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Elliptic flow of charged and strange hadrons in PbAu collisions at 158 AGeV / c measured in CERES experiment

Differential elliptic flow of v2(pT ) for π−, K0 S , p and Λ is measured at centerof-mass energy of √ sNN=17.3 GeV near the mid-rapidity region in rather central PbAu collisions collected by the CERES/NA45 experiment at CERN. The proton v2(pT ) is extracted from π sample and particle ratios measured by NA49 experiment adapted to CERES conditions. The proton v2(pT ) data show a downward swing towards low pT with excursions into negative v2 values which was not observed earlier. The results are compared with corresponding measurements performed at NA49 and STAR experiments as well as with theoretical predictions from ideal relativistic hydrodynamics. The obtained results for baryons are below hydrodynamic predictions even at the kinetic freeze-out temperature of T f=160 MeV which needs introducing of a viscous hydrodynamics at the late hadronic phase.


Introduction
The elliptic flow v 2 is characterized by the second harmonic coefficient of the azimuthal particle distribution measured with respect to the event plane [1,2]. The strong interaction between the constituents of the expanding, hot and dense system crated in the collision of two nuclei converts initial spatial anisotropy into the momentum anisotropy. The evolution of the system could be described by relativistic hydrodynamics [3]. This was interpreted as creation of a locally equilibrated system of strongly interacting quarks and gluons known as Quark Gluon Plasma (QGP). The QGP behaves as a nearly perfect liquid with a very small ratio η/s of shear viscosity to entropy density [4,5].

Experiment
A sample of ≈30x10 6 rather central PbAu collisions at √ s NN =17.3 GeV were collected with the CERES/NA45 detector at the CERN SPS. A few mixed trigger selections gave, in average, centrality of σ/σ geo = 5.5%. The detector itself is axially symmetric around the beam direction and covers a pseudorapidity range 2.05 < η < 2.70 close to midrapidity (y mid = 2.91) with full azimuthal angle. Thus, it is very suited for elliptic flow studies. The radial-drift Time Projection Chamber (TPC) [6] which is operated inside a magnetic field with maximum radial component of 0.5 T provided a precise measurement of the transverse momentum in the range from 50 MeV/c up to above 4 GeV/c. A detailed description of the CERES experiment is given in [7].

Identification and reconstruction of particles and method used
Ability to measure specific-energy loss sampled along the tracks in the TPC is used for partial identification of charged pion candidates [8]. In the two-dimensional scatter plot in Fig. 1, the measured specific energy loss dE/dx is shown as function of particle momentum p for both negative and positive charges. From the measured differential specific energy loss dE/dx in function of particle momentum, pion candidates were selected within ±1.5σ band (represented with dashed lines) around the nominal Bethe-Bloch formula. In the case of positive charge, over extended range in momentum, pions are mixed with positive kaons and protons. As one can see in Fig. 1, only at very low momenta (below 1.2 GeV/c), protons are clearly identified by dE/dx. We call them directly identified protons. The Λ (K 0 S ) particles are reconstructed via the decay channel Λ → p + π − (K 0 S → π + + π − ). Beside cuts on opening angle and secondary vertex, in order to suppress the contamination of K 0 S (Λ) in the Λ (K 0 S ) signal, an Armenteros-Podolanski cut was applied additionaly, admittedly with a considerable loss of signal. More details are given in [8].
The event plane (EP) method is used for the flow analysis itself [2,9,10]. The observed anisotropy parameter v 2 is corrected for the finite EP resolution. The EP resolution, , is calculated using the 2-and 4-subevent method. Here, Φ a and Φ b are event plane angles of corresponding subevents a and b. Depending on the centrality, it value goes from ≈0.15 to ≈0.30. The results are corrected for the quantum HBT effect using the standard procedure described in [11].

