Pseudorapidity dependence of the anisotropic flow of charged particles in Pb–Pb collisions at √sNN = 2.76 TeV

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Physics Letters B

www.elsevier.com/locate/physletb

Pseudorapidity dependence of the anisotropic flow of charged particles in Pb–Pb collisions at √

s _NN = ² . 76 TeV

.ALICE Collaboration

^1,

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

Articlehistory:

Received17May2016

Receivedinrevisedform21June2016 Accepted6July2016

Availableonline11July2016 Editor:L.Rolandi

Wepresentmeasurementsoftheelliptic(v2),triangular(v3)andquadrangular(v4)anisotropicazimuthal flowoverawiderangeofpseudorapidities(−³.5<η<5).ThemeasurementsareperformedwithPb–

Pbcollisionsat√_s

NN=².76 TeV usingtheALICEdetectorattheLargeHadronCollider(LHC).Theflow harmonicsareobtainedusingtwo- andfour-particlecorrelationsfromninedifferentcentralityintervals covering central to peripheral collisions. We find that the shape of vn(η) is largely independent of centrality for the flowharmonics n=^{2–4, howeverthe higher harmonics fall off more steeply with} increasing |η_|. We assess the validity of extended longitudinal scaling of v2 by comparing to lower energy measurements, and find that the higher harmonic flow coefficients are proportional to the charged particle densities at larger pseudorapidities. Finally, we compare our measurements to both hydrodynamicalandtransportmodels,andfindtheybothhavechallengeswhenitcomestodescribing ourdata.

©^{2016TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

The main goalof the heavy-ionphysics program atthe Large HadronCollider (LHC)isto studythequark–gluonplasma (QGP), a deconfinedstateofmatterexistingatextremetemperaturesand energy-densities. Experimental results from RHIC were the first to suggest that the QGP behaves as a nearly perfect fluid [1–4].

A particularly importantobservable whencharacterizing the QGP isanisotropic azimuthal flow. Theanisotropic flow developsfrom pressuregradientsoriginatingfromtheinitialspatial geometryof acollisionandisobservedasamomentumanisotropyinthefinal- stateparticles.Itisusuallydescribedbyflowharmonics,whichare definedastheFouriercoefficients:

v_n

=

^{cos [n}

( ϕ −

n

)

]

,

(1)

wherenistheorderoftheflowharmonic,

ϕ

istheazimuthalan- gle andn isthe symmetryplane angleof harmonicn.Thefirst three Fourier coefficients, v1, v2, and v3 are known asdirected, elliptic and triangular flow, respectively. The flow harmonics v1 to v6 have been studied extensively at RHIC [1–7] and the LHC [8–17].Theobservedanisotropicflowisconsideredtobeastrong indication ofcollectivity[18] andis described well by relativistic hydrodynamics[19].

1 SeeAppendix Aforthelistofcollaborationmembers.

E-mailaddress:[email protected].

Anisotropic flowstudies atRHICplayed amajor role inestab- lishing that theproduced systemis astrongly interactingquark–

gluon plasma(sQGP)[1–4]withashearviscositytoentropyden- sityratio(

η

/s)closetotheconjecturedlowerlimitof1/(4

π

)pre- dictedbytheAdS/CFTcorrespondence[20].Thefactthathigheror- derharmonicsareincreasinglysuppressedbyviscosity[21]makes it possibleto useanisotropic flow measurements to estimate the

η

/softheproducedsystem[22,23].

The pseudorapidity(

η

)dependenceoftheflowharmonics can play a key role in understanding thetemperature dependenceof

η

/s, something that can be determined usingQuantum Chromo- dynamics (QCD) [24–26]. At forward rapidities,the average tem- perature drops which implies

η

/s will also change. In addition, thelowertemperaturesatforwardrapiditiesmeanthesystemwill spend lesstime intheQGPphaseleading tothehadronicviscos- ityplayinga greaterrole inaffecting theflow harmonics[26,27].

Recently, it has been suggestedthat the symmetry plane angles maydepend on

η

[28–30].While thiseffectis notdirectly stud- iedinthisLetter,consideringthatthereferenceparticlesaretaken frommid-rapidity, the measured valuesofanisotropy coefficients atforwardrapidity willbe suppressedifthesymmetry-planean- glesfluctuatewith

η

.

