Pseudoscalar Mesons in the SU(3) Linear Sigma Model with Gaussian Functional Approximation

TL;DR

This paper investigates the properties of pseudoscalar mesons within the SU(3) linear sigma model using the Gaussian Functional Approximation, deriving meson masses and analyzing Nambu-Goldstone bosons in different symmetry limits.

Contribution

It introduces a variational GFA approach to compute meson masses and scattering properties in the SU(3) linear sigma model, including symmetry breaking effects.

Findings

Derived gap equations for dressed meson masses.

Calculated physical meson masses via Bethe-Salpeter equation.

Analyzed Nambu-Goldstone bosons in various symmetry limits.

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 pseudo-scalar 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 $U_L(3)\times U_R(3)$ symmetry.