither theGlauber modelortheIP-Glasmamodelinitialconditionswith an assumed linear flow response. This difference might indicate the needforanonlinearresponse term.The currentresults illus-tratethatLHCexperimentsnowhavetheprecisiontoexplorethe detailsoftheinitial-statefluctuations.
Acknowledgements
WecongratulateourcolleaguesintheCERNaccelerator depart-ments for the excellent performance of the LHC and thank the technical andadministrativestaffs atCERNand atother CMS in-stitutes for their contributions to the success of the CMS effort. Inaddition,wegratefullyacknowledgethecomputingcentersand personneloftheWorldwideLHCComputingGridfordeliveringso effectively thecomputinginfrastructure essentialto our analyses. Finally, we acknowledge the enduring support for the construc-tion andoperationofthe LHCandtheCMSdetectorprovided by thefollowingfundingagencies:BMWFWandFWF(Austria);FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIEN-CIAS(Colombia);MSESandCSF(Croatia);RPF(Cyprus);SENESCYT (Ecuador); MoER, ERC IUT, and ERDF (Estonia); Academy of Fin-land,MEC,andHIP(Finland);CEAandCNRS/IN2P3(France);BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hun-gary);DAEandDST(India);IPM(Iran);SFI(Ireland);INFN (Italy); MSIPandNRF (RepublicofKorea);LAS(Lithuania);MOE andUM (Malaysia); BUAP,CINVESTAV, CONACYT, LNS,SEP, andUASLP-FAI (Mexico); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland);FCT(Portugal);JINR(Dubna);MON,ROSATOM,RAS,RFBR andRAEP(Russia);MESTD (Serbia); SEIDI,CPAN,PCTIandFEDER (Spain);SwissFundingAgencies(Switzerland);MST(Taipei); ThEP-Center, IPST, STAR, and NSTDA (Thailand); TUBITAK and TAEK (Turkey);NASU andSFFR (Ukraine);STFC(United Kingdom);DOE andNSF(USA).
Individuals have received support from the Marie-Curie pro-gramandtheEuropeanResearchCouncilandHorizon2020Grant, contract No. 675440 (European Union);the Leventis Foundation; the A.P. Sloan Foundation; the Alexandervon Humboldt Founda-tion; the Belgian Federal Science Policy Office; the Fonds pour la Formationà laRecherche dansl’Industrie etdansl’Agriculture
(FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Council of Sci-ence and Industrial Research, India; the HOMING PLUS program of the Foundation for Polish Science, cofinanced from European Union,Regional DevelopmentFund, theMobilityPlus programof theMinistryofScienceandHigherEducation,theNationalScience Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/ 02861,Sonata-bis2012/07/E/ST2/01406;theNationalPriorities Re-search Program by Qatar National Research Fund; the Programa SeveroOchoa del Principado de Asturias; the Thalis andAristeia programscofinancedbyEU-ESFandtheGreekNSRF;the Rachada-pisekSompotFundforPostdoctoralFellowship,Chulalongkorn Uni-versity and the Chulalongkorn Academic into Its 2nd Century Project Advancement Project (Thailand); the Welch Foundation, contractC-1845;andtheWestonHavensFoundation(USA). References
