Kaon Condensation in Neutron Star Matter with Hyperons

Based on the Kaplan-Nelson Lagrangian, we investigate kaon condensation in dense neutron star matter allowing for the explicit presence of hyperons. Using various models we find that the condensate threshold is sensitive to the behavior of the scalar density; the more rapidly it increases with baryon density, the lower is the threshold for condensation. The presence of hyperons, particularly the $\Sigma^-$, shifts the threshold for $K^-$ condensation to a higher density. In the mean field approach, with hyperons, the condensate amplitude grows sufficiently rapidly that the nucleon effective mass vanishes at a finite density and a satisfactory treatment of the thermodynamics cannot be achieved. Thus, calculations of kaon-baryon interactions beyond the mean field level appear to be necessary.