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

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.

Comments: Accepted for publication by Communications in Theoretical Physics