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TheCMSCollaboration
A.M. Sirunyan,A. Tumasyan
Yerevan Physics Institute, Yerevan, Armenia
W. Adam, F. Ambrogi, E. Asilar,T. Bergauer, J. Brandstetter, E. Brondolin,M. Dragicevic, J. Erö,M. Flechl, M. Friedl,R. Frühwirth1,V.M. Ghete, J. Grossmann, J. Hrubec, M. Jeitler1, A. König, N. Krammer,
I. Krätschmer,D. Liko, T. Madlener,I. Mikulec, E. Pree, N. Rad, H. Rohringer, J. Schieck1, R. Schöfbeck, M. Spanring, D. Spitzbart,W. Waltenberger, J. Wittmann, C.-E. Wulz1, M. Zarucki
Institut für Hochenergiephysik, Wien, Austria
V. Chekhovsky, V. Mossolov,J. Suarez Gonzalez
Institute for Nuclear Problems, Minsk, Belarus
E.A. De Wolf,D. Di Croce, X. Janssen, J. Lauwers,M. Van De Klundert, H. Van Haevermaet, P. Van Mechelen, N. Van Remortel
Universiteit Antwerpen, Antwerpen, Belgium
S. Abu Zeid,F. Blekman, J. D’Hondt, I. De Bruyn, J. De Clercq, K. Deroover, G. Flouris, D. Lontkovskyi, S. Lowette,I. Marchesini, S. Moortgat, L. Moreels,Q. Python, K. Skovpen, S. Tavernier, W. Van Doninck, P. Van Mulders, I. Van Parijs
Vrije Universiteit Brussel, Brussel, Belgium
D. Beghin, H. Brun, B. Clerbaux, G. De Lentdecker, H. Delannoy, B. Dorney,G. Fasanella, L. Favart, R. Goldouzian, A. Grebenyuk,T. Lenzi, J. Luetic, T. Maerschalk, A. Marinov,T. Seva, E. Starling, C. Vander Velde, P. Vanlaer, D. Vannerom,R. Yonamine, F. Zenoni, F. Zhang2
Université Libre de Bruxelles, Bruxelles, Belgium
A. Cimmino, T. Cornelis,D. Dobur, A. Fagot,M. Gul, I. Khvastunov3,D. Poyraz, C. Roskas, S. Salva, M. Tytgat, W. Verbeke,N. Zaganidis
Ghent University, Ghent, Belgium
H. Bakhshiansohi,O. Bondu, S. Brochet,G. Bruno, C. Caputo, A. Caudron, P. David, S. De Visscher, C. Delaere, M. Delcourt, B. Francois,A. Giammanco, M. Komm, G. Krintiras,V. Lemaitre, A. Magitteri,
A. Mertens, M. Musich, K. Piotrzkowski,L. Quertenmont,A. Saggio, M. Vidal Marono, S. Wertz, J. Zobec
Université Catholique de Louvain, Louvain-la-Neuve, Belgium
W.L. Aldá Júnior, F.L. Alves,G.A. Alves,L. Brito, M. Correa Martins Junior,C. Hensel, A. Moraes,M.E. Pol, P. Rebello Teles
Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
E. Belchior Batista Das Chagas, W. Carvalho,J. Chinellato4, E. Coelho, E.M. Da Costa, G.G. Da Silveira5, D. De Jesus Damiao,S. Fonseca De Souza, L.M. Huertas Guativa, H. Malbouisson, M. Melo De Almeida, C. Mora Herrera,L. Mundim,H. Nogima, L.J. Sanchez Rosas,A. Santoro, A. Sznajder,M. Thiel,
E.J. Tonelli Manganote4,F. Torres Da Silva De Araujo, A. Vilela Pereira
Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
