Charged particle directed flow in Pb-Pb collisions at sqrt{s_NN} = 2.76 TeV measured with ALICE at the LHC
aa r X i v : . [ nu c l - e x ] J un Charged particle directed flow in Pb-Pb collisions at √ s NN = Ilya Selyuzhenkov ∗ for the ALICE Collaboration ∗ Research Division and ExtreMe Matter Institute EMMI,GSI Helmholtzzentrum f¨ur Schwerionenforschung, Darmstadt, GermanyE-mail: [email protected]
Abstract.
Charged particle directed flow at midrapidity, | η | < .
8, and forwardrapidity, 1 . < | η | < .
1, is measured in Pb-Pb collisions at √ s NN = 2.76 TeV withALICE at the LHC. Directed flow is reported as a function of collision centrality,charged particle transverse momentum, and pseudo-rapidity. Results are compared tomeasurements at RHIC and recent model calculations for LHC energies. Introduction.
Azimuthal anisotropic flow is a key observable indicating collectivityamong particles produced in non-central heavy ion collisions. Directed flow ischaracterized by the first harmonic coefficient, v , in the Fourier decomposition of theparticle azimuthal distribution with respect to the collision reaction plane. It developsat a very early stage of the collision and thus is sensitive to the properties and theequation of state of the hot and dense matter produced in nucleus-nucleus collisions.Among features of charged particle v measured at RHIC energies [1, 2] are negativeslope at midrapidity and absence of the so-called wiggle structure predicted by RQMDmodel calculations [3]. Recent calculations within quark-gluon string model with partonrearrangement [4], and fluid dynamical prediction [5] suggest much stronger signal atLHC energies with a positive slope of v vs. rapidity. We report on charged particle v measured in a wide range of rapidity in Pb-Pb collisions at √ s NN = 2.76 TeV. Resultsare compared to RHIC measurements and recent model calculations for LHC energies. Data analysis.
Minimum bias trigger and standard ALICE event selection criteria forPb-Pb collisions [6] were applied in the analysis. Only events within 0-80% centralityrange and reconstructed collision vertex within 10 cm from the centre of the TimeProjection Chamber (TPC) [7] were selected for the analysis (about 8 million eventstotal). A transverse momentum cut of p t > .
15 GeV/ c and pseudo-rapidity cut of | η | < . − . < η < − . . < η < . harged particle directed flow in Pb-Pb collisions measured with ALICE | η | ∼ .
8. Each ZDC, A-side( η >
0) and C-side ( η < × Q , defined by energy, E i , weightedmean of ZDC tower centers, r i = ( x i , y i )( a ) Q = ( X, Y ) = X i =1 r i E i / X i =1 E i ( b ) Q ′ = Q − h Q i . (1)To correct for the time dependent variation of the beam crossing position and event-by-event spread of the collision vertex with respect to the centre of TPC we perform therecentering procedure defined by Eq. 1(b). Recentering (subtracting the average centroidposition h Q i ) is performed as a function of time, collision centrality, and transverseposition of the collision vertex. Only after recentering we observe consistent correlationbetween shifts in the same direction for A and C sides ZDCs (Fig. 1(a)). Non-zero centrality, % Z DC c en t r o i d c o rr e l a t i on s , a . u . -3 × centroid correlations 〉 C X A X 〈 〉 C Y A Y 〈 cross-term syst. 〉 C Y A X 〈 〉 C X A Y 〈 Performance16/05/2011 stat. error only = 2.76 TeV NN sPb-Pb at η pseudorapidity, -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 d i r e c t ed f l o w , v -1-0.500.51 -3 × Centrality 0-80%
Scalar Product (SP) η × Fit (SP) = C Full Event PlaneSub Event PlanePerformance16/05/2011 stat. error only = 2.76 TeV NN sPb-Pb at (a) (b) Figure 1. (color online) (a) ZDC centroid correlation after recentering; (b) v vs.pseudorapidity: comparison of the scalar product and event plane methods. correlation for h X A X C i and h Y A Y C i reflects directed flow of spectators. No correlationbetween centroid shifts in orthogonal directions, h X A Y C i and h Y A X C i , indicates thatrecentering removes correlations originating from the beam parameter variation.The scalar product and the event plane methods are used for the v measurement.In the scalar product method, the directed flow is quantified by correlating ZDC centroidshifts with the first harmonic azimuthal asymmetry of charged particles v { SP } = √ h cos φ X C i / q h X A X C i = √ h sin φ Y C i / q h Y A Y C i . (2)Here φ is either charged particle azimuthal angle of TPC tracks or multiplicity weightedazimuthal position of tiles in VZERO scintillator arrays. No correction is appliedto account for non-primary tracks pointing to VZERO. In the event plane methodcentroid shifts define the full, Ψ Full = atan2 { Y A + Y C , X A + X C } , and subevent,Ψ A , C = atan2 { Y A , C , X A , C } , event plane angles, which are later used to calculated v according to equation v { EP } = h cos( φ − Ψ Full ) i / q h cos(Ψ A − Ψ C ) i . (3) harged particle directed flow in Pb-Pb collisions measured with ALICE v in Eqs. (2, 3) is fixed by the same convention as used atRHIC, i.e. spectators with η > v . Figure 1(b) shows consistencybetween results from two different methods. v { SP } is used to measure v at midrapiditywith TPC tracks, while v { EP } is used to extract v at forward rapidity with VZEROdetectors. Results.
