Application of Dispersion Relations to Meson-Nucleon Scattering

Relativistic nonforward scattering dispersion relations are used to obtain information about low-energy meson-nucleon scattering. It is determined which of the $s$-, $p$-, and $d$-wave phase shifts are predicted by dispersion theory. Charge independence is assumed. The form of the dispersion relations used is justified by relating the asymptotic energy dependence of the dispersion relation amplitudes to the assumption of a finite range of interaction and to the choice of a particular meson current and the usual equal time commutation relations. The relevence of the analytic properties of the scattering amplitude as a function of momentum transfer is discussed in connection with the partial wave expansion of the dispersion amplitudes. The contribution to the dispersion integrals from energies above the 33 resonance is estimated.