S. Ahujaa,C.A. Bernardesa, T.R. Fernandez Perez Tomeia,E.M. Gregoresb,P.G. Mercadanteb, S.F. Novaesa, Sandra S. Padulaa,D. Romero Abadb,J.C. Ruiz Vargasa
aUniversidade Estadual Paulista, São Paulo, Brazil bUniversidade Federal do ABC, São Paulo, Brazil
A. Aleksandrov, R. Hadjiiska,P. Iaydjiev, M. Misheva, M. Rodozov,M. Shopova, G. Sultanov
Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
A. Dimitrov,L. Litov, B. Pavlov,P. Petkov
University of Sofia, Sofia, Bulgaria
W. Fang6, X. Gao6,L. Yuan
Beihang University, Beijing, China
M. Ahmad, J.G. Bian, G.M. Chen,H.S. Chen, M. Chen, Y. Chen, C.H. Jiang, D. Leggat,H. Liao, Z. Liu, F. Romeo,S.M. Shaheen, A. Spiezia,J. Tao, C. Wang, Z. Wang, E. Yazgan, H. Zhang,S. Zhang, J. Zhao
Institute of High Energy Physics, Beijing, China
Y. Ban, G. Chen, J. Li,Q. Li, S. Liu, Y. Mao,S.J. Qian, D. Wang,Z. Xu
State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China
C. Avila,A. Cabrera, L.F. Chaparro Sierra, C. Florez,C.F. González Hernández, J.D. Ruiz Alvarez, M.A. Segura Delgado
Universidad de Los Andes, Bogota, Colombia
B. Courbon,N. Godinovic, D. Lelas,I. Puljak, P.M. Ribeiro Cipriano, T. Sculac
University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, Croatia
Z. Antunovic,M. Kovac
University of Split, Faculty of Science, Split, Croatia
V. Brigljevic,D. Ferencek, K. Kadija,B. Mesic, A. Starodumov7, T. Susa
Institute Rudjer Boskovic, Zagreb, Croatia
M.W. Ather,A. Attikis, G. Mavromanolakis, J. Mousa,C. Nicolaou, F. Ptochos, P.A. Razis, H. Rykaczewski
M. Finger8, M. Finger Jr.8
Charles University, Prague, Czech Republic
E. Carrera Jarrin
Universidad San Francisco de Quito, Quito, Ecuador
A.A. Abdelalim9,10, Y. Mohammed11, E. Salama12,13
Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
R.K. Dewanjee, M. Kadastik, L. Perrini, M. Raidal, A. Tiko, C. Veelken
National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
P. Eerola, H. Kirschenmann,J. Pekkanen,M. Voutilainen
Department of Physics, University of Helsinki, Helsinki, Finland
J. Havukainen, J.K. Heikkilä, T. Järvinen,V. Karimäki, R. Kinnunen, T. Lampén, K. Lassila-Perini,S. Laurila, S. Lehti, T. Lindén,P. Luukka, H. Siikonen, E. Tuominen, J. Tuominiemi
Helsinki Institute of Physics, Helsinki, Finland
T. Tuuva
Lappeenranta University of Technology, Lappeenranta, Finland
M. Besancon, F. Couderc,M. Dejardin, D. Denegri, J.L. Faure, F. Ferri, S. Ganjour, S. Ghosh, P. Gras, G. Hamel de Monchenault, P. Jarry,I. Kucher, C. Leloup,E. Locci, M. Machet, J. Malcles,G. Negro, J. Rander, A. Rosowsky, M.Ö. Sahin,M. Titov
IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
A. Abdulsalam, C. Amendola, I. Antropov, S. Baffioni, F. Beaudette, P. Busson, L. Cadamuro, C. Charlot, R. Granier de Cassagnac, M. Jo,S. Lisniak, A. Lobanov, J. Martin Blanco, M. Nguyen,C. Ochando,
