Z. X. Sun | Searcharxiv

arXiv2005

Model dependent analyses on the $N_c$ dependence of the $σ$ pole trajectory

We explore the nature of the$σ$ or $f_0(600)$ meson using large $N_c$ technique, assuming that the $σ$ pole dominates low energy physics in the IJ=00 channel. We trace the $N_c$ dependence of the $σ$ pole position using [1,1] Padé approximation of SU(3) chiral amplitude, [1,2] Padé approximation of SU(2) chiral amplitudes, and the PKU parametrization form. We find that in all 3 cases the $σ$ pole moves to the real axis of the complex $s$-plane. Finally we construct a pedagogical example using the SU(2) Padé amplitude to show that when the analyticity property of the scattering amplitude is violated, it is possible that the $σ$ pole resides on the complex $s$ plane when $N_c$ is large.

hep-ph↗

arXiv2004

On the nature of the lightest scalar resonances

We briefly review the recent progresses in the new unitarization approach being developed by us. Especially we discuss the large $N_c$ $ππ$ scatterings by making use of the partial wave $S$ matrix parametrization form. We find that the $σ$ pole may move to the negative real axis on the second sheet of the complex $s$ plane, therefore it raises the interesting question that this `$σ$' pole may be related to the $σ$ in the linear $σ$ model.

hep-ph↗