Charged particle directed flow in Pb-Pb collisions at √ s NN = 2 . 76 TeV measured with ALICE at the LHC

Abstract. Directed flow, v1, is measured over a wide range of pseudo-rapidity, |η| < 5.1, in Pb-Pb collisions at 2.76 TeV with ALICE at the LHC. v1 is reported as a function of the pseudo-rapidity, the transverse momentum and collision centrality. Using the neutral spectator deflection at beam rapidity we investigate both the rapidity asymmetric v1 which is sensitive to the collision reaction plane, and the rapidity symmetric v1 which is sensitive to the energy fluctuations in the initial geometry. The results are compared with those at RHIC, and the model calculations.


Introduction
The collective sideward motion of spectators and produced particles arises in non-central heavy-ion collisions.This effect is called the directed flow v 1 .Directed flow is considered to have origin at the early stage of the collision, when nuclei passing each other.At RHIC and LHC energies it could be established before the system reaches local equilibrium, hence it carries information on early collision dynamics and is sensitive to the system thermalization time [1].Directed flow, v 1 , is defined as first Fourier coefficient in an angular distribution of particles produced in collisions with respect to the collision symmetry plane Ψ RP , v 1 = cos(ϕ − Ψ RP ) = p x /p T .For the symmetric nuclei collision, due to momentum conservation, v 1 (η) is an odd function of pseudorapidity and is zero at η = 0.
At RHIC energies directed flow at midrapidity has been measured to have a negative slope.It was found that v 1 doesn't depend on the size of colliding nuclei and it decreases with increase of the collision energy [2].If plotted as a function of rapidity shift from the beam rapidity, the directed flow at different energies exhibits universal behaviour [2,3].
At RHIC and LHC energies, a "wiggle" structure of v 1 (η) may appear.In the microscopic model calculations such as RQMD and UrQMD, this could come from baryon stopping [4].In hydro models, this can be a signature that the matter evolved via the phase of deconfined quarks and gluons [5].Still, data don't support a wiggle structure at midrapidity in the observed charged particle directed flow [2].
There is a number of model predictions for the directed flow at the LHC energies.The fluid dynamic calculations for Pb-Pb at √ s NN = 2.76 TeV predicted a very large positive v 1 (η) at midrapidity with a presence of wiggle structure [6].Introducing initial center of mass rapidity fluctuation was shown to smear the magnitude of the v 1 , still keeping the slope positive.The quark gluon string model (QGSM) with parton rearrangement predicts the positive v 1 (η) for charged hadrons with wiggle a e-mail: eyyubov@mail.cern.ch√ s NN = 5.5 TeV [7].A suggested explanation of the positive slope is a very low viscosity of the created medium at mid-rapidity.The different viscosity at mid and forward rapidities causes the wiggle structure in this model.In these proceedings, the directed flow of charged particles is reported as a function of centrality, pseudorapidity and transverse momentum in Pb-Pb collisions at √ s NN = 2.76 TeV.

Data set and experimental methods
About 8 millions Pb-Pb events collected by ALICE experiment [8] within 0-80% centrality range are used for the current analysis.Centrality estimation is done with the VZERO detector.A reconstructed primary vertex position along the beam direction is set to be within ± 10 cm of the nominal interaction point.Reconstruction of charged particle tracks was performed with the Time Projection chamber (TPC) in rapidity range |η| < 0.8.Good track quality was ensured by requiring the tracks to have at least 70 clusters out of 159 in the TPC, a χ 2 per TPC cluster < 4 (with two degrees of freedom per cluster) and to point back to the primary interaction vertex within 3 cm.A cut to the transverse momentum p T > 0.15 GeV/c is imposed on all charged particle tracks.As a cross check the analysis was also performed using TPC and the Inner Tracking System (ITS).The Inner Tracking System is composed of six cylindrical layers of silicon detectors.The additional requirements for these tracks are at least two matching hits in the ITS and the distance of closest approach to the primary interaction vertex below 0.3 cm.The results for (TPC+ITS)-tracks and TPC standalone tracks agree very well.Directed flow at forward rapidity was measured using azimuthal distribution of hits in VZERO detectors.VZERO scintillators measure the signal which is proportional to the number of charged particles hitting the detector.The two VZEROs, each of which consists of four rings, are placed at both sides of the interaction point, located at different pseudorapidities (C-side: η =[-3.7,-3.2, -2.7, -2.2, -1.7] and A-side: η =[5.1, 4.5, 3.9, 3.4, 2.8]).Each ring is segmented into eight 45 o sectors in azimuth, covering 2π in azimuthal direction.
The scalar product and the event plane methods [9] were used for v 1 measurement.Reaction plane was reconstructed using the two neutron Zero Degree Calorimeters (ZDC).They are placed along the beam line at 114 meters apart from the interaction point from A-side (η > 8.8) and C-side (η < −8.8) and provide an estimate of the spectators deflection.Each neutron ZDC has a 2 × 2 tower geometry.Scalar product method employs the centroid coordinates {X, Y} of the deflection and the event plane method employs the angle Ψ EP = tan −1 (Y/X) derived from the coordinates.The centroid position is defined with four towers event-by-event: where weight w i = E α i .E i is the measured energy in a given tower, {x i , y i } are centers of each tower and α = 0.395 is a parameter.For the C-side the weights are put to be negative which takes into account the opposite sign of spectators deflection with respect to A-side.Ideally, when the spot of spectators is perfectly centered wrt. the center of ZDCs, the centroid position {X, Y} averaged over many events should be zero.Experimentally, the average can be shifted from the center of ZDCs what biases the event plane distribution.The average offset can be corrected for by recentering procedure, i.e X = X− X , Y = Y − Y , where the mean values can in general depend on time, event multiplicity (centrality), and event vertex position.After recentering a consistent correlations in the same direction for A-and C-sides of ZDCs are observed.As an example, Figure 1  A set of independent estimates of v 1 with ZDC A-and C-sides in the scalar product method is given by: Here φ is the azimuthal angle of the charged particle or the azimuthal position of VZERO sector, angle brackets denote the average other all events.In case of VZERO detector multiplicity in a given sector is used as a weight when calculating an average.The average of these four components is used as the final result.The event plane method was used in two forms: the one which uses subevent plane angles Ψ A;C EP from two ZDCs separately, and the other which uses full reaction plane angle, Ψ Full EP : . ( Here we use an approximation that the full event plane resolution can be obtained from correlation between independent subevents [9].The scalar product and the event plane method yield consistent results.
3 Results for directed flow