G. Ortona,P. Paganini, P. Pigard,R. Salerno, J.B. Sauvan, Y. Sirois, A.G. Stahl Leiton, T. Strebler, Y. Yilmaz, A. Zabi, A. Zghiche
Laboratoire Leprince-Ringuet, Ecole polytechnique, CNRS/IN2P3, Université Paris-Saclay, Palaiseau, France
J.-L. Agram14, J. Andrea, D. Bloch,J.-M. Brom, M. Buttignol,E.C. Chabert, N. Chanon, C. Collard, E. Conte14, X. Coubez, J.-C. Fontaine14,D. Gelé, U. Goerlach,M. Jansová, A.-C. Le Bihan, N. Tonon, P. Van Hove
Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France
S. Gadrat
Centre de Calcul de l’Institut National de Physique Nucleaire et de Physique des Particules, CNRS/IN2P3, Villeurbanne, France
S. Beauceron,C. Bernet, G. Boudoul, R. Chierici,D. Contardo, P. Depasse, H. El Mamouni,J. Fay, L. Finco, S. Gascon, M. Gouzevitch, G. Grenier, B. Ille, F. Lagarde, I.B. Laktineh,M. Lethuillier, L. Mirabito,
A.L. Pequegnot, S. Perries, A. Popov15,V. Sordini, M. Vander Donckt, S. Viret
Université de Lyon, Université Claude Bernard Lyon 1, CNRS-IN2P3, Institut de Physique Nucléaire de Lyon, Villeurbanne, France
T. Toriashvili16
Georgian Technical University, Tbilisi, Georgia
Z. Tsamalaidze8
C. Autermann,L. Feld, M.K. Kiesel, K. Klein, M. Lipinski,M. Preuten, C. Schomakers, J. Schulz, V. Zhukov15
RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany
A. Albert, E. Dietz-Laursonn,D. Duchardt, M. Endres, M. Erdmann,S. Erdweg, T. Esch, R. Fischer, A. Güth, M. Hamer,T. Hebbeker,C. Heidemann, K. Hoepfner, S. Knutzen,M. Merschmeyer, A. Meyer,P. Millet, S. Mukherjee,T. Pook,M. Radziej, H. Reithler, M. Rieger, F. Scheuch,D. Teyssier,S. Thüer
RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
G. Flügge,B. Kargoll, T. Kress,A. Künsken, T. Müller, A. Nehrkorn, A. Nowack,C. Pistone, O. Pooth, A. Stahl17
RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany
M. Aldaya Martin,T. Arndt, C. Asawatangtrakuldee, K. Beernaert,O. Behnke, U. Behrens, A. Bermúdez Martínez, A.A. Bin Anuar, K. Borras18,V. Botta, A. Campbell,P. Connor,
C. Contreras-Campana, F. Costanza, C. Diez Pardos,G. Eckerlin, D. Eckstein, T. Eichhorn, E. Eren, E. Gallo19, J. Garay Garcia, A. Geiser, J.M. Grados Luyando, A. Grohsjean, P. Gunnellini, M. Guthoff, A. Harb,J. Hauk, M. Hempel20, H. Jung,M. Kasemann, J. Keaveney, C. Kleinwort,I. Korol, D. Krücker, W. Lange,A. Lelek, T. Lenz, J. Leonard,K. Lipka, W. Lohmann20,R. Mankel, I.-A. Melzer-Pellmann, A.B. Meyer, G. Mittag, J. Mnich, A. Mussgiller, E. Ntomari,D. Pitzl, A. Raspereza,M. Savitskyi,P. Saxena, R. Shevchenko,S. Spannagel, N. Stefaniuk, G.P. Van Onsem,R. Walsh, Y. Wen, K. Wichmann,C. Wissing, O. Zenaiev
Deutsches Elektronen-Synchrotron, Hamburg, Germany
