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

TL;DR

This paper develops a parity doublet model incorporating scalar and vector mesons to describe dense nuclear matter, reproducing nuclear properties and analyzing phase transitions, including effects of asymmetry.

Contribution

It introduces a six-point sigma interaction in the parity doublet model, enabling realistic reproduction of nuclear matter properties and detailed phase diagram analysis.

Findings

Reproduces properties of normal nuclear matter with chiral invariant mass 500-900 MeV.

Shows the chiral condensate drops at phase transition points.

Finds the first order liquid-gas transition disappears in asymmetric matter.

Abstract

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.