Symmetry energy systematics and its high density behavior

We explore the systematics of the density dependence of nuclear matter symmetry energy in the ambit of microscopic calculations with various energy density functionals, and find that the symmetry energy from subsaturation density to supra-saturation density can be well determined by three characteristic parameters of the symmetry energy at saturation density ρ0, i.e., the magnitude Esym(ρ0), the density slope L and the density curvature Ksym. This finding opens a new window to constrain the supra-saturation density behavior of the symmetry energy from its (sub-)saturation density behavior. In particular, we obtain L = 46.7 ± 12.8 MeV and Ksym = −166.9 ± 168.3 MeV as well as Esym(2ρ0) ≈ 40.2 ± 12.8 MeV and L(2ρ0) ≈ 8.9±108.7 MeV based on the present knowledge of Esym(ρ0) = 32.5 ± 0.5 MeV, Esym(ρc) = 26.65±0.2 MeV and L(ρc) = 46.0±4.5 MeV at ρc = 0.11 fm−3 extracted from nuclear mass and the neutron skin thickness of Sn isotopes. Our results indicate that the symmetry energy cannot be stiffer than a linear density dependence. In addition, we also discuss the quark matter symmetry energy since the deconfined quarks could be the right degree of freedom in dense matter at high baryon densities