R. Aggleton,S. Bein, V. Blobel, M. Centis Vignali, T. Dreyer,E. Garutti, D. Gonzalez, J. Haller, A. Hinzmann, M. Hoffmann,A. Karavdina, R. Klanner, R. Kogler,N. Kovalchuk, S. Kurz, T. Lapsien, D. Marconi,M. Meyer, M. Niedziela, D. Nowatschin, F. Pantaleo17,T. Peiffer, A. Perieanu, C. Scharf, P. Schleper, A. Schmidt, S. Schumann,J. Schwandt,J. Sonneveld, H. Stadie,G. Steinbrück, F.M. Stober, M. Stöver,H. Tholen, D. Troendle, E. Usai, A. Vanhoefer, B. Vormwald
University of Hamburg, Hamburg, Germany
M. Akbiyik, C. Barth,M. Baselga,S. Baur, E. Butz, R. Caspart, T. Chwalek, F. Colombo, W. De Boer, A. Dierlamm,N. Faltermann, B. Freund,R. Friese, M. Giffels,M.A. Harrendorf,F. Hartmann17, S.M. Heindl,U. Husemann, F. Kassel17, S. Kudella, H. Mildner, M.U. Mozer,Th. Müller, M. Plagge, G. Quast, K. Rabbertz,M. Schröder, I. Shvetsov,G. Sieber, H.J. Simonis, R. Ulrich, S. Wayand,M. Weber, T. Weiler, S. Williamson,C. Wöhrmann, R. Wolf
Institut für Experimentelle Kernphysik, Karlsruhe, Germany
G. Anagnostou,G. Daskalakis, T. Geralis,A. Kyriakis, D. Loukas,I. Topsis-Giotis
Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece
G. Karathanasis,S. Kesisoglou, A. Panagiotou, N. Saoulidou
National and Kapodistrian University of Athens, Athens, Greece
K. Kousouris
National Technical University of Athens, Athens, Greece
I. Evangelou,C. Foudas, P. Gianneios, P. Katsoulis, P. Kokkas, S. Mallios,N. Manthos, I. Papadopoulos, E. Paradas, J. Strologas,F.A. Triantis, D. Tsitsonis
M. Csanad, N. Filipovic,G. Pasztor, O. Surányi,G.I. Veres21
MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary
G. Bencze,C. Hajdu, D. Horvath22,Á. Hunyadi, F. Sikler,V. Veszpremi
Wigner Research Centre for Physics, Budapest, Hungary
N. Beni, S. Czellar, J. Karancsi23,A. Makovec, J. Molnar,Z. Szillasi
Institute of Nuclear Research ATOMKI, Debrecen, Hungary
M. Bartók21,P. Raics, Z.L. Trocsanyi, B. Ujvari
Institute of Physics, University of Debrecen, Debrecen, Hungary
S. Choudhury, J.R. Komaragiri
Indian Institute of Science (IISc), Bangalore, India
S. Bahinipati24, S. Bhowmik, P. Mal, K. Mandal, A. Nayak25, D.K. Sahoo24, N. Sahoo, S.K. Swain
National Institute of Science Education and Research, Bhubaneswar, India
S. Bansal, S.B. Beri,V. Bhatnagar, R. Chawla, N. Dhingra, A.K. Kalsi,A. Kaur, M. Kaur, S. Kaur,R. Kumar, P. Kumari, A. Mehta,J.B. Singh, G. Walia
Panjab University, Chandigarh, India
A. Bhardwaj,S. Chauhan, B.C. Choudhary, R.B. Garg,S. Keshri,A. Kumar, Ashok Kumar, S. Malhotra, M. Naimuddin,K. Ranjan, Aashaq Shah, R. Sharma
University of Delhi, Delhi, India
R. Bhardwaj,R. Bhattacharya, S. Bhattacharya, U. Bhawandeep, S. Dey,S. Dutt, S. Dutta, S. Ghosh,
N. Majumdar, A. Modak, K. Mondal, S. Mukhopadhyay, S. Nandan, A. Purohit,A. Roy, S. Roy Chowdhury, S. Sarkar,M. Sharan, S. Thakur
Saha Institute of Nuclear Physics, HBNI, Kolkata, India
P.K. Behera
Indian Institute of Technology Madras, Madras, India
