Resonance Model for $\pi$N Scattering and $\eta$-Meson Production in the s${}_{11}$ Channel

Abstract

A model for $\pi$N scattering and $\eta$-meson production in the S${}_{11}$ channel is presented. The model includes $\pi$N-scattering Born terms as well as the N${}^{\ast }${} 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 $\pi$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 ${\pi }^{-}+p\to \eta +n$ is obtained without further adjustment of parameters.

LaTex 10 pages, 4 figures (not included;the postscript-figures are available from [email protected] in subdirectory pub/sauerman, files: fig1.ps, fig2.ps,fig3.ps,fig4.ps- or contact the authors via e-mail), GSI-94-45