New Dispersion Relations for Pion-Nucleon Scattering

Abstract

New relations expressing the imaginary part of the scattering amplitude as a coupling constant term and an integral over the physical spectrum of the real part of the amplitude are developed. These relations are applied to compute the meson-nucleon coupling constant from the experimental phase shifts, yielding the value ${f}^{2}=0.084$, and are used to compute the $s$-wave scattering lengths from the $p$-wave data.