R. Chudasama, D. Dutta, V. Jha,V. Kumar, A.K. Mohanty17,P.K. Netrakanti,L.M. Pant, P. Shukla,A. Topkar
Bhabha Atomic Research Centre, Mumbai, India
T. Aziz, S. Dugad,B. Mahakud, S. Mitra, G.B. Mohanty, N. Sur, B. Sutar
Tata Institute of Fundamental Research-A, Mumbai, India
S. Banerjee, S. Bhattacharya, S. Chatterjee,P. Das, M. Guchait, Sa. Jain, S. Kumar, M. Maity26, G. Majumder, K. Mazumdar,T. Sarkar26, N. Wickramage27
Tata Institute of Fundamental Research-B, Mumbai, India
S. Chauhan,S. Dube, V. Hegde, A. Kapoor, K. Kothekar, S. Pandey, A. Rane, S. Sharma
Indian Institute of Science Education and Research (IISER), Pune, India
S. Chenarani28, E. Eskandari Tadavani,S.M. Etesami28,M. Khakzad, M. Mohammadi Najafabadi, M. Naseri, S. Paktinat Mehdiabadi29,F. Rezaei Hosseinabadi, B. Safarzadeh30,M. Zeinali
M. Felcini,M. Grunewald
University College Dublin, Dublin, Ireland
M. Abbresciaa,b, C. Calabriaa,b, A. Colaleoa, D. Creanzaa,c,L. Cristellaa,b, N. De Filippisa,c,
M. De Palmaa,b, F. Erricoa,b,L. Fiorea,G. Iasellia,c,S. Lezkia,b, G. Maggia,c, M. Maggia,G. Minielloa,b, S. Mya,b, S. Nuzzoa,b, A. Pompilia,b,G. Pugliesea,c,R. Radognaa,A. Ranieria, G. Selvaggia,b, A. Sharmaa, L. Silvestrisa,17,R. Vendittia,P. Verwilligena
aINFN Sezione di Bari, Bari, Italy bUniversità di Bari, Bari, Italy cPolitecnico di Bari, Bari, Italy
G. Abbiendia,C. Battilanaa,b,D. Bonacorsia,b, L. Borgonovia,b,S. Braibant-Giacomellia,b,
R. Campaninia,b,P. Capiluppia,b,A. Castroa,b, F.R. Cavalloa, S.S. Chhibraa, G. Codispotia,b, M. Cuffiania,b, G.M. Dallavallea,F. Fabbria,A. Fanfania,b,D. Fasanellaa,b, P. Giacomellia, C. Grandia, L. Guiduccia,b, S. Marcellinia, G. Masettia,A. Montanaria,F.L. Navarriaa,b,A. Perrottaa,A.M. Rossia,b,T. Rovellia,b, G.P. Sirolia,b,N. Tosia
aINFN Sezione di Bologna, Bologna, Italy bUniversità di Bologna, Bologna, Italy
S. Albergoa,b, S. Costaa,b, A. Di Mattiaa,F. Giordanoa,b, R. Potenzaa,b,A. Tricomia,b, C. Tuvea,b
aINFN Sezione di Catania, Catania, Italy bUniversità di Catania, Catania, Italy
G. Barbaglia,K. Chatterjeea,b,V. Ciullia,b,C. Civininia,R. D’Alessandroa,b, E. Focardia,b, P. Lenzia,b, M. Meschinia, S. Paolettia,L. Russoa,31,G. Sguazzonia,D. Stroma,L. Viliania,b,17
aINFN Sezione di Firenze, Firenze, Italy bUniversità di Firenze, Firenze, Italy
L. Benussi,S. Bianco, F. Fabbri, D. Piccolo,F. Primavera17
INFN Laboratori Nazionali di Frascati, Frascati, Italy
V. Calvellia,b, F. Ferroa, E. Robuttia,S. Tosia,b
aINFN Sezione di Genova, Genova, Italy bUniversità di Genova, Genova, Italy
A. Benagliaa,A. Beschib,L. Brianzaa,b,F. Brivioa,b,V. Cirioloa,b,17, M.E. Dinardoa,b,S. Fiorendia,b, S. Gennaia,A. Ghezzia,b,P. Govonia,b,M. Malbertia,b,S. Malvezzia,R.A. Manzonia,b,D. Menascea, L. Moronia, M. Paganonia,b,K. Pauwelsa,b, D. Pedrinia,S. Pigazzinia,b,32,S. Ragazzia,b,
