$a_{0}(980)$ as a companion pole of $a_{0}(1450)$

TL;DR

This paper shows that the light scalar mesons $a_{0}(980)$ and $a_{0}(1450)$ are related through a dynamical process where the lower state appears as a companion pole in the propagator of the higher state, influenced by meson-loop effects.

Contribution

It demonstrates that the $a_{0}(980)$ can be understood as a companion pole of $a_{0}(1450)$ arising from meson-loop contributions in the propagator.

Findings

The full one-loop propagator of $a_{0}(1450)$ contains two poles.

The positions of these poles depend on the coupling strength between interaction parts.

The $a_{0}(980)$ appears as a dynamically generated companion pole.

Abstract

Light scalar hadrons are often understood as dynamically generated resonances. These arise as `companion poles' in the propagators of $q\bar{q}$ seed states when accounting for meson-loop contributions to the self-energies of the latter. Following this idea, we demonstrate that for the scalar--isovector state $a_{0}(1450)$ the full one-loop propagator has two poles: a pole of the seed state $a_{0}(1450)$ and a companion pole corresponding to $a_{0}(980)$. The positions of these poles are studied by varying the relative coupling strength between the non-derivative and derivative parts of the interactions.