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

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 $ππ\, K\bar K$ 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 $ππ$-$K\bar K$-$ηη$ 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 $σ$, are of Breit--Wigner type.

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