Asymmetric nuclear matter in a parity doublet model with hidden local symmetry

We construct a model to describe dense hadronic matter at zero and finite temperature, based on the parity doublet model of DeTar and Kunihiro, with including the iso-singlet scalar meson $\sigma$ as well as $\rho$ and $\omega$ mesons. We show that, by including a six-point interaction of $\sigma$ meson, the model reasonably reproduces the properties of the normal nuclear matter with the chiral invariant nucleon mass $m_0$ in the range from $500~{\rm MeV}$ to $900~{\rm MeV}$. Furthermore, we study the phase diagram based on the model, which shows that the value of the chiral condensate drops at the liquid-gas phase transition point and at the chiral phase transition point. We also study asymmetric nuclear matter and find that the first order phase transition for the liquid-gas phase transition disappears in asymmetric matter and that the critical density for the chiral phase transition at non-zero density becomes smaller for larger asymmetry.