Crossover-model approach to QCD phase diagram, equation of state and susceptibilities in the 2+1 and 2+1+1 flavor systems

Abstract

We construct a simple model for describing the hadron–quark crossover transition by using lattice QCD (LQCD) data in the [Formula: see text] flavor system, and draw the phase diagram in the [Formula: see text] and [Formula: see text] flavor systems through analyses of the equation of state (EoS) and the susceptibilities. In the present hadron–quark crossover (HQC) model, the entropy density [Formula: see text] is defined by [Formula: see text] with the hadron-production probability [Formula: see text], where [Formula: see text] is calculated by the hadron resonance gas model that is valid in low temperature [Formula: see text] and [Formula: see text] is evaluated by the independent quark model that explains LQCD data on the EoS in the region [Formula: see text] for the [Formula: see text] flavor system and [Formula: see text] for the [Formula: see text] flavor system. The [Formula: see text] is determined from LQCD data on [Formula: see text] and susceptibilities for the baryon-number [Formula: see text], the isospin [Formula: see text] and the hypercharge [Formula: see text] in the [Formula: see text] flavor system. The HQC model is successful in reproducing LQCD data on the EoS and the flavor susceptibilities [Formula: see text] for [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] in the [Formula: see text] flavor system, without changing the [Formula: see text]. We define the hadron–quark transition temperature with [Formula: see text]. For the [Formula: see text] flavor system, the transition line thus obtained is almost identical in [Formula: see text], [Formula: see text], [Formula: see text] planes, when the chemical potentials [Formula: see text] [Formula: see text] are smaller than 250 MeV. This [Formula: see text] approximate equivalence is also seen in the [Formula: see text] flavor system. We plot the phase diagram also in [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] planes in order to investigate flavor dependence of transition lines. In the [Formula: see text] flavor system, [Formula: see text] quark does not affect the [Formula: see text] flavor subsystem composed of [Formula: see text], [Formula: see text], [Formula: see text]. Temperature dependence of the off-diagonal susceptibilities and the [Formula: see text] show that the transition region at [Formula: see text] is [Formula: see text] for both the [Formula: see text] and [Formula: see text] flavor systems.