NewπNSuperconvergent Sum Rules and Determination ofP′-Trajectory Parameters

New superconvergent dispersion relations for the forward, crossing-even $\pi N$ scattering amplitude have been derived and compared with experiment. The essential point is the assumption of dominant Regge behavior at high energy and the inclusion of the real part of the scattering amplitude. Sum rules for the $P$ and $P^{\prime }$ residues involving only experimentally accessible quantities are computed, using data of Höler and Lindenbaum. The Regge $P^{\prime }$ parameters are found as ${\alpha }_{P^{\prime }}\approx 0.39$, ${\gamma }_{P^{\prime }}\approx 1.82{\mu }^{-1\mathrm{}}$.