Compact star and compact star matter properties from a baryonic extended linear sigma model with explicit chiral symmetry breaking
Based on a baryonic extended linear sigma model including explicit chiral symmetry breaking effect, the structure of neutron stars with the emergence of hyperons is investigated using the relativistic mean field approximation. It is found that, except for the lightest scalar meson $\sigma$ whose structure is not well understood so far, the vacuum mass spectra of relevant hadrons and nuclear matter properties around saturation density can be well reproduced. Nevertheless, based on the present model and the applied relativistic mean field approach, we found that, to have a realistic mass-radius relation of neutron stars, the $\pi N$ sigma term $\sigma_{\pi N}$ that denotes the contribution of explicit symmetry breaking should deviate from its empirical values at vacuum. Specifically, $\sigma_{\pi N}\sim -600$ MeV, rather than $(32\text{--}89) \rm \ MeV$ at vacuum. With an appropriate choice of $\sigma_{\pi N}$ and $K(n_0)$, our framework can give a more observationally favored mass-radius relation of neutron stars with the emergence of hyperons, suggesting a possible density dependence of the low energy constants, at least within the present leading order framework with the relativistic mean field approach. The present result provides a new perspective on the relation between microscopic explicit chiral symmetry breaking in dense matter and macroscopic structure of compact stars and calls for more systematic treatments beyond leading order relativistic mean field calculation.