Chemical freeze-out parameters in Beam Energy Scan Program of STAR at RHIC

The STAR experiment at RHIC has completed its first phase of the Beam Energy Scan (BES-I) program to understand the phase structure of the quantum chromodynamics (QCD). The bulk properties of the system formed in Au+Au collisions at different center of mass energy $\sqrt{s_{NN}} = $ 7.7, 11.5, 19.6, 27, and 39 GeV have been studied from the data collected in the year 2010 and 2011. The centrality and energy dependence of mid-rapidity ($|y|$<0.1) particle yields, and ratios are presented here. The chemical freeze-out parameters are extracted using measured particle ratios within the framework of a statistical model.


Introduction
The heavy-ion collider experiments such as STAR at RHIC, ALICE at LHC were designed to investigate matter similar to that formed at the very early stages of the universe i.e. matter under extreme conditions of high temperature or density (or both) [1]. Similar to the matter in its primordial state, a deconfined state of quarks and gluons is created called Quark-Gluon Plasma (QGP) at both RHIC and LHC [2,3]. The QCD as the theory of strong interactions predicts a transition at sufficiently high temperature T or baryon chemical potential µ B from hadronic matter to QGP state. So, by varying the T and µ B in laboratory we can study the phase transition associated with QCD matter [4][5][6][7]. The major part of the QCD phase diagram, which is generally known as the plot of T as a function of µ B , consists of two phases [8]. These are the high temperature QGP phase, where the relevant degrees of freedom are quarks and gluons, and the hadronic phase at low temperature. Other interesting phases related to neutron stars [9], color superconductivity [10], and the quarkya e-mail: sabita@rcf.rhic.bnl.gov onia [11] phase also appear in the QCD phase diagram in addition to the confined and de-confined phases [12]. Particle yields in high energy heavy-ion experiments at different collision energies can be used to obtain the T and µ B that set up the chemical freeze-out line in the QCD phase diagram. It appears to be very close to the phase boundary between QGP and hadronic phase, especially at low µ B . At high T and vanishing µ B , finite temperature lattice QCD calculations has established the transition from QGP to a hadron gas is a cross-over [13]. The existence of a first-order phase transition has been predicted by several QCD-based calculations at lower T and µ B [14]. The QCD critical point is a feature of the phase diagram, where the nature of the transition changes from a discontinuous (first-order) transition to an analytic crossover [15][16][17][18][19]. Here we will discuss the centrality dependence of identified particles, pions (π ± ), kaons (K ± ), protons (p), and anti-protons (p) produced in Au+Au collisions at BES energies √ s NN = 7.7, 11.5, 19.6, 27, and 39 GeV [22,23].
The experimental particle ratios obtained from the yields of π ± , K ± , p,p, Λ,Λ and Ξ − ,Ξ + [24] have been used in a grand-canonical ensemble (GCE) of THERMUS model [25] to extract the freeze-out parameters like chem-ical freeze-out temperature (T ch ), baryon chemical potential (µ B ), strangeness chemical potential (µ S ), charge chemical potential (µ Q ), and strangeness saturation factor (γ S ). The centrality and energy dependence of these parameters will also be discussed.

Particle Yields
The identified particle yields are measured using the . π − /π + , K − /K + , K − /π − , and K + /π + as a function of N part in Au+Au collisions at BES energies and top RHIC energies [21].
Errors are statistical and systematic errors added in quadrature.
cific ionisation energy loss whereas in TOF, they are identified using the particle velocities as a function of momentum. Figure 1 shows The increase in proton yield per participating nucleon with the increasing collision centrality is possibly due to large baryon stopping at the lower energies. The ratios of K + /π + and K − /π − gradually increase from peripheral to mid-central and saturate in mid-central to central collisions. The enhancement of the integrated K ± /π ± ratio in more central collisions is related to strangeness equilibration in various thermal models [27,28]. Thermodynamic models explain the increase of the K/π ratios with the system size from peripheral to central based on the transition from the canonical to grandcanonical ensemble [29,30].

Chemical freeze-out
The scenario when inelastic collisions among the particles stop and particle ratios get fixed, is called the chemical  assuming chemical equilibrium to study chemical freezeout dynamics for BES energies. The chemical freezeout parameters, T ch , µ B , µ S , and γ S , are extracted from the mid-rapidity particle ratios of different combinations which includes yields of π ± , K ± , p,p, Λ,Λ, Ξ − ,Ξ + [22][23][24]. Experimentally, the proton yields have not been corrected for feed-down contributions. The yields of π and Λ have been corrected for the feed-down from weak decays. tral collisions at all energies. We observe a centrality dependence of the chemical freeze-out curve (T ch vs. µ B ) at BES energies which was not observed at higher energies of Au+Au 200 GeV [21,22]. The strangeness chemical potential, µ S , seems to decrease with the increasing collision energy, following the same type of behaviour as µ B . The strangeness saturation factor γ S increases from peripheral to central for all the energies studied. In central collisions, γ S is close to unity for top RHIC energies.

Summary
The centrality and energy dependence of identified parti-