Does antikaon condensed phase exist in neutron stars?

Neutron star matter including all the baryon octets and condensed antikaons is investigated by the extended Zimanyi-Moszkowski model. It is only the relativistic mean-…eld model to take into account both the (hidden) strange mesons and the e¤ectively density-dependent meson-baryon coupling constants. Even if we assume the deep K optical potential U K = 160MeV and strong NN and NN coupling constants, which are necessary for antikaon condensation in neutron star but are not consistent to the results of the most re…ned theoretical investigations, the maximum mass of neutron star is lower than the canonical value 1:44M . Consequently, antikaon condensed phase is unlikely to exist in neutron stars. Recently there are large interests on kaons in nuclear physics. One of them is the possibility that the antikaon condensed phase [1] may be formed in dense strange baryonic medium as neutron star (NS) matter because the antikaons feel an attraction in the medium. For one thing the existence of such a novel phase depends on the strength of the attraction, and for another the realistic description of the dense medium is necessary to predict it reliably. For the former the theoretical investigations [2-7] unfortunately predict the rather wide range of K optical potentials being from U K 50MeV to U K 180MeV. For the latter, although the relativistic models are most reliable at present, there are some variants that are essentially di¤erent from each other. The relativistic Brueckner-Hartree-Fock (RBHF) [8] theory is the most fundamental model of nuclear matter, but its extension to include all the baryon octets is not feasible at present. Therefore many studies of NS matter [9] have been done by the relativistic mean…eld (RMF) theories based on or inspired by the Walecka model [10]. The most widely used nonlinear extensions [11] of the Walecka model however are not realistic because they do not consider the medium dependences of meson-baryon coupling constants, which are realized in the RBHF theory and are essentially important to dense hadronic matter. In the RMF models including hyperons, the (hidden) strange mesons and [12] should be taken into account for the realistic description of YY interactions. In this respect the so-called DDRHmodel [13] is not suitable because of the di¢ culty to include the explicitly density-dependent Y Y ( ) coupling constants. Consequently, there remain only two possibilities of the realistic RMF models for dense baryon matter. They are the Zimanyi-Moszkowski (ZM) model [14,15] and the quark-meson coupling (QMC) model [16,17]. In contrast to the DDRH model, these models introduce the density-dependences