The azimuthal anisotropy of charged particles in heavy ion collisions is an important probe of quark-gluon plasma evolution at early stages. The nuclear reaction plane can be determined independently by different detector subsystems and using different analysis methods. This paper reports the capability of the CMS detector at the LHC to reconstruct the reaction plane of the collision and to me asure elliptic flow with calorimetry and a tracking system. The analysis is based on a full CMS detector simulation of \rm{Pb+Pb} events with the HYDJET event generator

Eyyubova, G Kh

Korotkikh, V L

Krofcheck, D

Lokhtin, I P

Petrushanko, S V

Sarycheva, L I

Snigirev, A M

CERN Document Server

Available on CMS information server CMS CR-2008/022The Compact Muon Solenoid ExperimentMailing address: CMS CERN, CH-1211 GENEVA 23, SwitzerlandConference Report27 May 2008Elliptic flow studies using the CMS detectorG. Kh. Eyyubova, V. L. Korotkikh, I. P. Lokhtin, S. V. Petrushanko, L. I. Sarycheva, A. M. Snigirev,Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119992 Moscow, RussiaD. KrofcheckThe University of Auckland, Private Bag 92019, Auckland 1142, New ZealandAbstractThe azimuthal anisotropy of charged particles in heavy ion collisions is an important probe of quark-gluon plasma evolution at early stages. The nuclear reaction plane can be determined independently bydifferent detector subsystems and using different analysis methods. This paper reports the capabilityof the CMS detector at the LHC to reconstruct the reaction plane of the collision and to me asureelliptic flow with calorimetry and a tracking system. The analysis is based on a full CMS detectorsimulation of Pb+Pb events with the HYDJET event generator.Presented at Quark Matter 2008,4-10 February 2008,Jaipur,India1 IntroductionIn non-central collisions between two nuclei the beam direction and the impact parameter vector define a reactionplane for each event. A measurement of the azimuthal anisotropy of particle production with respect to the reactionplane is one of the important tools for studying the properties of the dense matter created in ultra relativisticheavy-ion collisions. The magnitude, the   and hadron mass dependencies of the radial and elliptic flows below  GeV/  are well described by ideal hydrodynamic models whose space-time evolution starts with a realisticQGP equation of state (EoS) with initial energy densities 	 GeV/fm  at thermalization times   fm/  .This report is dedicated to studying the capability of the CMS detector at the LHC to reconstruct the reactionplane and to measure elliptic flow, using calorimetry (HCAL, Hadron CALorimeter; and ECAL, ElectromagneticCALorimeter) and the tracking system. The high tracking efficiency and low rate of fake tracks, together with alarge calorimetric coverage, provide a precise measurement of global event characteristics, event by event.2 MethodsThe elliptic flow parameter,  , is defined as the second harmonic coefficient in the Fourier expansion of the particleazimuthal distribution with respect to the reaction plane:ﬁﬀﬁﬂﬃﬀ! "$#&%')(+*-,).0/ﬂ21436587%'!9*-,).:;/ﬂ1436587%<= >@? (1)where3A5is the true reaction plane angle andﬀ stands for full multiplicity. Then ) is the average over particlesof *-,ﬁ.0/@;/ﬂ143A5B7C7.There exists a wealth of anisotropic flow measurement methods, each of which has its advantages and limitations.Here we apply two wide-spread methods to calculate the ﬁ coefficient. The first one uses the event plane angledetermination, and the second one does not involve the event plane angle determination. The basic idea of thelatter method is that the   coefficient can be expressed in terms of particle azimuthal correlations. Usually the trueelliptic flow coefficient in the event plane (EP) method is evaluated by dividing the observed   value by a factor,D [1], which accounts for the event plane resolution:'EGFIHKJﬃﬁLNMOEPFQHKJD ﬃR*-,ﬁ.;/ﬂ1S37CTR*,)./31S36587UT (2)Here event plane angle3 is the estimate of the true reaction plane angle35. The mean was taken over allcharged particles in a given event and then over