T. Tabarelli de Fatisa,b
aINFN Sezione di Milano-Bicocca, Milano, Italy bUniversità di Milano-Bicocca, Milano, Italy
S. Buontempoa, N. Cavalloa,c,S. Di Guidaa,d,17, F. Fabozzia,c,F. Fiengaa,b, A.O.M. Iorioa,b,W.A. Khana, L. Listaa,S. Meolaa,d,17,P. Paoluccia,17,C. Sciaccaa,b,F. Thyssena
aINFN Sezione di Napoli, Napoli, Italy bUniversità di Napoli ‘Federico II’, Napoli, Italy cUniversità della Basilicata, Potenza, Italy dUniversità G. Marconi, Roma, Italy
P. Azzia, N. Bacchettaa, L. Benatoa,b,D. Biselloa,b,A. Bolettia,b,R. Carlina,b,
A. Carvalho Antunes De Oliveiraa,b,P. Checchiaa, M. Dall’Ossoa,b,P. De Castro Manzanoa, T. Dorigoa, F. Gasparinia,b, U. Gasparinia,b,A. Gozzelinoa,M. Gulminia,33,S. Lacapraraa, P. Lujan,M. Margonia,b, A.T. Meneguzzoa,b,N. Pozzobona,b,P. Ronchesea,b, R. Rossina,b, E. Torassaa,S. Venturaa, M. Zanettia,b, G. Zumerlea,b
bUniversità di Padova, Padova, Italy cUniversità di Trento, Trento, Italy
A. Braghieria,A. Magnania,P. Montagnaa,b, S.P. Rattia,b,V. Rea, M. Ressegottia,b, C. Riccardia,b, P. Salvinia, I. Vaia,b, P. Vituloa,b
aINFN Sezione di Pavia, Pavia, Italy bUniversità di Pavia, Pavia, Italy
L. Alunni Solestizia,b,M. Biasinia,b, G.M. Bileia,C. Cecchia,b, D. Ciangottinia,b,L. Fanòa,b, R. Leonardia,b,
E. Manonia, G. Mantovania,b, V. Mariania,b,M. Menichellia,A. Rossia,b,A. Santocchiaa,b, D. Spigaa
aINFN Sezione di Perugia, Perugia, Italy bUniversità di Perugia, Perugia, Italy
K. Androsova,P. Azzurria,17,G. Bagliesia,T. Boccalia, L. Borrello, R. Castaldia, M.A. Cioccia,b, R. Dell’Orsoa,G. Fedia, L. Gianninia,c,A. Giassia, M.T. Grippoa,31, F. Ligabuea,c,T. Lomtadzea,
E. Mancaa,c,G. Mandorlia,c,A. Messineoa,b,F. Pallaa, A. Rizzia,b, A. Savoy-Navarroa,34, P. Spagnoloa, R. Tenchinia,G. Tonellia,b, A. Venturia, P.G. Verdinia
aINFN Sezione di Pisa, Pisa, Italy bUniversità di Pisa, Pisa, Italy
cScuola Normale Superiore di Pisa, Pisa, Italy
L. Baronea,b,F. Cavallaria, M. Cipriania,b,N. Dacia, D. Del Rea,b,17, E. Di Marcoa,b,M. Diemoza, S. Gellia,b,E. Longoa,b,F. Margarolia,b,B. Marzocchia,b, P. Meridiania,G. Organtinia,b, R. Paramattia,b, F. Preiatoa,b,S. Rahatloua,b,C. Rovellia,F. Santanastasioa,b
aINFN Sezione di Roma, Rome, Italy bSapienza Università di Roma, Rome, Italy
N. Amapanea,b, R. Arcidiaconoa,c,S. Argiroa,b,M. Arneodoa,c,N. Bartosika,R. Bellana,b, C. Biinoa, N. Cartigliaa, F. Cennaa,b,M. Costaa,b, R. Covarellia,b,A. Deganoa,b,N. Demariaa, B. Kiania,b,
C. Mariottia, S. Masellia, E. Migliorea,b,V. Monacoa,b,E. Monteila,b,M. Montenoa, M.M. Obertinoa,b, L. Pachera,b, N. Pastronea,M. Pelliccionia,G.L. Pinna Angionia,b,F. Raveraa,b, A. Romeroa,b,M. Ruspaa,c, R. Sacchia,b, K. Shchelinaa,b, V. Solaa, A. Solanoa,b,A. Staianoa, P. Traczyka,b
