Compact star and compact star matter properties from a baryonic extended linear sigma model with explicit chiral symmetry breaking

TL;DR

The paper develops a three-flavor baryon extended linear sigma model with explicit chiral symmetry breaking (bELSM-$ξ$) within a relativistic mean-field framework to study dense nuclear matter and neutron star structure with hyperons. It shows that vacuum hadron spectra and NM properties near saturation can be reproduced, but achieving realistic neutron star mass–radius relations requires negative explicit symmetry-breaking contributions to the nucleon mass at high density, characterized by $σ_{\,πN}$ around $-600$ MeV, along with a stiffer incompressibility $K(n_0) \approx 500$ MeV. With these adjustments, the model yields NS mass–radius curves compatible with GW170817 and MSP J0740+6620, and predicts hyperons emerging near $2.5n_0$. The work highlights the potential role of density-dependent explicit symmetry breaking in connecting QCD-level chiral dynamics to macroscopic NS observables and outlines future refinements including higher-order effects and scalar-meson substructure.

Abstract

Based on a baryonic extended linear sigma model including explicit chiral symmetry breaking effect, the structure of neutron star with the emergence of hyperons is investigated using the relativistic mean field approximation. It's found that, except the lightest scalar meson $σ$ whose structure is not well understood so far, the vacuum mass spectra of relevant hadrons and NM properties around saturation density can be well reproduced. Nevertheless, we found that, to have a realistic mass-radius relation of neutron stars, the $πN$ sigma term $σ_{πN}$, which denotes the contribution of explicit symmetry breaking, should deviate from its empirical values at vacuum. Specifically, $σ_{πN}\sim -600$ MeV, rather than $(32-89) \rm \ MeV$ at vacuum. With an appropriate choice of $σ_{πN}$ and $K(n_0)$, our framework can give a more data favored mass-radius relation of neutron stars with the emergence of hyperons. The effect of explicit symmetry breaking at densities is hoped to provide a new insight to the relation between microscopic symmetries in medium and macroscopic phenomena.

Figures (7)

• Figure 1: The EOMs of $\sigma$ and $\omega$ defined in Eqs. \ref{['eq:eom-omega']} and \ref{['eq:eom-sigma']}, for pure neutron matter (PNM) as functions in $\sigma-\omega$ space. The red plane is the EOM of $\sigma$, the blue plane is the EOM of $\omega$, and the yellow one is the zero plane. The intersection of the three planes is the solution of the EOMs.
• Figure 2: The $t$-channel and $u$-channel interactions of nucleons at densities illustrated in OBE picture. The transferred momentum in $3$-momentum space can be obtained by Fermi-Dirac distribution. The incoming and outgoing nucleons have the same momentum due to Fermi-Dirac statistics at zero temperature.
• Figure 3: The NS structure with $\sigma_{\pi N}$-$75^+$ parameter set. The upper pannel is for the M-R relation and the lower pannel is for the baryon fraction. The constraints of the NSs are from the MSP J0740+6620 NANOGrav:2019jur and GW170817 LIGOScientific:2018cki.
• Figure 4: The NS structures with $\sigma_{\pi N}$-$400^-$ and $\sigma_{\pi N}$-$600^-$ parameter sets. The constraints are the same as in Fig. \ref{['fig:ns-p75']}.
• Figure 5: The NS structures with $\sigma_{\pi N}$-$100^-K$, $\sigma_{\pi N}$-$400^-K$, and $\sigma_{\pi N}$-$600^-K$ parameter sets. The constraints are the same as in Fig. \ref{['fig:ns-p75']}.