At RHIC, thePHOBOS experiment reportedthe pseudorapidity dependence of elliptic flow over a wide range (−⁵.0<

η

<5.3) and variety of collision energies [31–33], andsystem sizes [34].

It was foundthat intherestframe ofone ofthecollidingnuclei (

η

₋ybeam), v2 is energyindependent. This featurewas alsoob- http://dx.doi.org/10.1016/j.physletb.2016.07.017

0370-2693/©^{2016TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

ALICE Collaboration / Physics Letters B 762 (2016) 376–388 377

servedinmultiplicitydensitydistributions[35,36]andforv1 [37].

Thissuggeststhatatforwardrapidity,inthefragmentationregion, particleproductionisindependentofthecollisionenergy,aneffect knownasextendedlongitudinalscaling.

InthisLetter,wepresentmeasurementsofv2,v3,andv4overa widepseudorapidityrange(−³.5<

η

<5.0) inPb–Pbcollisionsat

√s_NN=².76 TeV usingtheALICEdetector. AttheLHC, thepseu- dorapidity dependence of the flow harmonics has already been reportedby ATLAS [12,38] andCMS [13,16]in a limited

η

-range (|

η

|<2.5 and|

η

|<2.4, respectively). The extended longitudinal scalinghasbeenshowntoholdformultiplicitydensities[39] and directed flow [15], andappears tooccur forellipticflow [13,38].

Here,the

η

-range isextended considerably compared tothe for- mer resultsandwe will investigate whetherthe extendedlongi- tudinalscalingofellipticflowcontinuestohold. Wewillcompare ourdatatohydrodynamicalandtransportmodels,andinvestigate thedecreaseofvn intheforwardregionsrelativetodN_ch/d

η

.

2. Experimentalsetup

Adetailed description of the ALICE detectoris available else- where[40].Inthissection,thesub-detectorsusedinthisanalysis aredescribed:theV0detector,theTimeProjectionChamber(TPC), theInner TrackingSystem(ITS) andtheForwardMultiplicityDe- tector(FMD). TheV0 detectorconsistsof2 arraysofscintillators located on opposite sidesof the interaction point (IP) along the beamline. Thedetectorhasfullazimuthalcoverage intheranges of2.8<

η

<5.1 (V0-A)and−³.7<

η

<−¹.7 (V0-C)[41].Thede- tector actsasan onlinetrigger and, withits large coverage, asa centralityestimator.

ChargedparticletracksarereconstructedusingtheTPC,alarge TimeProjection Chamber[42].The detector can provideposition andmomentum information. Particles that traverse the TPCvol- umeleaveionization trails thatdrift towards theendcaps,where they are detected. Full length tracks can be reconstructed in the range |

η

|<0.8. For thisanalysis, a transverse momentum range of 0.2< pT<5.0 GeV/c was used. To ensure good track qual- ity,thetracks are requiredto haveatleast70 reconstructedTPC space points (cluster) out of 159 possible and an average

χ

²

per TPC cluster ≤^{4. In addition, to reduce} contamination from secondary particles (weak decays or interactions with material), a cutonthedistanceofclosestapproach(DCA)betweenthetrack and the primary vertex is applied both in the transverse plane (DCAxy<2.4 cm)andonthez-coordinate(DCAz<3.2 cm).

TheITSismadeupofsixcylindricalconcentricsiliconlayersdi- videdintothreesub-systems,theSiliconPixelDetector(SPD),the SiliconDrift Detector (SDD) and the SiliconStrip Detector (SSD), each consistingof two layers [40]. ITSclusters can be combined with the TPC information to improve track resolution. The SPD hasadditionalapplications[40].Firstly, itisused toestimate the primary vertexasit is located closeto thebeam pipe.Secondly, clustersfromtheSPDinnerlayer,whichconsistsof3.3×^{106 pixels} ofsize50×^{425 μm2,areusedtoestimatethenumberofcharged} particlesintherange|

η

_|<2.0.

The FMD consists of five silicon rings, providing a pseudora- piditycoverage intheranges −³.5<

η

<−¹.7 and1.7<

η

<5.0 [43].Theringsaresingle-layerdetectorsandonlychargedparticle hits, nottracks, are measured.This means that primary andsec- ondaryparticles cannot be distinguished. There are two typesof FMD rings: inner ring and outer rings. Inner rings have512 ra- dialstripseachcovering18^◦ inazimuthandouter ringshave256 radialstripseachcovering9^◦ inazimuth. Thechargedparticlees- timation in the FMD isdescribed in more detail elsewhere [39].

