$a_{0}(980)$ revisited

TL;DR

This paper revisits the nature of the light scalar meson $a_{0}(980)$, demonstrating it as a dynamically generated resonance arising as a companion pole in the propagator of the quark-antiquark state $a_{0}(1450)$, with results matching experimental data.

Contribution

The study extends previous models by constructing an effective Lagrangian and calculating self-energies, showing the $a_{0}(980)$ as a companion pole of $a_{0}(1450)$ with accurate pole positions.

Findings

Identified two poles in the propagator: $a_{0}(980)$ and $a_{0}(1450)$.

Pole positions agree quantitatively with experimental data.

Supports the interpretation of light scalar mesons as dynamically generated resonances.

Abstract

Light scalar hadrons can be understood as dynamically generated resonances. These arise as `companion poles' in the propagators of quark-antiquark seed states when accounting for meson-loop contributions to the self-energies of the latter. Along this line, we extend previous calculations of T\"ornqvist and Roos and of Boglione and Pennington, where the resonance $a_{0}(980)$ appears as companion pole in the propagator of $a_{0}(1450)$ which is predominantly a quark-antiquark state. We also construct an effective Lagrangian where $a_{0}(1450)$ couples to pseudoscalar mesons with both non-derivative and derivative interactions. Computing the one-loop self-energy, we demonstrate that the propagator has two poles: a companion pole corresponding to $a_{0}(980)$ and a pole of the seed state $a_{0}(1450)$. The positions of these poles are in quantitative agreement with experimental data.