Identified particle production and freeze-out properties in heavy-ion collisions at RHIC Beam Energy Scan program

The first phase of Beam Energy Scan (BES) program at the Relativistic Heavy-Ion Collider (RHIC) was started in the year 2010 with the aim to study the several aspects of the quantum chromodynamics (QCD) phase diagram. The Solenoidal Tracker At RHIC (STAR) detector has taken data at $\sqrt{s_{NN}} = $ 7.7, 11.5, 19.6, 27, and 39 GeV in Au+Au collisions in the years 2010 and 2011 as part of the BES programme. For these beam energies, we present the results on the particle yields, average transverse mass and particle ratios for identified particles in mid-rapidity ($|y|$<0.1). The measured particle ratios have been used to study the chemical freeze-out dynamics within the framework of a statistical model.


Introduction
To understand the properties of matter under extreme conditions of high temperature or density, heavy-ion collision experiments are conducted at RHIC in BNL and the LHC in CERN. These are the conditions, in which the deconfined phase of QCD matter, the Quark-Gluon Plasma (QGP), is created. It is conjectured that the formed hot and dense partonic matter rapidly expands and cools down. During the evolution it undergoes a transition back to the hadronic matter [1,2]. Both RHIC and LHC have confirmed the formation of the QGP in central Au+Au and Pb+Pb collisions [3,4]. In QCD, there are three conserved charges, baryon number B, electric charge Q and strangeness S . Thus the equilibrium thermodynamic state of QCD matter is completely determined by temperature T ch and the three chemical potentials µ B , µ Q , and µ S corresponding to B, Q and S respectively. The QCD phase diagram is plotted with the temperature (T ) as a function of baryon chemical potential (µ B ) [5]. From a e-mail: sabita@rcf.rhic.bnl.gov finite-temperature QCD calculations on the lattice it is theoretically established that the transition from QGP to a hadron gas happens at high temperature and µ B close to zero and is a cross-over [6]. Several QCD-based calculations [7] suggest existence of first-order phase transition at a lower T and large µ B . Therefore, there should be an end point for the first-oder phase transition in the QCD phase diagram, known as the critical point.
Several QCD based models and also calculations on lattice predict the existence of the critical point at high µ B [8] and its exact location depends on the different model assumptions [9,[11][12][13]. It is worth to mention that not all QCD-based models or lattice groups do predict the existence of critical point [14].
Theoretically, the phase diagram is explored through nonperturbative QCD calculations on lattice which indicates the energy scale can be explored experimentally. Now to explore various aspects of the QCD phase diagram [15] such as the search for the signals of phase boundary, and the search the location of the critical point has become arXiv:1412.0499v1 [nucl-ex] 1 Dec 2014 EPJ Web of Conferences Figure 1. dN/dy of π ± , K ± , p, andp scaled by 0.5N part as a function of center of mass energy ( √ s NN ) including collisions at BES energies (red points) along with AGS [16][17][18], SPS [19], top RHIC [20], and LHC energies [21] [24]. The process of hadron decoupling from an interacting system in heavyion collisions is known as freeze-out. They are of two types, kinetic and chemical freeze-out. We will present here the study on chemical freeze-out, characterised by temperature (T ch ) and baryon chemical potential (µ B ), when inelastic collisions cease and the particle yields become fixed. The T ch and µ B can be extracted using the particle ratios obtained from the measured particle yields and comparing with model calculations which assume the XLIV International Symposium on Multiparticle Dynamics 2014 BES energies along with AGS [16][17][18], SPS [19], RHIC [20], and LHC energies [21] for central collisions. Errors are statistical and systematic errors added in quadrature.
system is in chemical and thermal equilibrium.
To extract the chemical freeze-out temperature (T ch ), baryon chemical potential (µ B ), strangeness chemical potential (µ S ) and strangeness saturation factor (γ S ), the experimental particle ratios are used in both grand canonical ensemble (GCE) and strangeness canonical ensemble (SCE) approach of the model. The centrality and energy dependence of T ch , µ B , µ S , γ S in Au+Au collisions at the above BES energies are studied.

Particle Yields
The mid-rapidity (|y| < 0.1) BES data presented here are obtained using the STAR Time Projection chamber (TPC) and Time-Of-Flight (TOF) detectors [32]. The particles are identified by measuring the specific ionisation energy loss in the TPC and the particle velocities using TOF as a function of momentum. Figure 1 show the dN/dy normalised to the average number of participant nucleus (dN/dy/ 0.5N part ) vs.