The inner layer ofthe SPD andthe five FMDrings allow one to measurechargedparticlehitsintherange−³.5<

η

<5.0.

3. Datasampleandanalysisdetails

We analysed 10 million minimum bias Pb–Pb collisions at

√s_NN=².76 TeV. The sample was recorded during the first LHC heavy-iondata-takingperiodin2010. Aminimum-biastriggerre- quiringacoincidencebetweenthesignalsfromV0-AandV0-Cwas used.Inaddition,itisrequiredthattheprimaryvertex,determined by theSPD,be within |^vz|<10.0 cm, wherevz=^{0 cm is thelo-} cationofthenominalinteractionposition.The measurementsare grouped accordingto fractions of theinelastic cross section, and coverthe80% mostcentral collisions.TheV0detectorisusedfor thecentralityestimatewhichisdescribedinmoredetailelsewhere [44].Forthemostcentraltothemostperipheralevents,theV0has acentralityresolutionof0.5% to2%,respectively.

The flow harmonics are estimated using the Q-cumulants method [45] for two- and four-particle correlations, denoted as vn{²}^andvn{⁴}respectively.Thetwo- andfour-particlecumulants respond differently to flow fluctuations. The two-particle cumu- lantsareenhanced, whilefour-particlecumulantsare suppressed.

Atforwardrapidities,thepseudorapidity densityisrelativelylow.

This means that it is not always possible to get statistically sig- nificant results usingonly particles from a smallregion in

η

. To circumventthisusingtheQ-cumulantsmethod,thereferenceflow measurementisperformedusingthechargedparticletracksfrom theTPC, wherethe correlationsatmid-rapidityare measured.As a systematiccheck, thecharged particle tracksusing a combina- tionoftheTPCandITSarealsoused.Then,forthe vn(

η

)analysis, the correlations between charged particle hits (from the SPD or FMD)andthetracksaremeasuredin

η

-bins 0.5 unitsofpseudo- rapidity wide.ToavoidautocorrelationsbetweentheSPDclusters andtracks, thetracks forthe referenceparticles are located ina different

η

-regionthantheSPDhits.Effectively,forSPDhitswith

η

<0,tracksarerequiredtohave

η

>0 andviceversa.Thesame considerationsapply forFMDhits. Duetotheuseofparticlehits, only the pT-integrated flow is measured. The φ distribution for the SPDorFMDclustersisnot uniform, thereforea non-uniform acceptance correction is applied based on relations derived else- where[46].

AstheinnerringsoftheFMDhaveonly20azimuthalsegments, theflowharmonicsareslightlysuppressed.Theeffectofthiswas recentlycalculated [47] andfound to be 1.6%, 3.7% and6.5% for v₂,v₃ andv₄ respectively.Thissuppression istakenintoaccount in the final results. When using charged particle hits it is not possibletodistinguishsecondary particles(frommaterial interac- tions anddecays) fromprimaryparticles. Fortheregionscovered by the SPD, the contamination from secondary particles is small (<10%), astheinner layer ofthe SPDis veryclose tothe beam pipe. Away from mid-rapidity, in the FMD, dense material such as cooling tubes and read-out cables causea very large produc- tion ofsecondary particles– up totwice the numberofprimary particles accordingtoMonteCarlo(MC) studies.Thesesecondary particles are deflected in

ϕ

with respect to the mother particle, which causesa reduction in the observed flow. The reduction of flowcausedbythesecondaryparticlesisestimatedusinganevent generatorcontainingparticleyields,ratios,momentumspectraand flowcoefficients,whicharethensubjecttoafulldetectorsimula- tion using GEANT3 [48]. Tomake sure that the correction isnot model dependent, the AMPT MC event generator [49,50] is used asan independent input, withGEANT3 againused to model the detectorresponse.Usingthesesimulations,thereduction isfound to be larger forhigher harmonics, up to 41% for v4. Finally, the correction alsoaccountsformissingvery low p_T particles, which increase theobserved vn astheseparticles haveavery small vn. However,asthecorrectionisalwayslessthan1,thedominantef- fectcomesfromthesecondaryparticles,whichreducev_n.

