The baryon coupling scheme in an unified SU(3) and SU(6) symmetry formalism

TL;DR

This paper develops a unified symmetry-based approach to calculate baryon-meson coupling constants, applying them to neutron star matter, revealing the prominent role of the $ ext{Delta}^-$ in neutron star interiors and its impact on stellar properties.

Contribution

It introduces a symmetry-invariant method for determining baryon-meson couplings applicable to all particles, extending previous models and analyzing neutron star compositions with hyperons and deltas.

Findings

The $ ext{Delta}^-$ is the most significant exotic particle in neutron star cores.

The $ ext{Delta}^-$ appears at very low densities in neutron stars.

Presence of $ ext{Delta}^-$ can increase the maximum mass of neutron stars.

Abstract

We calculate the baryon-meson coupling constants for the spin-1/2 baryonic octet and spin-3/2 decuplet in a unified approach relying on symmetry arguments such as the fact that the Yukawa couplings, present in the Lagrangian density of the Walecka-type models, must be an invariant under SU(3) and SU(6) group transformations. The coupling constants of the baryon with the scalar $\sigma$ meson are fixed to reproduce the known potential depths for the hyperons and $\Delta$ resonances, in an approach that can be extended to all particles. We then apply the calculated coupling constants to study neutron star matter with hyperons and deltas admixed to its composition. We conclude that the $\Delta^-$ is by far the most important exotic particle that can be present in the neutron star interior. It is always present, independent of the chosen parameterization, and might appear in almost every known neutron star, once its onset happens at very low density. Yet, its presence affects the astrophysical properties of the canonical 1.4 M$_\odot$ star, and, in some cases, it can even contribute to an increase in the maximum mass reached.