Isovector potential of $\Sigma$ in nuclei and neutron star matter

We determine the coupling constants of $\Sigma$ hyperon with mesons in relativistic mean field (RMF) models using $\Sigma^-$ atomic shift data and examine the effects of $\Sigma$ on the neutron star maximum mass. We find that we need to reduce the vector-isovector meson coupling with $\Sigma$ ($g_{\rho\Sigma}$) from the value constrained by the SU(3)v symmetry in order to explain the $\Sigma^-$ atomic shifts for light symmetric and heavy asymmetric nuclei simultaneously. With the atomic shift fit value of $g_{\rho\Sigma}$, $\Sigma^-$ can emerge in neutron star matter overcoming the repulsive isoscalar potential for $\Sigma$ hyperons. Admixture of $\Sigma^-$ in neutron stars is found to reduce the neutron star maximum mass slightly.