Abstract

Motivated by the $\frac{1}{{N}_{c}}$ expansion, we present a simple model of $\ensuremath{\pi}\ensuremath{\pi}$ scattering as a sum of a current-algebra contact term and resonant pole exchanges. The model preserves crossing symmetry as well as unitarity up to 1.2 GeV. Key features include chiral dynamics, vector meson dominance, a broad low energy scalar ($\ensuremath{\sigma}$) meson, and a Ramsauer-Townsend mechanism for the understanding of the 980 MeV region. We discuss in detail the regularization (corresponding to rescattering effects) necessary to make all these nice features work.

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