Resonance Model for $π$N Scattering and $η$-Meson Production in the s$_{11}$ Channel

Abstract

A model for $π$N scattering and $η$-meson production in the S$_{11}$ channel is presented. The model includes $π$N-scattering Born terms as well as the N$^*${} resonances S$_{11}$(1535) and S$_{11}$(1610). The $T$-matrix is computed in the $K$-matrix approximation. The parameters of the model are determined by fitting the elastic $π$N-scattering $T$-matrix to empirical data. We find an excellent fit for all energies up to $\sqrt{s}$ = 1.75 GeV. Furthermore, a good description of the cross section for $π^- + p \rightarrow η+ n$ is obtained without further adjustment of parameters.