all events. In order to avoid the trivial autocorrelation of particles,the event plane angle3 and, hence, D are calculated from the angular distribution of a sample of events, and  from another event sample with the same multiplicity. The samples may be selected, for instance, in two distinctregions of pseudorapidity, such as VXWY and VXZY .The second method is based on two particle correlations [2, 3]. It is free from the need to determine the event planeangle. The procedure involves constructing the two-particle correlator, or cumulant,!EJﬃR*-,ﬁ.:/ﬂ\[+1]ﬂ_^G7CTa`R*-,ﬁ.:;/b/ﬂ\[+1S36587UTR/ﬂ9^c1S365\7b7UT (3)The event plane angle,36d, can be determined from the measured e -th harmonics via the standard method [1, 4]:fhg!ie3dﬃj[lk[.Cmi/neﬂ[7j[ok[*-,ﬁ./neﬂ[7? e2p#?qKr3dWs! utGe8? (4)whereﬂ\[is the azimuthal angle of the v -th particle andk[is a weight. The sum runs over all particles in each givenevent.3 Analysis and discussionFor the estimation of the azimuthal anisotropy of particles in heavy ion collisions, the HYDJET event generatorwas used. The final state in nuclear collisions from HYDJET is obtained as a combination of soft hydro-typeparticle production and hard (mini)jet fragmentation [5].The accuracy of the event plane determination is mainly sensitive to two model factors: the strength of the ellipticflow signal and the particle multiplicity of the event,ﬀ . To illustrate the dependence of the accuracy of the event2plane determination on the event centrality, sets of 1000 HYDJET Pb+Pb events were created at the generator levelfor each of twelve centrality bins, covering the range of impact parameters from   ﬃ  to   ﬃ  D ( D is thenuclear radius, D M  6.7 fm). The mean total multiplicity of the soft part of central Pb+Pb events was 26000,corresponding to a mean total multiplicityﬀ (   = 0 fm)  58000 and a mean charged particle density at V ﬃ  ofﬁﬀ	tV+/  = 0 fm) = 3000. Stable charged particles within the pseudorapidity window  V;Ws   were consideredfor the event plane analysis, using e ﬃ  andk[ﬃ#. An additional cut of  Z   GeV/  on charged particletransverse momentum was applied, to take into account that these particles do not generally reach the calorimeter,since they curl up in the 4 T magnetic field and are absorbed in the material in front of the calorimeter.Figure 1-left shows the calculated resolution 8/3A7, defined here as the width of a Gaussian fit of the distributionof the difference between the generated,3I5, and the calculated,3 , azimuthal angles of the event plane (Eq. 4),as a function of the impact parameter of the Pb+Pb collisions.The elliptic flow coefficient of charged particles is presented in Fig. 1-right, as a function of the impactparameter,   . The coefficient is defined in the standard way: the cosine of twice the azimuthal angle of aparticle relative to the reaction plane angle (which is known in each simulated event), and averaged over all chargedparticles in each event. As expected, the elliptic flow coefficient grows with increasing impact parameter (i.e. withb, fm2 4 6 8 10 12), radΨ∆(σ00.10.20.30.40.50.60.7> 0.9 GeV/cTp> 0Tpb, fm0 2 4 6 8 10 12gen2v00.020.040.060.080.10.12 > 0.9 GeV/cTp> 0TpFigure 1: Left: Reaction plane resolution 8/	3A7as a function of impact parameter in Pb+Pb collisions at the“generator level”. Right:  values as a function of impact parameter in Pb+Pb collisions by HYDJET generator.increasing azimuthal anisotropy of the initial nuclear overlap region). Since in HYDJET   /   7 increases withtransverse momentum up to  #ﬁﬀ GeV/  (the kinematic region where hydro-type behaviour of particle spectradominates over the contribution from jet production), introducing the cut  _ Z ;  GeV/  (solid histograms)results in a much stronger elliptic flow, compared with the case without such a cut (dashed histograms). Thefollowing results were obtained for one fixed impact parameter,   ﬃ  fm, in Pb+Pb collisions.Study of event plane resolution with CMS Calorimeters (ECAL, HCAL). Table 1 shows the resolutions ob-tained with the calorimetric system of CMS [6]. Stable particles (charged pions and