In order to characterize the higher order moments of the particle multiplicity, we implement the linear-sigma model with Polyakov-loop correction. We first studied the critical phenomena and estimated some thermodynamic quantities. Then, we compared
all these results with the first--principle lattice QCD calculations. Then, the extensive study of non-normalized four moments is followed by investigating their thermal and density dependence. We repeat this for moments normalized to temperature and chemical potential. The fluctuations of the second order moment is used to estimate the chiral phase--transition. Then, we implement all these in mapping out the chiral phase transition, which shall be compared with the freeze-out parameters estimated from the lattice QCD simulations and the thermal models are compared with the chiral phase--diagram.
The hadron ratios measured in central Au-Au collisions are analysed by means of Hadron Resonance Gas (HRG) model over a wide range of nucleon-nucleon center-of-mass energies ranging from 7.7 to 200 GeV as offered by the STAR Beam Energy Scan I (BES-I
). We restrict the discussion on STAR BES-I, because of large statistics and over all homogeneity of STAR measurements (one detector) against previous experiments. Over the last three decades, various heavy-ion experiments utilizing different detectors (different certainties) have been carried out. Regularities in produced particles at different energies haven been studied. The temperature and baryon chemical potential are deduced from fits of experimental ratios to thermal model calculations assuming chemical equilibrium. We find that the resulting freeze-out parameters using single hard-core value and point-like constituents of HRG are identical. This implies that the excluded-volume comes up with no effect on the extracted parameters. We compare the results with other studies and with the lattice QCD calculations. Various freeze-out conditions are confronted with the resulting data set. The effect of feed-down contribution from week decay and of including new resonances are also analysed. At vanishing chemical potential, a limiting temperature was estimated as T=158.5 MeV with 3 MeV uncertainty.