Results and discussion
In Fig. 2 (left) is shown differential elliptic flow, v 2 (p T ), of identified negative pions corrected on K − mesons admixture as well as on the Bose-Einsten 1 correlation effect. Using the Eq. (1), the 1 also known as HBT effect EPJ Web of Conferences 00089-p.2 contribution of the negative kaons have been subtracted from the measured elliptic flow of the π − candidates denoted as " Here, r K − denotes the particle ratio r K − = N K − /N π − . Based on a similar quark content, as input for v K − 2 we used differential elliptic flow of K 0 S , measured by CERES, which will be presented later. All quantities in Eq. (1) are p T -dependent. In the same figure is also shown the elliptic flow of π + candidates denoted as "π + ". The corresponding v 2 magnitude is smaller with respsect to the one from π − which indicates that beside presence of a small admixture of K + mesons (similarly as in the case of π − ) exists a significant proton admixture in the sample of "π + " candidates. These distributions,  Figure 2. Left: The differential elliptic flow v 2 (p T ) of π + candidates and identified π − mesons. Right: The proton elliptic flow v 2 (p T ) (closed circles) reconstructed from the flow of π + candidates. The first four point (stars) represent the elliptic flow of protons directly identified using the dE/dx. together with charged particle spectra measured in the CERN NA49 experiment made possible to extract the proton elliptic flow statistically using the following Eq. (2).
Similarly as in the case of Eq. (1), on the r.h.s of Eq.
(2) the measured v K 0 S 2 is substituted for v K + 2 . The particle ratios r K + = N K + /N π + and r p = N p /N π + specify the contents of K + and protons in the "π + " sample, respectively. In Fig. 2 (right) with closed circles is shown statistically extracted proton elliptic flow, while with stars is shown the elliptic flow from directly identified protons. The first three of these data points, corresponding to directly identified protons, are consistent with zero. The fourth one seems to bridge to the statistically reconstructed points. At low transverse momenta, the proton v 2 magnitude shows an excursion below zero. It takes a minimum near 0.4 GeV/c with v 2 = −0.0290±0.0092 which is 3.2σ below zero. The systematic error near the minimum is about 0.005 and increases up to 0.012 at 2.3 GeV/c. Elliptic flow of particles with a strange (s) quark, Λ and K 0 S , is measured in a way that these particles are reconstructed differentially in both p T and in φ. The φ bins are determined with re-  Figure 3. Comparison between the CERES measurements of K 0 S (left) and Λ (right) elliptic flow to those from the NA49 [12] at SPS and STAR [13] at RHIC. The measurements are performed for similar centralities. spect to the event plane. In each p T bin, the obtained distributions dN (Λ,K 0 S ) /dφ are then fitted with c[1 + 2v 2 cos(2φ)]. The v 2 values, corrected for the event plane resolution, are shown in Fig. 3 with red circles. Systematic errors are significantly smaller with respect to the statistical ones. The measurements are performed in mid-central PbAu collisions characterized with σ/σ geo =9.8%. In the same figure, the obtained results are compared with those from the NA49 experiment (blue squares) extracted from PbPb collisions at the same energy of √ s NN =17.3 GeV and from the STAR experiment (black stars) at RHIC from AuAu collisions at √ s NN =200 GeV. One can see a reasonably good agreement between the NA49 and CERES data. In order to compare STAR to CERES results, the former have been rescaled to the centrality used in the CERES experiment. By plotting the STAR v 2 values vs centrality for different transverse momenta of Λ and K 0 S particles, the appropriate scaling factor has been obtained. After rescaling, due to the higher beam energy, the STAR the v 2 values measured at the RHIC are somewhat higher with respect to the ones from the CERES.
The measured elliptic flow values are compared to the results from ideal hydrodynamics calculated by P. Huovinen [14] in 2 + 1 dimensions assuming 1-st order phase transition to QGP at critical temperature of T c =165 MeV. The calculations were performed for two choices of kinetic freeze-out temperature T f =120 MeV and T f =160 MeV.
In Fig. 4 the differential pion elliptic flow is compared with hydrodynamics predictions for the two centrality classes called top-and mid-central collisions. The pion v 2 in the top-central collisions is in a very good agreement with the hydrodynamics results obtained with the 'standard' temperature T f =120 MeV as it is shown in Fig. 4 (left). In the case of mid-central collisions, Fig. 4 (right), the data up to p T =1.2 GeV/c suggests position between the two hydro curves and then it saturates. As it is expected, up to p T =1.2 GeV/c, the pion v 2 stays significantly above the curve which corresponds to T f =160 MeV. For p T above 1.2 GeV/c, the data are below hydro curves. These two CERES data sets seem to confirm that departures from ideal hydrodynamics increase with enlarging of impact parameter of the collision. Such behaviour with respect to the ideal hydrodynamics have also been reported from RHIC experiments [13,15]. It is not known yet whether this indicates incomplete thermalization during primary stages of collision [16,17], or increasing viscous corrections [18,19], or a mixture of both. The reduction seen in proton v 2 persist for Λ elliptic flow too (right plot in Fig. 5). The Λ results could be termed 'perfectly in line' with findings for protons. Even an excursion into negative v 2 values as seen for protons would fit into the Λ flow data at very low p T . The reduction in v 2 with respect to ideal hydrodynamics grow with particle mass. The deviations seen in Λ flow are not stronger than ICNFP 2013 00089-p.5 those in proton flow may well be due to the small mass difference: the relative gain from m(p) to m(Λ) is only 19%, compared to the steps m(π) to m(K) (250%), and m(K) to m(p) (90%); and to limited data precision.

Summary
We have presented differential elliptic flow measurements from mid-central PbAu collisions at √ s NN =17.3 GeV of π − , K 0 S and Λ. Additionally, we presented differential elliptic flow of protons directly identified using the dE/dx, as well as elliptic flow of protons reconstructed from impure positive pion sample. The obtained results are compared with those from the NA49 experiment at CERN and from the STAR experiment at RHIC. Also, the results are compared with ideal hydrodynamics predictions. That comparisons show faster decrease of experimental v 2 values towards low p T , getting stronger for the larger hadron mass. The negative values are reached in proton v 2 which is maybe seen as the most prominent feature of this trend. In general, viscosity in the late hadronic phase suppresses elliptic flow. For protons, the consequences are striking as it could turn their v 2 into negative values. But incomplete thermalization during primary stages of collision could do the same, or a mixture of these two effects.