kaons, protons, neutrons,photons and electrons), within the pseudorapidity window  VﬂW  (CMS barrel+endcap calorimetry acceptance),were considered for the event plane analysis, using ﬃ[ﬃ [in Eq. 4. An additional cut    Z ;  GeV/  on thecharged particle transverse momentum was applied. Although the anisotropic flow is maximal at midrapidity, themuch larger total energy deposition in the endcaps results in reduced relative fluctuations and, accordingly, in amuch better event plane resolution. Moreover, energy flow measurements in the endcaps are less sensitive to themagnetic field than in the barrel. The ECAL is more suitable than the HCAL for event plane determination. Thisis primarily due to the better energy resolution of the ECAL for low and moderate  _ particles, along with a largerdistorting influence of the magnetic field on the HCAL energy flow.Study of   reconstruction with the CMS Tracker. A sample of 100 thousand Pb+Pb events at impact parameter ﬃ fm within the pseudorapidity window  VW ;  (the CMS Tracker acceptance) was utilized. The standardsettings were used to reconstruct tracks (i.e. more than 12 hits per track and a track fit probability above 1 % [7]).A cut on    Z   GeV/  was set in both simulated and reconstructed events. At this centrality, the number ofreconstructed tracks per event is about 170.The differential    and V dependencies of the elliptic flow in Pb+Pb collisions for impact parameter   ﬃ  fm areshown in Fig. 2. Here we have calculated the dependencies using the event plane angle determination from Eq. (4).3Table 1: Event plane resolution, 8/	3A7in rad, for Pb+Pb collisions at   ﬃ  fm.Calorimeter Barrel Endcaps Barrel+ EndcapsECAL 0.53 0.39 0.37HCAL 1.11 0.62 0.58ECAL+HCAL 0.58 0.41 0.39For the    dependence, two sub-event sets were used, with V Z and V W . For the V dependence, the factorDin each histogram bin was calculated using particles from other bins (excluding neighboring bins).1 1.5 2 2.5 3 3.5 4 4.500.020.040.060.080.10.120.14, GeV/cTp) T(p{EP}2v-2 -1 0 1 200.020.040.060.080.10.120.14η)η({EP}2vFigure 2: The (left) andV(right) dependencies of!EPFIHKJ , in Pb+Pb collisions for impact parameter ﬃfm, calculated with the simulated events (open circles) and reconstructed events (closed squares). Statistical errorsare shown for 100k events. Non-flow systematic uncertainties not included.4 SummaryWe have shown that, at central rapidities (  V:W ;  ), CMS will be able to determine the reaction plane for a verywide range of particle multiplicities and elliptic flow magnitudes, using the calorimeters and the tracker. The CMSelectromagnetic calorimeter is found to be more suitable than the hadron calorimeter for event plane determination.Using the endcaps for the event plane reconstruction and the barrel for reconstructing the jets should provide a morerobust analysis of elliptic flow.The transverse momentum and rapidity dependencies of the elliptic flow coefficient   can be reconstructed in theCMS Tracker with high accuracy using the event plane or the cumulant methods. The CMS track reconstructionperformance induces a systematic error estimated to be about 3% on the determination.The authors thank David d’Enterria, Olga Kodolova, Christof Roland, Stephen Sanders, Constantin Loizides andBoleslaw Wyslouch for fruitful discussions. G. Eyyubova thanks the organizers of “Quark Matter 2008” for thewarm welcome and hospitality. This work was supported by grants RFBR 08-02-91001, RFBR 08-02-08031-z andby Grants of President of Russian Federation for support of Leading Scientific Schools (No 1456.2008.2).References[1] A. M. Poskanzer and S. A. Voloshin, Phys. Rev. C 58, (1998) 1671.[2] S. Wang et al., Phys. Rev. C 44, (1991) 1091.[3] N. Borghini, P.M. Dinh and J.-Y. Ollitrault, Phys. Rev. C 64, (2001) 054901.[4] S. A. Voloshin and Y. Zhang, Z. Phys. C 70, (1996) 665.[5] I.P. Lokhtin and A.M. Snigirev, Eur. Phys. J. C 46, (2006) 211.[6] D. d’Enterria et al., J. Phys. G 34, (2007) 2307-2455.[7] C. Roland, CMS Note 2006/031 (2006).4

Elliptic flow studies using the CMS detector

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