Neutral pion condensation in the chiralSU(3)⊗SU(3)model

Abstract

A pure p-wave ${\ensuremath{\pi}}^{0}$ condensation in the chiral $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ model is studied within the relativistic mean-field approximation and its effect on the equation of state is compared with that of a pure s-wave ${K}^{\ensuremath{-}}$ condensation. To this end, three models are considered, which are distinguished from each other in the ways \ensuremath{\sigma}, \ensuremath{\omega}, and \ensuremath{\rho} mesons contribute to the system's energy. We find that, although the details of the result are model dependent, the ${\ensuremath{\pi}}^{0}$ condensation forming a standing wave is commonly observed in the intermediate region of density. In particular, in case \ensuremath{\omega}'s mass is generated through coupling to \ensuremath{\sigma}, ${\ensuremath{\pi}}^{0}$ condensation reduces the system's energy significantly. The pure ${\ensuremath{\pi}}^{0}$ condensation tends to be taken over by the pure uniform ${K}^{\ensuremath{-}}$ condensation at high densities because of the dominance of the KN sigma term.