Few-particlecorrelations,notoriginatingfromtheinitialgeom- etrytermednon-flow(decays,jets,etc.),enhancethetwo-particle cumulant measurements. The non-flow contribution to the four- particlecumulantisfound to benegligible [45,51],however,it is necessary to apply a correction to the two-particle cumulant. In theFMDandSPD,thereisalsoanon-flowcontributionfromsec- ondaryparticles,astheyaresometimesproducedinpairs.Forthe differentialflowmeasurement,thereisarapidity-gapbetweenthe chargedparticlehitsandthechargedparticletracks.FortheSPD,it isbetween0and2unitsinpseudorapidity,whilefortheFMDitis between0.9and4.2unitsinpseudorapidity.Thelargerapiditygap suppressesthenon-flowcontributionatforwardrapidity.However, atmid-rapidities,thiscontributionisnon-negligibleandneedsap- propriate corrections. For the referenceflow measurement there is no rapidity gap, and non-flow removal is important. For this analysis, the non-flow contributions are estimated using the HI- JINGeventgenerator[52]andGEANT3forthedetectorsimulation.

Thenon-flow contribution isestimatedandsubtracted separately forthereferenceanddifferentialflow,beforethecorrectionforthe deflection ofsecondary particles isapplied andthe v_n estimates arederived.

4. Systematicuncertainties

Numeroussourcesofsystematicuncertaintywere investigated, includingeffectsduetodetectorcuts,choiceofreferenceparticles anduncertaintiesrelatedtothesecondaryparticlecorrection.Four major contributors tothe systematicuncertainty were identified:

thechoice ofreferencetracks, themodeldependenceof thesec- ondaryparticlecorrection,thedescriptionofthedetectorusedfor the simulations,and finally thenon-flow correction.As the non- flowcontribution tothe four-particlecumulantisnegligible,only the first three systematic uncertainties are considered for v₂{⁴}^. The systematic uncertainties assigned to each of the sources are showninTable 1,andaredescribedinmoredetailbelow.

Thedependenceofthedifferentialflowonthereferencetracks was tested by using tracks with combined information fromthe TPCandITS,ratherthantrackswithonlyTPCinformation.Thesys- tematicuncertaintyfromthechoiceofreferencetrackswasfound tovaryslightlywithcentrality,withthemostcentraleventshaving thelargestuncertainty.Totestthemodeldependenceofsecondary particle production,the correction from the toy-model described above is compared to the one derived from AMPT tuned to LHC data.Boththesecondaryparticlecorrectionandthenon-flowcor- rection derived from HIJING are sensitive to inaccuracies in the description of the detector used for the simulation. To test this sensitivity,theoutputoftwoHIJINGsimulationswithaflowafter- burner,onewith+7% materialdensityandonewith−7% material density, are compared to the output from having normal mate- rial density. In this case the systematic uncertainty has a small

η

-dependence,astherearesignificantlyfewersecondaryparticles atmid-rapidity.The3%uncertaintyisapplicabletotheSPD,while the4%uncertaintyisapplicabletotheFMD.

We assessed the systematic uncertainty associated with the non-flowcorrectionintwoways.Firstly,followinganothermethod proposed to subtract non-flow [53], the two-particle cumulants were obtained fromminimum bias pp collisions, where it is as- sumed that there is negligible anisotropic flow. The pp refer- ence and differential cumulants are then rescaled according to their multiplicity, M, using the ratio M^pp/M^cent, then subtracted fromthecorrespondingA–Acumulants.Anydifferencesfoundbe- tween this method and the default HIJING method are treated assystematicuncertainties. Secondly, by using onlycharged par- ticle hits from the SPD and FMD, it is possible to construct a two-particlecumulantwithalargerapidity-gap,v_n{²,|

η

|>2.0}^,

Table 1

Listofthesystematicuncertaintiesforeachobservable.

