The scalar-isovector sector in the extended Linear Sigma Model

TL;DR

This paper investigates scalar isovector mesons within the extended Linear Sigma Model, focusing on their masses and decay widths, and finds that hadronic loops have limited impact on these properties.

Contribution

It provides a detailed analysis of the $a_{0}(1450)$ resonance and demonstrates that hadronic loop effects do not significantly alter tree-level predictions in the eLSM.

Findings

Hadronic loops minimally affect the $a_{0}(1450)$ properties.

The $a_{0}(980)$ is not generated as a pole by hadronic loops.

Tree-level results remain robust after loop inclusion.

Abstract

We study basic properties of scalar hadronic resonances within the so-called extended Linear Sigma Model (eLSM), which is an effective model of QCD based on chiral symmetry and dilatation invariance. In particular, we focus on the mass and decay width of the scalar isovector state $a_{0}(1450)$ and perform a numerical study of the propagator pole(s) on the unphysical Riemann sheets. In this work, this meson is understood as a seed state explicitly included in the eLSM. Our results show that the inclusion of hadronic loops does not modify much the previously obtained tree-level results. Moreover the $a_{0}(980)$ cannot be found as a propagator pole generated by hadronic loop contributions.