Some Consequences from Superconvergence forπNScattering

Sum rules of the superconvergent type are obtained for the $\pi N$ helicity-flip and helicity-nonflip amplitudes. The sum rules for the helicity-nonflip amplitudes are shown to be consistent with the Regge-pole-dominance model. Investigation of the sum rule for $B^{\mathrm{}(-)\mathrm{}}\left(\nu \right)$ leads us to speculate as to the existence of resonances on $N_{\beta }$, ${\Delta }_{\gamma }$, and $N_{\delta }$ baryon trajectories.