Source v2{²} ^v3{²} ^v4{²} ^v2{⁴}

Reference particle tracks 2–4% 2–4% 2–6% 2–4%

Model dependence 5% 5% 7% 5%

Material budget 3–4% 3–4% 3–4% 3–4%

Non-flow correction 2–10% 2–10% 2–10% -

Total 6–12% 6–13% 6–14% 6–8%

which largely removes all non-flow contributions. Unfortunately, this observable is statistically stableonly for v₂ and v₃, so it is used as a further cross check. In Table 1, the 2% uncertainties correspond to mid-central collisions where the ratio of flow to non-flowislargest,whilethe10%uncertaintiescorrespondtovery central andvery peripheral collisions where the ratio offlow to non-flow issmallest. Finally,weusedthe AMPTmodel[49,50] to investigateiftherearedifferencesbetweenvn(

η

)andvn(y),as

η

issupposedtoapproximate y.Wefoundthereare15%differences in the flow coefficientsat mid-rapidity, which reducedto 0% for

η

>2.Wedidnotassignanysystematicuncertaintiesduetothese differences,asweareexplicitlyreportingmeasurementsasafunc- tionof

η

(asinthecaseofdNch/d

η

measurements).

Thesystematicuncertaintyassignedtothenon-flowcorrection is the largest contributor to the total systematicuncertainty, ex- cept for v2{⁴} ^duetothe four-particlecumulant’s insensitivity to non-flow.Thetotalsystematicuncertaintiesareslightlydependent oncentralityandpseudorapidity.

5. Results

An overviewofthe fourobservablesineachcentralityclass is shown inFig. 1.Due to thechanging overlap geometry,a strong centralitydependenceoftheellipticflowisobservedovertheen- tirepseudorapidityrange.Theweakercentralitydependenceofthe higherordercoefficientsv3andv4isanindicationthatinitial-state fluctuationsplayaprominentrole,asthecentralitydependenceof thecorrespondingeccentricitiesaremoremodestrelativeton=² [21]. The different behaviour of v2{²} ^andv2{⁴} ^{caused by flow} fluctuations is also clearly seen. For the most peripheral events, therearenotenoughparticlestogetstatisticallystableresultsfor v2{⁴}^{andsimilarlyforv}4{²} ^{duetotherelatively smallquadran-} gularflow.

The pT-integratedellipticflowwasalsomeasuredbyCMS[13]

and ATLAS [38] in Pb–Pb collisions at √

s_NN=².76 TeV and by PHOBOS in Au–Au collisions at √

sNN=^{200 GeV[32].A compar-} ison between those results and this analysis is shown for the 25–50% centrality classin Fig. 2. Inthe commonregion ofpseu- dorapidity acceptance,the results of present analysis are consis- tent with the results obtained by CMS and ATLAS experiments within thesystematicuncertainties. Thepresentanalyses extends themeasurements toawider rangeofpseudorapidity. Thevalues of v₂ atall pseudorapiditiesmeasured atLHCenergies are larger than the corresponding values at RHIC, as reported by PHOBOS.

Thisincreaseinellipticflowcoincideswithalarger pT attheLHC energy[8].

Theextended longitudinalscalingobservedbyPHOBOSinAu–

Au collisions withcentre-of-massenergies from19.6 to200 GeV [33] isfoundtoholduptotheLHCenergy(showninFig. 3).This is consistent withwhat was found by CMS [13] andATLAS [38].

Here itis shownasaneventaverage forthe0–40% most central events.Theeventaveragemeansthattheanalysiswasperformed insmallercentralitybinsusingmultiplicityweights,andwasthen averagedoverthecentralitybinsusingthenumberofeventsasa weight[45].Toexamineboostinvariance,itwouldbepreferableto

ALICE Collaboration / Physics Letters B 762 (2016) 376–388 379

Fig. 1.Measurementsofthepseudorapiditydependenceofv2,v3andv4ineachcentralitybin.Theverticallinesrepresentthestatisticaluncertaintiesandtheboxesrepresent thesystematicuncertainties.Thestatisticaluncertaintiesareusuallysmallerthanthemarkersize.

Fig. 2.Ellipticflowforthe25–50% centralityrange.Boxesrepresentsystematicun- certaintiesanderrorsbarsrepresentstatisticaluncertainties.Theresultsforv2{²} fromthis analysisarecomparedtomeasurementsusingtheeventplanemethod from CMS [13] and ATLAS [38] at the same energy and lower energy results fromPHOBOS [32]. For the comparable LHCenergy, the pT rangefor ALICE is pT>0 GeV/c,forCMSis0.3<pT<3 GeV/c,andforATLASispT>0.07 GeV/c.

userapidity(y)insteadofpseudorapidity,unfortunatelythatisnot possibleusingtheFMDasthemomentumcannotbemeasured.

