van der Waals hadron resonance gas and QCD phase diagram

Abstract

Taking into account the recently developed van der Waals (VDW) like equation of state (EoS) for grand canonical ensemble of fermions, the temperature dependent profiles of normalized entropy density ($s /T^3$) and the ratio of shear viscosity and entropy density ($\eta/ s$) for hadron resonance gas have been evaluated. The VDW parameters, corresponding to interactions between (anti)baryons, have been obtained by contrasting lattice EoS for QCD matter at finite chemical potentials ($\mu_{B}$) and for $T \le$ 160 MeV. The temperature and chemical potential dependent study of $s /T^3$ and $\eta /s$ for hadron gas, by signalling onsets of first order phase transition and crossover in the hadronic phase of QCD matter, helps in understanding the QCD phase diagram in the ($T, \mu_{B}$) - plane. An estimation of probable location of critical point matches predictions from other recent studies.