Kaon-baryon coupling schemes and kaon condensation in hyperon-mixed matter

TL;DR

This paper compares two kaon-baryon coupling schemes within relativistic mean-field theory to understand their effects on kaon condensation onset and the equation of state in hyperon-rich dense matter, relevant for neutron star physics.

Contribution

It introduces a detailed comparison between contact interaction and meson-exchange schemes for kaon-baryon interactions, highlighting their impact on kaon condensation and the equation of state.

Findings

Meson-exchange scheme raises the kaon condensation onset density due to scalar self-interaction.

Nonlinear self-interacting meson terms do not significantly stiffen the equation of state at high densities.

Contact interaction scheme requires additional effects to match observations of massive neutron stars.

Abstract

Possible coexistence of kaon condensation and hyperons in highly dense matter [the ($Y+K$) phase] is investigated on the basis of the relativistic mean-field theory combined with the effective chiral Lagrangian. Two coupling schemes for the $s$-wave kaon-baryon interaction are compared regarding the onset density of kaon condensation in the hyperon-mixed matter and equation of state for the developed ($Y+K$) phase: One is the contact interaction scheme related to the nonlinear effective chiral Lagrangian. The other is the meson-exchange scheme, where the interaction vertices between the kaon field and baryons are described by exchange of mesons (sigma, sigma^* mesons for scalar coupling, and omega, rho, phi mesons for vector coupling). It is shown that in the meson exchange scheme, the contribution from the nonlinear scalar self-interaction gives rise to a repulsive effect for kaon effective energy, pushing up the onset density of kaon condensation as compared with the case of the contact interaction scheme. In general, the difference of kaon-baryon dynamics between the contact interaction scheme and the meson-exchange scheme relies on the specific forms of the nonlinear self-interacting meson terms. It is shown that the nonlinear self-interacting term is not relevant to repulsive energy leading to stiffening of the equation of state at high densities and that it cannot be compensated with large attractive energy due to the appearance of the ($Y$+$K$) phase in the case of the contact interaction scheme. We also discuss in the contact interaction scheme what effects are necessary so as to make the equation of state with (Y+K) phase stiff enough to be consistent with recent observations of massive neutron stars.