PHOBOSfoundtheshapeofv₂(

η

)tobelargelyindependentof centrality,withonlytheoveralllevelchangingbetweencentraland peripheral events [32]. The ratios of central to peripheral events forv2, v3 andv4 using the two-particle cumulantare shownin Fig. 4.Hereitisobservedthatnoneoftheharmonicsshowaclear centralitydependence inthe shape ofvn(

η

) within uncertainties (albeit hints of such a dependence are present in the v2 ratio), consistentwiththeresultsfromPHOBOSatlowerenergy.

It is known that the suppression from viscous effects to the flowharmonicsincreaseswithn[21].Thehadronicphaseisspec- ulatedtobemoredominantatforwardrapidity[26,27].Therefore, therelativedecreaseoftheflowharmonicsmayhelptodisentan-

Fig. 3.Theellipticflowasobservedintherestframeofoneoftheprojectilesby usingthevariable|η|−ybeam(ybeam=7.99)fortheeventaveraged0–40% central- ityrange.Theresultsfromv2{2}fromthisanalysisarecomparedtolowerenergy resultsfromPHOBOS[33].Theverticallinesrepresentthestatisticaluncertainties andtheboxesrepresentthesystematicuncertainties.ForthePHOBOSresultsonly statisticalerrorsareshown.

gle the viscous effects fromthe hadronic phase withthose from theQGPphase. Whentheratiovm/vn (n=^m)is formedmostof thecommonsystematicuncertaintiescancel,leavingthecontribu- tion fromthenon-flow correction. Theratios ofv3/v2 andv4/v3 areshownforthe30–40% mostcentraleventsinFig. 5.Asmallde- creasewith

η

isobserved forv3/v2, qualitativelyconsistent with theexpectationfromviscouseffectssuppressinghigherharmonics.

Thev₄/v₃ratioremainsconstantwith|

η

|^withintheuncertainties.

Thefigurealsoshowsv4/v²₂,whichiscommonlyusedtoestimate thenon-linear contributionto v4 fromtheellipticanisotropy [5].

Given the uncertainties, it isdifficult to conclude whetherv₄/v²₂ changeswithrespectto

η

.

As mentioned previously, at forward rapidities the steepness ofv_n(

η

)hasbeenlinked to thehadroniccontributionto thevis-

Fig. 4.Ratioofvn{2}betweencentral(0–5%)andperipheral(50–60%)eventsforv2, v3 andv4.Theverticallinesrepresentthestatisticaluncertaintiesandtheboxes representthesystematicuncertainties.Thev2resultsaremultipliedby3tofiton thesamescaleasv3andv4.

Fig. 5.Ratios betweendifferentharmonics for the 30–40% centralityrange.The verticallinesrepresent the statisticaluncertainties andthe boxes representthe commonsystematicuncertainties.Inthebottompaneltheratiosarerescaledto 1 atmid-rapidityandthecommonsystematicuncertaintiesareshownasthethick barsontheleft.

cosity to entropy ratio [26,27]. The larger the hadronic

η

/s, the steeperthefalloff.Wealsonotethatthepseudorapiditydensities ofchargedparticlesdecreaseinthisregion.Inordertoinvestigate thecorrespondenceofthelatter,inFig. 6weshowtheratioofvar- ious vn coefficients to previous ALICE measurements of dN_ch/d

η

[39]. In order to avoid any influence of the Jacobian translation from y to

η

,onlytherange

η

>2 isshown.Wefindthatthisra- tioisgenerally flat,withtheexception ofv2 atthelarger values of

η

.Thisindicatesthatwithinafixedcentralityinterval,v3andv4 arelargelydrivenbythelocalparticledensity.Indeed,whencom- paring p–Pb and Pb–Pb collisions at LHC energies, it was found that values of v3{²} ^{were similar for similar values of dN}ch/d

η

[51]. Thecorrelation found betweenboth quantities maybesim-

ply attributed to the fact that both particle production and the development ofanisotropic flow aredriven bythe numberofin- teractionsinthesystem.

