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 $Sigma$ ($g_{rhoSigma}$) 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 $g_{rhoSigma}$, $Sigma^-$ 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.