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Isovector potential of $Σ$ in nuclei and neutron star matter

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