In Fig. 7, we compare our data to hydrodynamic calculations tuned toRHICdata[26].Thetuninginvolvesfindingaparameter- izationofthetemperaturedependenceof

η

/s,sothat thehydro- dynamical calculations describe PHOBOS measurements of v₂(

η

) [32,33]. It is clear that the same parameterization does not de- scribetheLHCdataaswell.Forboth centralities,theellipticflow coefficient v₂ isgenerallyunderestimated,while thehigherorder coefficients v3 andv4 are generallyoverestimated. This points to theneedforaneitheranalternativeparameterizationof

η

/s that describes boththe RHIC andLHC datasimultaneously, or further investigationsintowhethertheinitialstatemodelusedisapplica- blefortheLHCenergies.

In contrasttohydrodynamical models,AMPT isa non-equilib- riummodelthatattemptstosimulatepartonproductionafterthe initial collision, and collective behaviour arises from parton and hadronicrescatterings.Ithaspreviouslybeentunedtoagreewith ALICEmeasurementsofv₂ vs. p_T andmultiplicity forthe40–50%

most central events. It was found to reproduce v3(pT) well us- ing thesameparameters. InFig. 8the resultsofthisanalysisare comparedtotheoutputoftheAMPTmodelfortwodifferentcen- tralities.Forthecentralityrangeof40–50%,whichAMPT istuned to match,there isgoodagreement atmid-rapidityforallobserv- ables modulov₂{⁴}^atlarger|

η

|^,whereAMPT underestimatesthe data.Theunderestimationatforwardrapidityisfoundtobeinde- pendent ofthe choice ofreferenceparticles, suggestingthat it is unrelated tosymmetryplane anglefluctuationswith

η

.Formore centraleventsAMPTtendstooverestimateflowatforwardrapidi- ties, except for v4 which it describes quite well over the entire range. At mid-rapidity AMPT agrees withthe observed values of v₂,v₃ andv₄ within thesystematicuncertainties. Further tuning mayleadtoan improvementatforwardrapidities,andshouldbe investigatedinfuturestudies.

6. Conclusions

The pseudorapidity dependence of the anisotropic flow har- monics v2, v3 andv4 havebeenmeasured inPb–Pb collisions at

√sNN=².76 TeV using the ALICE detector. The measurement is performed over the widest

η

-range at the LHC, −³.5<

η

<5.0, inninecentralitybinscovering0 to80% ofthetotalinelasticcross section.Itwasfoundthattheshapeofvn(

η

)doesnotdependob- viouslyoncentrality.Comparingtolowerenergymeasurementsat RHIC, elliptic flowis larger atthe LHC overthe entirepseudora- pidity rangeandextended longitudinal scaling of v2 observed at lower collisionenergies isstill validup totheLHC energy.Inthe range|

η

|<2.5 theresultswerefoundtobeconsistentwithprevi- ousLHCmeasurements.Atforwardrapidities,thehigherharmonic flowcoefficientsareproportionaltothechargedparticledensities foragivencentrality,whiletheratioofv₂ todN_ch/d

η

riseswith increasing

η

.Acomparisontohydrodynamic calculationstunedto RHICdatahasdifficultiesindescribingourdatainsome

η

regions, andthissuggeststhat the LHCdataplay a keyrole in constrain- ing eitherthetemperaturedependenceof

η

/sortheinitial state.

Finally,comparingourdatatoAMPT,themodeldescribestheflow wellatmid-rapidity,butfailsforv2 atforwardrapidities.

Acknowledgements

The ALICECollaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstotheconstruc- tionoftheexperimentandtheCERNacceleratorteamsfortheout- standingperformanceoftheLHCcomplex.TheALICECollaboration

ALICE Collaboration / Physics Letters B 762 (2016) 376–388 381

Fig. 6.Ratiosbetweenvn coefficientsand dNch/dη valuesfor differentcentralities.Measurements ofdNch/dηaretaken fromapreviousALICEpublication[39].Only systematicuncertaintiesareshown,asthestatisticaluncertaintiesaresmallerthanthesymbols.

