CERN-PH-EP-2011-124 Measurement of the pseudorapidity and transverse momentum dependence of the elliptic flow of charged √ particles in lead-lead collisions at s = 2.76 TeV NN with the ATLAS detector 2 1 0 The ATLAS Collaboration 2 n a J 8 1 Abstract ] This paper describes the measurement of elliptic flow of charged particles in x √ lead-lead collisions at s = 2.76 TeV using the ATLAS detector at the e NN - Large Hadron Collider (LHC). The results are based on an integrated lumi- p nosity of approximately 7 µb−1. Elliptic flow is measured over a wide region e h in pseudorapidity, |η| < 2.5, and over a broad range in transverse momentum, [ 0.5 < p < 20 GeV. The elliptic flow parameter v is obtained by correlating T 2 individual tracks with the event plane measured using energy deposited in the 3 v forward calorimeters. As a function of transverse momentum, v2(pT) reaches a 8 maximumatpT ofabout3GeV,thendecreasesandbecomesweaklydependent 1 on p above 7–8 GeV. Over the measured pseudorapidity region, v is found to T 2 0 beonlyweaklydependentonη,withlessvariationthanobservedatlowerbeam 6 energies. The results are discussed in the context of previous measurements at . 8 lower collision energies, as well as recent results from the LHC. 0 1 Keywords: LHC, ATLAS, Heavy Ions, Elliptic Flow 1 : v i 1. Introduction X r The measurement of collective phenomena in nuclear collisions at high en- a ergies has been a subject of intensive theoretical and experimental studies. Anisotropic flow, which manifests itself as a large anisotropy in the event-by- eventazimuthalangledistributionofproducedparticles,isgenerallyunderstood tobeaconsequenceofthespatialanisotropyoftheinitialenergydepositionfrom nucleon-nucleon collisions in the overlap of the colliding nuclei. Anisotropies in the initial energy density are converted into final state momentum anisotropies via strong rescattering processes which induce pressure gradients, following the laws of relativistic hydrodynamics. Consequently, azimuthal anisotropies are sensitive to the initial state and its subsequent dynamical evolution. Preprint submitted to Physics Letters B January 19, 2012 Anisotropic flow is commonly studied by measuring the Fourier coefficients (v ) of the azimuthal angle distributions of the emitted particles. The second n harmonic, v , referred to as “elliptic flow”, is the most extensively studied as 2 it most directly relates the anisotropic shape of the overlap of the colliding nuclei to a corresponding anisotropy of the outgoing momentum distribution (forareview,seeRef.[1]). Ellipticflowhasbeenmeasuredoverawiderangeof energies,collisionsystems,andcollisioncentralitiesbyalloftheRHICheavyion experiments [2, 3, 4, 5] and several experiments at lower energies (see Ref. [1]). Predictions for v at the LHC energy varied widely, covering all possibilities 2 from a strong rise, no change, or even a decrease of v [6] relative to lower 2 energy collisions. Measurements of v for inclusive charged-particles from the 2 ALICE experiment [7] indicate that, integrated over p , it increases by about T 30% from RHIC to LHC energies. However, ALICE also observed that v (p ) 2 T for inclusive charged particles was identical with RHIC results for the same collision centrality (or impact parameter) up to p =4 GeV. This implies that T the observed rise is driven primarily by an increase in the average transverse momentum with the higher collision energy. Inthisletter,wepresentameasurementoftheellipticflowofchargedparti- √ clesinlead-leadcollisionsat s =2.76TeVwiththeATLASdetectoratthe NN LHC. The elliptic flow is measured in the pseudorapidity region |η| < 2.5 over the full azimuthal range 0 < φ < 2π, for transverse momenta1 0.5 < p < 20 T GeV. This allows stringent tests of the applicability of hydrodynamics in the LHCenergyregime,andprovidesinformationonthetransitionbetweenlowp , T where hydrodynamics is expected to dominate, and higher p , where particle T production is expected to stem from the fragmentation of jets modified by the hot, dense medium [8]. 