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 A hyperon, whose coupling can be constrained by its binding in nuclear matter and other observations, by itself, or also aided by the Xi (-), introduces 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 similar to (1.5-1.7)M-. independent of the uncertainties, the limit being imposed by any one of hyperonization, deconfinement, or kaon condensation. Interestingly, such a limit is barely higher than the Chandrasekhar limit on the iron core mass of presupernova stars. This leaves a very small mass window for the existence of neutron stars, for the occurrence of supernovas, and therefore for a universe containing heavy elements and at least one planet with life.