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

Z. X. Sun·L. Y. Xiao·Z. G. Xiao·H. Q. Zheng
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Abstract

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.

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Z. X. Sun, L. Y. Xiao, Z. G. Xiao, H. Q. Zheng. 2005-03-19. Model dependent analyses on the $N_c$ dependence of the $σ$ pole trajectory. https://doi.org/10.1142/s0217732307023304

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