Analyticity and the $N_c$ counting rule of $S$ matrix poles

Details Analyticity and the $N_c$ counting rule of $S$ matrix poles Analyticity and the $N_c$ counting rule of $S$ matrix poles

2005-02-22

arxiv.org/abs/hep-ph/0502199v1

Mod.Phys.Lett.A22:55-64,2007

Physics

High Energy Physics

High Energy Physics - Phenomenology

This paper replaces hep-ph/0412175. The latter is withdrawn

Scientific paper

10.1142/S0217732307020713

By studying $\pi\pi$ scattering amplitudes in the large $N_c$ limit, we clarify the $N_c$ dependence of the $S$ matrix pole position. It is demonstrated that analyticity and the $N_c$ counting rule exclude the existence of $S$ matrix poles with ${\cal M}, \Gamma\sim O(1)$. Especially the properties of $\sigma$ and $f_0(980)$ with respect to the $1/N_c$ expansion are discussed. We point out that in general tetra-quark resonances do not exist.

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