2. ATLAS detector and trigger The ATLAS detector [9] is well suited for measurements of azimuthal an- isotropies over a large pseudorapidity range. The relevant detectors for this analysis are the inner detector (ID) and forward calorimeter (FCal). The ID is contained within the 2 T field of a superconducting solenoid magnet, and mea- sures the trajectories of charged particles in the pseudorapidity region |η|<2.5 and over the full azimuthal range. The precision silicon tracking detectors con- sist of pixel detectors (Pixel) and a semiconductor microstrip tracker (SCT). In the “barrel” region, these are arranged on cylindrical layers surrounding the beampipe,whileinthe“endcap”regionstheyaremountedondisksperpendic- ular to the beam axis. A charged particle typically traverses three layers of the 1ATLASusesaright-handedcoordinatesystemwithitsoriginatthenominalinteraction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis pointsfromtheIPtothecentreoftheLHCring,andthey axispointsupward. Cylindrical coordinates (r,φ) are used in the transverse plane, φ being the azimuthal angle around the beampipe. Thepseudorapidityisdefinedintermsofthepolarangleθ asη=−lntan(θ/2). TransversemomentumandenergyaredefinedaspT=psinθ andET=Esinθ,respectively. 2 Pixel detector and four double-sided layers of the SCT. The silicon detectors aresurroundedbyatransitionradiationtracker(TRT),composedofdrifttubes and covering up to |η|=2. TheFCalcoversapseudorapidityrange3.2<|η|<4.9. Itusestungstenand copperabsorberswithliquidargonastheactivemedium,withatotalthickness of about 10 interaction lengths. This analysis uses the energy deposition in the entire FCal for the centrality determination, while for the reaction plane measurement only the energy deposition in the first sampling layer of the FCal (Layer 1) is used, as doing this was found to minimize the effect of fluctuations on the reaction plane measurement. Thetriggersystemhasthreestages,thefirstofwhich(Level-1)ishardware- based,whilethelaterstages(Level-2andEventFilter[9])arebasedonsoftware algorithms. Theminimum-biasLevel-1triggerusedforthisanalysisrequiressig- nalsineitherthetwosetsofminimum-biastriggerscintillator(MBTS)counters, covering 2.1<|η|<3.9 on each side of the experiment, or the two zero-degree calorimeters (ZDC), each positioned at |z| = 140 m relative to the centre of the detector, detecting neutrons and photons with |η|>8.3. The ZDC Level-1 triggerthresholdsweresetjustbelowthesingleneutronpeakoneachside. The MBTS trigger was configured to require at least one hit above threshold from each side of the detector. A Level-2 timing requirement on signals from the MBTS was then imposed to remove beam backgrounds, while the ZDC had no further requirements beyond the Level-1 decision. The Event Filter was not needed for the minimum-bias triggering and was run in pass-through mode. 3. Event selection and reconstruction The lead-lead data set analysed here corresponds to an integrated luminos- ity of approximately L = 7 µb−1. Three main event selection requirements int were applied offline to reject both non-collision backgrounds and Coulomb pro- cesses, in particular highly-inelastic photonuclear events. First, an offline event selection required a time difference |∆t| < 3 ns between the positive and neg- ative η MBTS counters as well as a reconstructed vertex in order to suppress non-collision backgrounds. Second, a coincidence of the ZDCs at forward and backward pseudorapidities was required in order to reject a variety of back- ground processes, while maintaining high efficiency for non-Coulomb processes. Finally,inthisanalysisonlyeventswithavertexwith|z |<10cmwereused. vtx Simulations show the vertex algorithm to be essentially 100% efficient for the event sample considered here. Pile-up events, defined as additional minimum bias events in the same bunch crossing, are expected to be present at the 10−4 level and so are negligible. In total, approximately 4×107 events passed the selection criteria. Tracks were reconstructed within the full acceptance of the inner detector. ToimprovethereliabilityoftheIDtrackreconstructioninthetrackingenviron- ment in heavy ion collisions, the track quality requirements are more stringent thanthosedefinedforproton-protoncollisions[10]. Tracksarerequiredtohave atleasteighthitsintheSCT,atleasttwoPixelhitsandahitinthePixellayer 3 closest to the interaction