Equation of state for hot QCD and compact stars from a mean-field approach

The thermodynamic properties of high temperature and high density QCD matter are explored within the chiral SU(3)-flavor parity-doublet Polyakov-loop quark-hadron mean-field model, CMF. The quark sector of the CMF model is tuned to describe the ${\ensuremath{\mu}}_{B}=0$ thermodynamics data of lattice QCD. The resulting lines of constant physical variables as well as the baryon number susceptibilities are studied in some detail in the temperature--chemical-potential plane. The CMF model predicts three consecutive transitions: the nuclear first-order liquid-vapor phase transition, chiral symmetry restoration, and the crossover transition to a quark matter phase. All three phenomena are crossovers, for most of the $T\text{\ensuremath{-}}{\ensuremath{\mu}}_{B}$ plane. The deviations from the free ideal hadron gas baseline at ${\ensuremath{\mu}}_{B}=0$ and $T\ensuremath{\approx}100\text{--}200$ MeV can be attributed to remnants of the liquid-vapor first-order phase transition in nuclear matter. The chiral crossing transition determines the baryon fluctuations at much higher ${\ensuremath{\mu}}_{B}\ensuremath{\approx}1.5$ GeV. At high baryon densities, ${\ensuremath{\mu}}_{B}\ensuremath{\approx}2.4$ GeV, the behavior of fluctuations is controlled by crossover to quark matter. The CMF model also describe well the static properties of high ${\ensuremath{\mu}}_{B}$ neutron stars as well as recent neutron star merger observations. The effective equation of state presented here describes simultaneously lattice QCD results at ${\ensuremath{\mu}}_{B}=0$ as well as observed physical phenomena (nuclear matter and neutron star matter) at $T\ensuremath{\cong}0$ and high densities, ${\ensuremath{\mu}}_{B}>1$ GeV.