  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.
