Nuclear matter properties and neutron star structures from an extended linear sigma model

TL;DR

This paper uses an extended linear sigma model to analyze nuclear matter and neutron star properties, highlighting the roles of meson couplings and chiral symmetry breaking in determining the equation of state and neutron star characteristics.

Contribution

It introduces a chiral symmetry breaking term and explores its impact on the EOS and neutron star maximum mass, providing new insights into the density dependence of nuclear matter properties.

Findings

Introduction of the δ meson creates a plateau in the symmetry energy at intermediate densities.

A negative pion-nucleon sigma term leads to a stiffer EOS and larger neutron star maximum mass.

The model suggests the sigma term value needed for astrophysical constraints is negative.

Abstract

The properties of nuclear matter and the structures of neutron stars are analyzed with a baryonic extended linear sigma model in mean-field approximation, where the masses of baryons and mesons are generated via the spontaneous chiral symmetry breaking. The couplings between the iso-scalar scalar meson and nucleons, $g_{\sigma NN}$, the iso-vector scalar meson and nucleons, $g_{a_0 NN}$, and the four-vector meson couplings play an important role in the properties of nuclear matter and neutron stars. The introduction of the $\delta$ meson leads to a plateau structure of the symmetry energy, $E_{\rm sym}(n)$, at intermediate densities, which is crucial to the consistency of neutron skin thickness of $^{208}$Pb and the tidal deformability of a canonical neutron star. The explicit chiral symmetry breaking term is then introduced with a constant background field, $\xi$, which can be related to the current quark mass and thus the pion-nucleon sigma term, $\sigma_{\pi N}$. A negative $\sigma_{\pi N}$ leads to a stiffer EOS of neutron star matter and thus a larger maximum mass of neutron stars, but the value of $\sigma_{\pi N}$ needed to satisfy the astrophysical constraints is negative, not positive as the vacuum value. The study may provide insights into the running behaviors of the parameters in the low-energy effective model to give the density-dependent description for the EOS of neutron star matter.