Properties of a kaon-condensed phase in hyperon-mixed matter with three-baryon forces

Coexistent phase of kaon condensates and hyperons [$(Y+K)$ phase] in beta equilibrium with electrons and muons is investigated as a possible form of dense hadronic phase with multistrangeness. The effective chiral Lagrangian for kaon-baryon and kaon-kaon interactions is utilized within the chiral symmetry approach in combination with the interaction model between baryons. For the baryon-baryon interactions, one adopts the minimal relativistic mean-field theory with exchange of scalar mesons $(\ensuremath{\sigma},$ ${\ensuremath{\sigma}}^{*})$ and vector mesons $(\ensuremath{\omega},$ $\ensuremath{\rho},$ $\ensuremath{\phi})$ between baryons without including the nonlinear self-interacting meson-field terms. In addition, the universal three-baryon repulsion and the phenomenological three-nucleon attraction are introduced as density-dependent effective two-body potentials. The repulsive effects leading to a stiff equation of state at high densities consist of both the two-baryon repulsion via the vector-meson exchange and the universal three-baryon repulsion. Interplay of kaon condensates with hyperons through chiral dynamics in dense matter is clarified, and the resulting onset mechanisms of kaon condensation in hyperon-mixed matter and the equation of state with the ($Y+K$) phase and characteristic features of the system are presented. It is shown that the slope $L$ of the symmetry energy controls the two-baryon repulsion beyond the saturation density and the resulting stiffness of the equation of state. The stiffness of the equation of state in turn controls the admixture of hyperons and the onset and development of kaon condensates as a result of competing effects between kaon condensates and hyperons. The equation of state with the ($Y+K$) phase becomes stiff enough to be consistent with recent observations of massive neutron stars. Static properties of neutron stars with the ($Y+K$) phase are discussed, such as gravitational mass to radius, mass to baryon number density relations, and density distribution in the core with the ($Y+K$) phase for typical masses of neutron stars.