Directed flow over extended rapidity range is shown in Fig. 2(a). We observethat charged particle v ( η ) has a negative slope similar to that at RHIC energies. v shifted to beam rapidity (Fig. 2(b)) exhibits longitudinal scaling previously observed atRHIC [1, 2]. Figure 2(c) shows that v at LHC has a weak centrality dependence and η pseudorapidity, -4 -2 0 2 4 d i r e c t ed f l o w , v -505 -3 × Centrality 0-80%
TPCVZEROReflected η + C η ) = A η Fit (Preliminary = 2.76 TeV NN sPb-Pb at stat. error only beam - y η -8 -6 -4 -2 0 d i r e c t ed f l o w , v -0.06-0.04-0.020 Centrality 30-60% = 2.76 TeV NN sALICE Pb-Pb at = 200 GeV NN sSTAR Au-Au at = 62 GeV NN sSTAR Au-Au at = 200 GeV NN sSTAR Cu-Cu at = 62 GeV NN sSTAR Cu-Cu at Preliminary stat. error only (a) (b) centrality, % d i r e c t ed f l o w , v -8-6-4-20 -3 × = 2.76 TeV NN s| < 0.8, Pb-Pb at η ALICE | = 200 GeV NN s| < 1.3, Au-Au at η STAR | = 62 GeV NN s| < 1.3, Au-Au at η STAR | Preliminary stat. error only (GeV/c) t transverse momentum, p d i r e c t ed f l o w , v -202 -3 × NN sALICE Pb-Pb at = 0.2 TeV NN s STAR Au-Au at Preliminary stat. error only (c) (d) Figure 2. (color online) (a) v over extended rapidity range; (b) longitudinal scalingof v ; comparison with RHIC: (c) v ( p t ), (d) v vs. centrality. is significantly smaller than at RHIC. As a function of p t , v at RHIC and LHC showsa similar trend (Fig. 2(d)), i.e. sign change around p t ∼ . c in central collisions,with no zero crossing for peripheral collisions. Flow fluctuations.
Recent theoretical calculations [8, 9] predict an η -even v whichoriginates from fluctuations in the initial geometry of the collision. Experimentally wecan separate η -even and η -odd v by symmetrizing or anti-symmetrizing measured v exp1 as a function of rapidity, v exp1 = v odd1 + v even1 , v odd1 = [ v exp1 ( η ) − v exp1 ( − η )] / , v even1 = [ v exp1 ( η ) + v exp1 ( − η )] / . (4) harged particle directed flow in Pb-Pb collisions measured with ALICE v odd1 , reflects correlations with respect to the reaction plane, whilesymmetric part, v even1 , can be non-zero due to flow fluctuations. Figure 3(a) showsresults for v ( η ) with A and C side ZDC separately which reveal the symmetric part in v . As a function of p t even and odd v have a similar shape and magnitude (Fig. 3(b)). η pseudorapidity, -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 d i r e c t ed f l o w , v -1-0.500.51 -3 × centrality 0-80% > 0 η ZDC A: < 0 η ZDC C: ZDC A + C η × ) = C η Fit ( PreliminaryPreliminary stat. and sys. errors = 2.76 TeV NN sPb-Pb at (GeV/c) t transverse momentum, p d i r e c t ed f l o w , v -3 × centrality 0-80%| < 0.8 η | {ZDC A} even1 v (-1) × {ZDC C} even1 v }A - C {ZDC even1 v }A + C {ZDC odd1 v + C p t ) = A p t Fit (p Preliminary stat. and syst. errors = 2.76 TeV NN sPb-Pb at (a) (b) Figure 3. (color online) Even and odd v components: (a) v ( η ), (b) v ( p t ). This p t dependence is also very similar to that of midrapidity v extracted from Fourierfits of two particle correlations [10], while the magnitude of even and odd v measuredwith spectators is smaller by a factor 40. Summary.
Directed flow, v , of charged particles is measured over a wide range ofrapidity, | η | < .
1, in Pb-Pb collisions at √ s NN =2.76 TeV. Magnitude of v is about 3-4times smaller than at top RHIC energy with a weak centrality dependence. v ( p t ) crosseszero at p t ∼ . c . v ( η ) has the same (negative) slope as at RHIC in contrastto some of the theoretical expectations. As a function of beam rapidity, measured v isconsistent with a picture of longitudinal scaling observed at RHIC.Fluctuation of directed flow of spectators and particles produced at midrapidityare found to be correlated. Observed similarity in p t shape of rapidity even and odd v components as well as in v extracted from two particle correlations might indicate acommon origin for all three effects. References [1] B. I. Abelev et al. [STAR Collaboration], Phys. Rev. Lett. , 252301 (2008).[2] B. B. Back et al. [PHOBOS Collaboration], Phys. Rev. Lett. , 012301 (2006).[3] R. J. M. Snellings et al. Phys. Rev. Lett. , 2803-2805 (2000).[4] J. Bleibel, G. Burau, C. Fuchs, Phys. Lett. B659 , 520-524 (2008).[5] L. P. Csernai, V. K. Magas, H. St¨ocker, D. D. Strottman, arXiv:1101.3451 [nucl-th].[6] K. Aamodt et al. [ALICE Collaboration], Phys. Rev. Lett. , 252302 (2010).[7] F. Carminati et al. [ALICE Collaboration], J. Phys. G: Nucl. Part. Phys.30