Sigma meson and lowest possible glueball candidate in an extended linear $\sigma$ model

TL;DR

This paper develops an extended linear sigma model incorporating quarkonia, tetraquarks, and glueball fields to analyze the scalar meson spectrum, focusing on the sigma meson and the lowest scalar glueball candidate.

Contribution

It introduces a comprehensive model that includes quark, tetraquark, and glueball components to study scalar mesons and their symmetries, providing insights into their masses and nature.

Findings

Estimated mass range for the lowest scalar glueball.

Insights into the nature of the sigma ($f_0(600)$) meson.

Discussion on symmetry breaking effects on scalar mesons.

Abstract

We formulate an extended linear $\sigma$ model of a quarkonia nonet and a tetraquark nonet as well as a complex iso-singlet (glueball) field to study the low-lying scalar meson. Chiral symmetry and $U_A(1)$ symmetry and their breaking play important role to shape the scalar meson spectrum in our work. Based on our study we will comment on what may be the mass of the lowest possible scalar and pseudoscalar glueball states. We will also discuss on what may be the nature of the sigma or $f_0(600)$ meson.