Rapidity, transverse momentum and centrality dependence of v 1
Figure 2 shows charged particle directed flow versus pseudorapidity for 0-80% centrality class.A negative slope for v 1 (η), opposite to that of spectators, is observed in the region |η| < 5.A mid-rapidity v 1 is very well approximated with a linear function of η.A turnover point changing the v 1 (η) slope should occur at some rapidity where the produced particles are predominantly coming from nuclear fragments (fragmentation region).Note, that the beam rapidity at the LHC energy √ s NN =2.76 TeV is y beam = 7.98.The existing predictions [6], [7] for the LHC energy give a positive slope at midrapidity, opposite to that observed in the data.Fluid dynamical model [6] has a positive v 1 slope due to overestimation of the initial tilt of the system.Figure 3 shows the so-called longitudinal scaling of η pseudorapidity,  Figure 4 shows integrated sign(η) × v 1 (η) as a function of centrality at LHC √ s NN =2.76 TeV compared to RHIC Au-Au results at √ s NN =200 and 62.4 GeV.The magnitude of v 1 decreases with the collision energy.The p T dependence of v 1 is measured by combining results at positive pseudorapidity with that at negative η < 0 taken with an opposite sign.Figure 5 presents the v 1 (p T ) at mid-rapidity, |η| < 0.8 for two centrality classes (0-40% and 40-80%) compared to RHIC √ s NN =200 GeV results.A similar trend as for RHIC is observed, i.e v 1 (p T ) changes sign from negative to positive value around p T ≈ 1.5 GeV/c.The zero crossing point moves towards higher p T for more peripheral events.

Directed flow fluctuation
Fluctuations in the initial geometry of the collision may result in non-zero even v 1 component at midrapidity [1,1].Experimentally we separate η-even and η-odd v 1 by symmetrizing or anti-symmetrizing measured v 1 with spectators in two ZDCs: TeV.
Results for v 1 (η) obtained from each ZDC separately reveal a shift independent on pseudorapidity, see Figure 6 (left), which corresponds to the even component of v 1 .

Summary
The ALICE Collaboration has measured the directed flow of charged particles in heavy-ion collisions at the LHC with the reaction plane defined from the deflection of spectators.The observed charged particle v 1 has an opposite sign to that of spectators in the rapidity range |η| < 5.

Figure 1 .
Figure 1.(color online).Correlation between the centroid position reconstructed with the ZDC on A-and C-side for the aligned and orthogonal directions as a function of centrality.

Figure 2 .
Figure 2. (color online).Charged particle directed flow v 1 (η) for 0-80% centrality interval in Pb-Pb collisions at √ s NN =2.76 TeV.The bars represent the statistical errors and the shaded bands are systematic errors.

Figure 6 (Figure 5 .
Figure 6 (right)  shows that as a function of p T even and odd v 1 have a similar shape and magnitude at low and intermediate p T region.

1 .
Directed flow has a weak centrality dependence at midrapidity.As a function of transverse momentum, directed flow changes sigh from negative to positive value around p T ≈ 1.5 GeV.Compared to the top RHIC energy, EPJ Web of Conferences 00075-p.6