Reciprocal Bootstrap of theNandN*Using the Static-Model Bethe-Salpeter Equation

Abstract

The Bethe-Salpeter equation is written down for the static model of $\pi N$ scattering. This equation satisfies unitarity exactly in the elastic region, but includes at least some inelasticity at higher energies. It is solved below the inelastic threshold by using the Noyes technique, and then making a Pagels-type approximation. It is applied to the reciprocal bootstrap problem of Chew, where $N^{*}$ exchange is assumed to provide the dominant force for binding the $N$, and $N$ exchange for giving rise to the $N^{*}$. Experimental values are used for the crossed-channel masses and couplings. The cutoff is adjusted to give the correct position for the direct-channel nucleon pole. This gives an output $N^{*}$ mass and residues which are in rough agreement with experiment.