On the uncertainty of hyperon couplings and the electrochemical potential in neutron star matter

Uncertainty of the hyperon couplings, in particular, that of the $\Sigma^-$, in dense matter raises the question of the behavior of the electrochemical potential in neutron star matter, which is crucial to the possible presence of the kaon condensed phase. We show that regardless of this uncertainty, the $\Lambda$ hyperon, whose coupling can be constrained by its binding in nuclear matter and other observations, also aided by the $\Xi^-$, introduce a saturation of the electrochemical potential just as the $\Sigma^-$ would otherwise do, which tends to mitigate against kaon condensation. The maximum possible mass of neutron stars appears to be $\sim 1.5 \msun$ independent of the uncertainties.