Average Transverse Mass
BES energies along with data for Pb+Pb/Au+Au collisions from AGS [16][17][18], SPS [19], RHIC [20], and LHC energies [21].  Figure 3 shows the variation of different particle ratios as a function of center-of-mass energy in Au+Au collisions at BES energies and its comparison with the results from AGS [16][17][18], SPS [19], RHIC [20], and LHC energies [21]. The variation of K − /K + as a function of p/p for 0-5% centrality from SPS-LHC energies has been shown. Errors are statistical and systematic errors added in quadrature.

Particle Ratios
As the collision energy increases, π − /π + ratio decreases to unity whereas K − /K + ratio rise systematically. At higher energy, pair production, which results in the same number of positive and negative pions dominates the resonance decays. Following this logic, the π − /π + ratio is supposed to reach unity as the energy goes up. The K − /K + ratio is indicative of the relative contribution of associated and pair production. The associated production mechanism can only produce K + via N + N → N + X + K + , π+N → X+K + where N is nucleon and X is hyperon (Λ or Ξ), while the pair production mechanism produces K + and K − via N + N → N + N + K + + K − . The rise of K − /K + ratio as a function of energy can be attributed to the nature of kaon production channels. At lower energy the associated production dominates, due to a lower energy threshold. As the energy increases, the pair production which produces the same number of K + and K − becomes more significant. With increasing energy, the net baryon density decreases and thus the associated production of K + also decreases, while pair production increases due to gluongluon fusion into strange quark-antiquark pairs [35,36].
All these results combined, when compared with previous experiments, seem to be consistent with an enhancement in the strangeness production. At lower energies due to the non-zero net baryon density in the collisions zone, the associated production of kaons with hyperons will be different from these produced with anti-hyperons.
The K − /K + , which represents net-strange chemical potential (µ S ) vs.p/p, representing net-baryon chemical potential (µ B ) for 0-5% centrality in Au+Au collisions together with results from top RHIC, has been shown in Fig. 3. Both ratios are affected by the net baryon content; they show a strong correlation. In a hadron gas, both chemical potentials, µ S and µ B depends on temperature and they follow the relation µ S = µ B /3 [37]. It is worth noting that at low energies, the absorption of antiprotons in the baryon-rich environment plays a vital role.

Chemical freeze-out
At chemical freeze-out, inelastic collisions among the particles stop, particle yields and ratios of particle yields get fixed. Particle ratios are calculated taking the ratios from the measured integrated yields. A set of different particle ratios which involves the particle yields of π ± , K ± , p, p, Λ,Λ, Ξ − ,Ξ + can be collectively used to extract the information on the chemical freeze-out conditions. The extraction of freeze-out parameters is very senstive to the contribution of weak decays, commonly called feed-down.
Experimentally different particles are corrected in different ways. At STAR, proton yields have not been corrected for feed-down contributions, and are commonly called "inclusive", where as π and Λ yields have been corrected for the feed-down from K 0 S , Ξ and Ξ 0 weak decays, respectively. In model, the appropriate feed-down as in experimental data has been considered. Different freezeout parameters are extracted using those ratios comparing with the corresponding ratios calculated in the THERMUS model assuming chemical equilibrium.
In the THERMUS model, in thermodynamical equilibrium, the particle abundance of i-th particle (N i ) in a system of volume V can be given by [28] where T is the chemical freeze-out temperature, m i is the particle mass, g i is the degeneracy, β ≡ 1 T , K 2 is the second order Bessel function and µ i is the chemical potential of hadron species i which is given by  The temperature of kinetic freeze-out (T kin ), where elastic collisions stop and particle spectra get fixed, obtained using a Blast-Wave fit to the identified transverse momentum spectra is found to takes place after chemical freezeout [40].

Summary
The identified particle production have been discussed in possibility of successive hadronization [43]. This could lead to further understanding and refinement of the statistical models. In addition to BES program at RHIC [44], new experimental facilities have been designed at the Facility for Antiproton and Ion Research (FAIR) at GSI and Nuclotron-based Ion Collider fAcility (NICA) at JINR in order to search for the QCD critical point [45].