point. A track must have no missing Pixel hits and at most one missing SCT hit, where such hits are expected. Finally, the trans- verse and longitudinal impact parameters with respect to the vertex (|d | and 0 |z sinθ|) were each required to be less than 1 mm. These additional require- 0 ments were made to improve the purity of the track sample. The inefficiency of this selection is driven by the loss due to hadronic interactions in the detector material, which increases with |η| [10]. This results in an additional inefficiency of approximately 15%at |η|>1 comparedto the central regionof the detector. However, the results shown here are found to be insensitive to the absolute tracking efficiency (discussed below), and the effect of the efficiency decrease at high |η| is minimized when measurements are performed in limited transverse momentum and pseudorapidity intervals. The tracking performance has been studied in detail by comparing data to Monte Carlo simulations based on the HIJING event generator [11] and a full GEANT4 [12] simulation of the detector [13]. In general the simulated distributions of the number of Pixel and SCT hits on tracks describe the data well, particularly after reweighting the simulated momentum distribution to account for the differences in the charged particle spectrum reconstructed in data and HIJING. Monte Carlo calculations show that the tracking efficiency forchargedhadronsinthisanalysisisabout72%nearη =0incentralcollisions, lower than in proton-proton collisions due to the more stringent requirements andthehigheroccupancyintheSCT.Faketracksfromrandomcombinationsof hits are generally negligible, e.g. reaching only 0.1% in |η|<0.3 for the highest multiplicity collisions, although the rate of fake tracks increases slightly with increasing |η|. 4. Data analysis In order to systematically select various geometries of the initial state, the datawereanalysedincentralityintervalsdefinedbyselectionsonFCalΣE ,the T total transverse energy deposited in the FCal (always stated at the electromag- netic energy scale, which does not correct for the response of the calorimeter to hadrons). Theseintervalsareexpressedinpercentiles ofthetotal inelasticnon- Coulomb lead-lead cross section (0–10%, 10–20%,..., 70–80%) with the most central interval (0-10%) corresponding to the 10% of events with the largest FCalΣE . ThemeasuredFCalΣE distributionforasubsetofthedata(with T T L approximately200mb−1),takenwithalessrestrictiveprimarytriggerthan int used for the bulk of the data and used for the calibration procedure described below, is shown divided into centrality intervals in Fig. 1. To establish the fraction f of the total non-Coulomb inelastic cross section selected by our trigger and event selection criteria, we have performed a convo- √ lution of FCalΣE distributions measured in proton-proton data at s=2.76 T TeV with a full Monte Carlo Glauber calculation [14]. The calculation assumes the number of effective proton-proton collisions per lead-lead event, N, scales according to the “two-component model” (from e.g. Ref [15]). This model 4 1] -eV Data ATLAS [TT 1 Model Pb+Pb sNN=2.76 TeV E L = 200 mb-1 int Sd /vt 10-1 Ne )d %% % % % % % (1/Nevt 10-2 70-80%60-7050-60 40-50 30-40 20-30 10-20 0-10 10-3 10-4 0 1 2 3 4 FCal S E [TeV] T Figure 1: Measured F√Cal ΣET distribution divided into 10% centrality intervals (black). Proton-proton data at s = 2.76 TeV, convolved with a Glauber Monte Carlo calculation withx=0.088(grey),asdescribedinthetext. combines the number of participants (N , the number of nucleons which in- part teract inelastically at least once) and the number of binary collisions (N ) as coll N =(1−x)Npart +xN . Inthisapproach,theonlyfreeparameterisx,which 2 coll controlstherelativecontributionofN andN . Thebestdescriptionofthe part coll dataisfoundtobeforx=0.088. Thevalueoff anditsuncertaintyisestimated by systematically varying the effect of trigger and event selection inefficiencies aswellasbackgroundsinthemostperipheralFCalΣE intervaltoachievethe T best agreement between the measured and simulated distributions. Using this analysis of the FCal ΣE distribution, the fraction of the total cross section T sampled by the trigger and event