The light scalars: four- vs. two-quark states in the complex energy plane from Bethe-Salpeter equations

TL;DR

This paper investigates the nature of light scalar mesons by analyzing their quark composition and resonance properties using Bethe-Salpeter equations, revealing their dominant components and how these change with quark mass.

Contribution

It introduces a coupled Bethe-Salpeter framework to study scalar mesons' mixing and extends the analysis into the complex energy plane to determine their widths and internal structure.

Findings

The sigma meson is mainly a pi-pi resonance at physical quark masses.

The f0(980) and a0(980) have strong K-Kbar molecular components.

The quark composition of scalar mesons varies with quark mass.

Abstract

We study the dynamical generation of scalar mesons in the light quark sector ($q\in\{u,d,s\}$) and calculate the masses and widths for the $f_0(500),a_0(980)$ and $f_0(980)$. To this end we study the mixing of conventional $q\bar{q}$ and `exotic' $q\bar{q}q\bar{q}$ states via a coupled set of two-body Bethe-Salpeter equations based on a symmetry-preserving truncation of the underlying Dyson-Schwinger equations. This allows us to determine the dominant components of each state. Furthermore, we extend our previous framework into the complex energy plane such that we can study the analytic structure of the states in question and extract their width. At the physical point of small quark masses, the $\sigma$ meson is predominantly a $\pi\pi$ resonance. Consequently, its mass and width is driven by the effects of chiral symmetry breaking. At larger quark masses, however, the conventional $q\bar{q}$ components take over. Furthermore, we find a strong molecular $K\bar{K}$ component for both, the strange-light $f_0(980)$ and the $a_0(980)$.