Fig. 7. Comparisonsto hydrodynamicspredictions[26], whereinput parameters (temperature dependence of η/s) have been tuned to RHIC data for the Pb–

Pb20–30% (top)and40-50%(bottom)centralities.ThepredictionsareforPb–Pb

√sNN=2.76 TeV collisions.

gratefully acknowledges the resources and support provided by all Gridcentres andtheWorldwide LHC ComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the follow- ing funding agencies for their support in building and running theALICEdetector:StateCommittee ofScience,WorldFederation of Scientists (WFS)and SwissFonds Kidagan, Armenia; Conselho Nacional de DesenvolvimentoCientífico e Tecnológico (CNPq), Fi- nanciadorade Estudos eProjetos(FINEP),Fundação de Amparoà Pesquisa doEstado de São Paulo (FAPESP); Ministryof Science&

Technology ofChina (MSTC),NationalNatural ScienceFoundation ofChina(NSFC) andMinistryofEducationofthePeople’sRepub- licofChina (MOEC)”;MinistryofScience,EducationandSportsof Croatia and Unity through Knowledge Fund, Croatia; Ministry of Education,YouthandSports oftheCzechRepublic;DanishNatural Science ResearchCouncil, the CarlsbergFoundation andthe Dan- ishNationalResearchFoundation;TheEuropeanResearchCouncil undertheEuropeanCommunity’sSeventhFrameworkProgramme;

Helsinki Institute of Physics andthe Academy of Finland; French CNRS-IN2P3, the ‘Region Pays de Loire’, ‘Region Alsace’, ‘Region Auvergne’ and CEA, France; German Bundesministerium für Bil- dungundForschung (BMBF) andtheHelmholtzAssociation;Gen- eral Secretariat for Research and Technology, Ministry of Devel- opment, Greece; National Research, Development andInnovation Office (NKFIH), Hungary; Council of Scientific and Industrial Re- search (CSIR), New Delhi; DepartmentofAtomic Energy, Govern- ment ofIndia and Department ofScience and Technology of the GovernmentofIndia;InstitutoNazionale diFisicaNucleare (INFN) and Centro Fermi – Museo Storico della Fisica e Centro Studi e Ricerche“Enrico Fermi”,Italy; Japan Societyforthe Promotionof Science(JSPS)KAKENHIandMEXT,Japan;NationalResearchFoun- dation of Korea (NRF); Consejo Nacional de Cienca y Tecnologia (CONACYT),DirecciónGeneraldeAsuntosdelPersonalAcadémico, Universidad Nacional Autónoma de México (DGAPA), Amerique

Fig. 8.ComparisontoAMPT[49,50]forthecentralityranges5–10% and(top)and 40–50% (bottom).TheAMPTpredictionsareforPb–Pb√

sNN=2.76 TeV collisions.

Latine FormationAcademique – European Commission (ALFA-EC) andtheEPLANETProgram (EuropeanParticlePhysicsLatin Amer- ican Network); Stichting voor Fundamenteel Onderzoek der Ma- terie (FOM) and the Nederlandse Organisatie voor Wetenschap- pelijkOnderzoek(NWO),Netherlands;ResearchCouncilofNorway (NFR); Pontificia Universidad Católica del Perú; National Science Centre,Poland;MinistryofNationalEducation/InstituteforAtomic Physicsand NationalCouncil ofScientific Research inHigher Ed- ucation (CNCSI-UEFISCDI),Romania;JointInstituteforNuclearRe- search,Dubna; MinistryofEducationandScienceofRussianFed- eration, Russian Academy of Sciences, Russian Federal Agency of AtomicEnergy,RussianFederalAgencyforScienceandInnovation andTheRussianFoundationforBasicResearch;MinistryofEduca- tion,Science, ResearchandSport oftheSlovak Republic;Depart- mentofScienceandTechnology,RepublicofSouthAfrica; Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas (CIEMAT),E-InfrastructuresharedbetweenEuropeandLatinAmer- ica(EELA), MinisteriodeEconomíayCompetitividad(MINECO)of Spain,XuntadeGalicia(ConselleríadeEducación),CentrodeApli- cacionesTecnológicasyDesarrolloNuclear(CEADEN),Cubaenergía, Cuba,andIAEA(InternationalAtomicEnergyAgency);SwedishRe- search Council (VR) and Knut and Alice Wallenberg Foundation (KAW);NationalScienceandTechnologyDevelopmentAgency(NS- DTA),Suranaree University ofTechnology (SUT) and Officeofthe HigherEducationCommissionunderNRUprojectofThailand;Min- istryofEducationandScienceofUkraine;UnitedKingdomScience andTechnology Facilities Council (STFC); The U.S. Department of Energy,theUnitedStatesNationalScienceFoundation,theStateof TexasAttorneyGeneral,andtheStateofOhio.

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