selection has been estimated to be 98%, with an uncertainty of 2%. This is similar to estimates given in a previous ATLAS publication [16]. The FCalΣE ranges defined from this subsample have been T found to be stable for the full data set, both by counting the number of events and by measuring the average number of reconstructed tracks in each interval. The20%ofeventswiththesmallestFCalΣE arenotincludedinthisanalysis, T duetotherelativelylargeuncertaintiesindeterminingtheappropriateselection criteria. The final state momentum anisotropy can be quantified by studying the Fourier decomposition of the azimuthal angle distribution [17]: d3N 1 d3N 1 E d2N (cid:32) (cid:88)∞ (cid:33) E = = 1+2 v cos[n(φ−Ψ )] , (1) dp3 p dφdp dy 2πp p dp dη n n T T T T n=1 where y, p and φ are the rapidity, transverse momentum, and azimuthal angle T 5 of final-state charged particle tracks and Ψ denotes the azimuthal angle of the n n-th order reaction plane. In more peripheral events, Ψ is close to Φ , the 2 RP reaction plane angle, defined by the impact parameter ((cid:126)b, the vector separation of the barycentres of the two nuclei) and the beam axis (z). In more central events, Ψ primarily reflects fluctuations in the initial-state configurations of 2 colliding nucleons. This analysis was confined to the second Fourier coefficient (n = 2), v ≡ (cid:104)cos[2(φ−Φ )](cid:105), where angular brackets denote an average 2 RP first over particles within each event relative to the eventwise reaction plane, and then over events. In this analysis, the n = 2 event plane is determined from the data on an event-by-event basis, according to the scheme outlined in Ref. [17]: Ψ = 1tan−1(cid:32)(cid:80)ETto,wierwisin(2φi)(cid:33), (2) 2 2 (cid:80)Etowerw cos(2φ ) T,i i i where sums run over tower transverse energies Etower as measured in the first T samplinglayeroftheforwardcalorimeters,witheachtowercovering∆η×∆φ= 0.1 × 0.1. The tower weights, w = w (φ ,η ), are used to correct for local i i i i variations in detector response. They are calculated in narrow ∆η slices (∆η = 0.1) over the full FCal η range in such a way as to remove structures in the uncorrected φ distributions of Etower in every ∆η slice. The final results of T this analysis are found to be insensitive to the weighting, and results obtained with all w = 1 were consistent with those reported here, and well within the i systematic uncertainties estimated below. Thecorrelationofindividualtrackazimuthalangleswiththeestimatedevent plane is shown in Fig. 2 for tracks with p =1−2 GeV. There is a clear sinu- T soidal modulation at all centralities. The modulation is largest in the 20–50% centralityintervals,anddecreasesforthemorecentralandperipheralevents. In the centrality intervals where the correlation is strongest, the correlation does notfollowaperfect1+αcos(2φ)form,indicatingsignificantcontributionsfrom higher order harmonics. However, in this letter we rely on the orthogonality of the Fourier expansion and do not extract the other coefficients. To verify that this does not bias the measurement, we have extracted v from a fit containing 2 all Fourier components v up to n=6, and found v values consistent with the n 2 results extracted below. The odd amplitudes are found to be consistent with zero, as expected when measuring odd harmonic functions relative to Ψ [17]. 2 Themeasuredvaluesofv aregenerallyunderestimatedbecauseofthefinite 2 experimental resolution in extracting the event plane angle. The event plane resolutioncorrectionfactor, R, wasobtainedusingthesubeventtechnique, also described in Ref. [17]. Two “subevents” are defined in each event, one each in the forward and backward η directions. For the measurement of the event planeusingtheFCal,thefirstsamplinglayeronthepositiveη sidewasselected as subevent “P”, with a corresponding subevent “N” formed for negative η. The resolution correction for the event plane measured by each subevent was 6 calculated as a function of FCalΣE according to the formula T (cid:113) (cid:10) (cid:11) R(ΣE )= cos[2(ΨN −ΨP)] , (3) T 2 2 whereangularbracketsdenoteanaverageoveralleventsinaFCalΣE interval. T The left panel of Fig. 3 shows the distribution of the difference ΨP −ΨN. The 2 2 right panel