Pion-Nucleon Scattering Lengths

Pion-nucleon scattering lengths have been calculated using a model in which $N$, $N^{*}$, $\rho$, and $\epsilon$ exchanges are assumed to dominate the low-energy pion-nucleon interaction. This simple model yields remarkably good agreement with the experimental $s$- and $p$-wave scattering lengths. We find that the coupling of the $\epsilon$ meson to the nucleon is consistent with estimates made using chiral symmetry and current algebra.