Pole Analysis of Unitarized One Loop $\chi$PT Amplitudes - A Triple Channel Study

TL;DR

This paper extends a pole analysis method to a three-channel system involving $ o$, $Kar{K}$, and $ o o$ interactions, confirming the nature of certain resonances like $f_0(980)$ and $$.

Contribution

It generalizes a previous pole analysis method to a three-channel system, providing insights into the dynamical origin of scalar mesons.

Findings

$f_0(980)$ is identified as a $Kar{K}$ molecule.

Most poles are of Breit-Wigner type.

The analysis confirms previous predictions about resonance nature.

Abstract

In a previous paper (Commun. Theor. Phys. 57 (2012) 841), we proposed a method to distinguish poles of different dynamical origin, in a unitarized amplitude of $\pi\pi\, K\bar K$ system. That is based on the observation that `A Breit-Wigner resonance should exhibit two poles on different Riemann sheets which meet each other on the real axis when $N_c=\infty$'. In this paper, we extend our previous work (Commun.Theor.Phys. 57 (2012) 841) to the $\pi\pi$-$K\bar K$-$\eta\eta$ three channel system. We reconfirm most of the previous predictions. Especially the $f_0(980)$ is of $K\bar K$ molecule nature. Other poles, including the $\sigma$, are of Breit--Wigner type.