shows the FCal ΣE dependence of the resolution correction for T the event plane determined using the full FCal Layer 1 as well as a reduced- acceptance version used in the systematic studies discussed below. The final, resolution-corrected, v is calculated in intervals of centrality, η 2 and p as T events tracks v (η,p )= 1 (cid:88) 1 (cid:88) c cos[2(φ −ΨN/P)], (4) 2 T Ntrk R(ΣE ) i i 2,j tot j T i where Ntrk denotes the total number of the reconstructed tracks in a given tot centrality, η and p range, and the c are weights similar to the w for tracks, T i i designed to flatten the φ distribution in a small ∆η slice. For ΨN/P (the event 2,j planeforeventj)wetaketheeventplanemeasuredintheoppositeηhemisphere (i.e. “P”atpositiveη,or“N”atnegativeη)toeachtrackwithazimuthalangle φ . Using the track in the opposite hemisphere maximizes the pseudorapidity i gap between the reaction plane estimate and the v estimate (|∆η| > 3.2), 2 minimizing potential non-flow correlations between them. The systematic uncertainty on v as a function of p , η and centrality was 2 T evaluated by varying several different aspects of the analysis procedure. • TheresolutioncorrectionwaschangedbylimitingtheFCalacceptanceto a smaller range in pseudorapidity. • Tighter tracking requirements were applied (both |d | and |z sinθ| less 0 0 than 0.5 mm, instead of the nominal 1 mm requirement). • Results were compared using negatively and positively charged tracks. • Resultswerecomparedbetweenv measuredatpositiveandnegativepseu- 2 dorapidities. • Results were studied as a function of time during the heavy ion run. Additional sources of systematic uncertainties were examined, including the following: Deviations from zero of (cid:104)sin(2[φ−Ψ ])(cid:105), which are sensitive to resid- 2 ual biases in the reaction plane determination and detector non-uniformities, were measured. Monte Carlo studies were performed based on HIJING, with a special procedure applied to the generated particle azimuthal angles so as to simulate elliptic flow (from Ref. [17]), with a magnitude extrapolated from RHIC data. Deviations from the flow induced at the generator level were ob- tained by applying the same analysis procedure to the simulated data as with 7 Centrality 0-10% 40-50% pT [GeV] 0.8-0.9 2.4-2.7 8-10 0.8-0.9 2.4-2.7 8-10 Smaller η acceptance of event 0.6 1.2 5.7 0.7 0.7 2.0 planedetermination Residualdeviationfromzeroof 0.7 0.6 0.4 0.5 0.7 1.2 sineterms Varyingtrackingcuts 0.4 0.1 1.7 0.1 <0.1 0.2 Negativevspositivetracks 0.5 0.3 3.3 0.3 0.1 1.6 Asymmetry with respect to η 0.1 0.1 0.2 <0.1 <0.1 0.1 reflection Timedependence 0.2 0.2 MonteCarloreconstruction 1.2 1.2 1.2 0.3 0.3 0.3 Totalsystematicerror 1.6 1.9 6.9 1.0 1.0 2.9 Table1: Principalsystematicuncertainties(statedasapercentageofthevalueofv2)onthe v2 measurementforthreepT intervalsandtwocentralityintervals,allfor|η|<1. real data. The event plane determined from the reconstructed tracks was also investigated as an independent cross-check on the FCal reaction plane. In this case, forthetrackswithpositive(negative)η theeventplanedeterminedinthe negative (positive) η subevent was used. The uncertainty in the fraction of the total inelastic cross section sampled by our trigger and event selection criteria gives an overall scale uncertainty on v , ranging from 1% in central events up 2 to 5% in peripheral events. Deviations in individual contributions from the baseline results have been quantified as relative systematic uncertainties on v (in percent), which are 2 listed in Table 1 for several centrality and p intervals, all for |η| < 1. The T differentcomponentshavebeenaddedinquadratureandexpressedas1σ point- to-pointsystematicuncertainties. Notethatthesomewhatlargeincreaseinthe scale of the uncertainties from moderate to high p can be partly attributed to T the limited track statistics at high p . It should also be pointed out that the T systematic uncertainties only include those associated with the measurements themselves; no attempt is made to disentangle the potential contributions from non-flow effects, since their nature is not yet fully understood. 