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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 $μ_B=0$ 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 cross-over transition to a quark-dominated phase. All three phenomena are cross-over, for most of the $T-μ_B$-plane. The deviations from the free ideal hadron gas baseline at $μ_B=0$ and $T\approx 100-200$ 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 $μ_B\approx1.5$ GeV, and at even higher baryon densities $μ_B\approx2.4$ GeV, the behavior of fluctuations is controlled by the deconfinement cross-over. The CMF model also describe well the static properties of high $μ_B$ neutron stars as well as the new neutron star merger observations. The effective EoS presented here describes simultaneously lattice QCD results at $μ_B=0$, as well as observed physical phenomena (nuclear matter and neutron star matter) at $T\cong0$ and high densities, $μ_B>1$ GeV.