aINFN Sezione di Torino, Torino, Italy bUniversità di Torino, Torino, Italy
cUniversità del Piemonte Orientale, Novara, Italy
S. Belfortea,M. Casarsaa, F. Cossuttia, G. Della Riccaa,b,A. Zanettia
aINFN Sezione di Trieste, Trieste, Italy bUniversità di Trieste, Trieste, Italy
D.H. Kim,G.N. Kim, M.S. Kim,J. Lee, S. Lee,S.W. Lee, C.S. Moon, Y.D. Oh, S. Sekmen,D.C. Son, Y.C. Yang
Kyungpook National University, Daegu, Republic of Korea
A. Lee
Chonbuk National University, Jeonju, Republic of Korea
H. Kim,D.H. Moon, G. Oh
Chonnam National University, Institute for Universe and Elementary Particles, Kwangju, Republic of Korea
J.A. Brochero Cifuentes, J. Goh,T.J. Kim
Hanyang University, Seoul, Republic of Korea
S. Cho, S. Choi,Y. Go,D. Gyun, S. Ha, B. Hong, Y. Jo,Y. Kim, K. Lee,K.S. Lee, S. Lee,J. Lim,S.K. Park, Y. Roh
J. Almond,J. Kim, J.S. Kim, H. Lee,K. Lee, K. Nam,S.B. Oh, B.C. Radburn-Smith, S.h. Seo, U.K. Yang, H.D. Yoo,G.B. Yu
Seoul National University, Seoul, Republic of Korea
H. Kim,J.H. Kim, J.S.H. Lee, I.C. Park
University of Seoul, Seoul, Republic of Korea
Y. Choi,C. Hwang, J. Lee,I. Yu
Sungkyunkwan University, Suwon, Republic of Korea
V. Dudenas, A. Juodagalvis,J. Vaitkus
Vilnius University, Vilnius, Lithuania
I. Ahmed,Z.A. Ibrahim, M.A.B. Md Ali35,F. Mohamad Idris36,W.A.T. Wan Abdullah, M.N. Yusli, Z. Zolkapli
National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia
M.C. Duran-Osuna, H. Castilla-Valdez,E. De La Cruz-Burelo, G. Ramirez-Sanchez, I. Heredia-De La Cruz37, R.I. Rabadan-Trejo,R. Lopez-Fernandez, J. Mejia Guisao, R. Reyes-Almanza,A. Sanchez-Hernandez
Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
S. Carrillo Moreno, C. Oropeza Barrera, F. Vazquez Valencia
Universidad Iberoamericana, Mexico City, Mexico
J. Eysermans,I. Pedraza, H.A. Salazar Ibarguen, C. Uribe Estrada
Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
A. Morelos Pineda
Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico
D. Krofcheck
University of Auckland, Auckland, New Zealand
P.H. Butler
University of Canterbury, Christchurch, New Zealand
A. Ahmad, M. Ahmad, Q. Hassan,H.R. Hoorani, A. Saddique, M.A. Shah,M. Shoaib, M. Waqas
National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan
H. Bialkowska,M. Bluj, B. Boimska,T. Frueboes, M. Górski, M. Kazana, K. Nawrocki, M. Szleper, P. Zalewski
National Centre for Nuclear Research, Swierk, Poland
K. Bunkowski, A. Byszuk38,K. Doroba, A. Kalinowski, M. Konecki,J. Krolikowski, M. Misiura, M. Olszewski,A. Pyskir, M. Walczak
Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland
P. Bargassa,C. Beirão Da Cruz E Silva, A. Di Francesco, P. Faccioli,B. Galinhas, M. Gallinaro, J. Hollar, N. Leonardo,L. Lloret Iglesias, M.V. Nemallapudi, J. Seixas,G. Strong,O. Toldaiev, D. Vadruccio, J. Varela