5. Results The top panel of Fig. 4 shows the v dependence on p for eight 10% cen- 2 T trality intervals and for tracks with |η| < 1. It is observed that all centrality intervals show a rapid rise in v (p ) up to p = 3 GeV, a decrease out to 7–8 2 T T GeV, and then a weak p -dependence beyond 9–10 GeV. The same trends are T also seen for 1<|η|<2 (Fig. 4 middle) and 2<|η|<2.5 (Fig. 4 bottom). The pseudorapidity dependence of v is shown in Fig. 5. The top row shows 2 the centrality and η dependence of v (η,p ) for five p intervals, which char- 2 T T acterize the trend shown in Fig. 4, and the four most-central intervals. The bottom row shows the same information for the four most-peripheral intervals. 8 It is observed that v depends very weakly on η over the measured pseudora- 2 pidity region. In the two lowest p intervals, below 1.2 GeV, v drops by about T 2 5–10% over the range |η| = 0−2.4. At higher transverse momenta, a decrease on the order of few percent can be seen, although, due to the large point-to- point errors, a flat η dependence cannot be excluded. This is in contrast to the √ strong variation in v (η) observed by the PHOBOS experiment at s =200 2 NN GeV [18], which drops by approximately 30% between η =0 and η =2.5. Fig. 6 shows v (p ) for |η| < 1 in the 40–50% centrality interval compared 2 T todatafromtheLHC(ALICE,fromRef.[7])aswellasfromRHIC(STAR[19] andPHENIX[20])withacentre-of-massenergyafactorofnearly14lower. The ALICE and STAR data are shown for the second cumulant v {2}, which gives 2 results closest to the event-plane method used in this analysis. The PHENIX dataareobtainedwithasimilarmethodasATLAS,butwithv measuredonly 2 for identified π0 hadrons, detected through their two-photon decay mode. It is observed that all of the data sets are quite similar as a function of p , both at T lowerp (ALICEandSTAR)andevenathigherp ,withinthelimitedstatisti- T T cal precision of the PHENIX data. The observation of similar v at low p has 2 T beennotedrecently[7],andhasbeenreproducedusinghydrodynamicalsimula- tions assuming the same shear viscosity to entropy density ratio but initialized at a higher energy density. However, the similarities at high p will require T additional theoretical study to see if they are consistent with the differential energy loss of jets in the hot, dense medium. 6. Conclusions √ Elliptic flow measurements in lead-lead collisions at s = 2.76 TeV ob- NN tained with the ATLAS detector are presented for an integrated luminosity of approximately7µb−1. Theseresultsrepresentthefirstmeasurementofv over 2 a broad range in η and p at the LHC energy. As a function of transverse mo- T mentum, at all |η|, v rises rapidly up to p =3 GeV, decreases somewhat less 2 T rapidly out to p = 7–8 GeV, and then varies weakly out to 20 GeV. Over the T measuredpseudorapidityregion, |η|<2.5, v isfoundtobeonlyweaklydepen- 2 dentonη,withlessvariationthanobservedatlowerbeamenergies. Comparison of the 40–50% interval with lower energy data shows little change both at low and high p . These results provide strong constraints on models which aim T to describe the dynamical evolution of the system created in ultra-relativistic heavy ion collisions. 7. Acknowledgements We thank CERN for the efficient commissioning and operation of the LHC duringthisinitialheavyiondatatakingperiodaswellasthesupportstafffrom our institutions without whom ATLAS could not be operated efficiently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq 9 and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF, DNSRC and Lund- beck Foundation, Denmark; ARTEMIS, European Union; IN2P3-CNRS, CEA- DSM/IRFU, France; GNAS, Georgia; BMBF, DFG, HGF, MPG and AvH Foundation,Germany;GSRT,Greece;ISF,MINERVA,GIF,DIPandBenoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; FOM and NWO, Netherlands; RCN, Norway; MNiSW, Poland; GRICES and FCT, Portugal; MERYS (MECTS), Romania; MES of Russia and ROSATOM, Rus- sian Federation; JINR; MSTD, Serbia; MSSR, Slovakia; ARRS and MVZT, Slovenia;DST/NRF,SouthAfrica;MICINN,Spain;SRCandWallenbergFoun- dation, Sweden; SER, SNSF and Cantons of Bern and Geneva, Switzerland; NSC, Taiwan; TAEK, Turkey; STFC, the Royal Society and Leverhulme Trust, United Kingdom; DOE and NSF, United States of America. 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