Pseudoscalar mesons in theSU(3)linear sigma model with Gaussian functional approximation

Abstract

We study the $SU(3)$ linear sigma model for the pseudoscalar mesons in the Gaussian functional approximation (GFA). We use the $SU(3)$ linear sigma model Lagrangian with nonet scalar and pseudoscalar mesons, including symmetry breaking terms. In the GFA, we take the Gaussian Ansatz for the ground state wave function and apply the variational method to minimize the ground state energy. We derive the gap equations for the dressed meson masses, which are actually just variational parameters in the GFA method. We use the Bethe-Salpeter equation for meson-meson scattering, which provides the masses of the physical nonet mesons. We construct the projection operators for the flavor $SU(3)$ in order to work out the scattering $T$ matrix in an efficient way. In this paper, we discuss the properties of the Nambu-Goldstone bosons in various limits of the chiral ${U}_{L}(3)\ifmmode\times\else\texttimes\fi{}{U}_{R}(3)$ symmetry.