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Nuclear Matter Properties and Neutron Star Structures from an Extended Linear Sigma Model

Yao Ma

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, $g_{σNN}$, 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 $δ$ 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, $ξ$, which can be related to the current quark mass and thus the pion-nucleon sigma term, $σ_{πN}$. A negative $σ_{πN}$ leads to a stiffer EOS of neutron star matter and thus a larger maximum mass of neutron stars, but the value of $σ_{πN}$ 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.

Nuclear Matter Properties and Neutron Star Structures from an Extended Linear Sigma Model

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, , the iso-vector scalar meson and nucleons, , and the four-vector meson couplings play an important role in the properties of nuclear matter and neutron stars. The introduction of the meson leads to a plateau structure of the symmetry energy, , at intermediate densities, which is crucial to the consistency of neutron skin thickness of Pb and the tidal deformability of a canonical neutron star. The explicit chiral symmetry breaking term is then introduced with a constant background field, , which can be related to the current quark mass and thus the pion-nucleon sigma term, . A negative leads to a stiffer EOS of neutron star matter and thus a larger maximum mass of neutron stars, but the value of 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.
Paper Structure (4 sections, 6 equations, 2 figures, 1 table)

This paper contains 4 sections, 6 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Nuclear properties and neutron star structures
  3. Explicit chiral symmetry breaking and neutron star structures
  4. Summary and outlook

Figures (2)

  • Figure 1: The $E_{\rm sym}(n)$ and M-R relation of NSs for different cases. The constraints MSP J0740+6620 are from Ref. NANOGrav:2019jur and GW170817 are from Ref. LIGOScientific:2018cki. Both are at $95\%$ confidence level.
  • Figure 2: The NS structures with $\sigma_{\pi N}$-$400^-(K)$ and $\sigma_{\pi N}$-$600^-(K)$ parameter sets, where the number means the value of $-\sigma_{\pi N}$ in MeV and the $K$ indicates the incompressibility at saturation density is around $500$ MeV. $\sigma_{\pi N}=m_N-m$ means the pion-nucleon sigma term, where $m_N$ is the nucleon mass and $m$ is the mass of the nucleon in the chiral limit. The constraints are the same as in Fig. \ref{['fig:2-flavor']}.