Superconvergence and Regge Poles. I. Odd-Signature Exchanges

A method is used in which the usual analytic properties of the $\pi N$ scattering amplitude are exploited in a more complete way to obtain information about $\rho$-type Regge poles. It is found that the low-energy data determine the forward Reggeized $\rho$-meson-exchange parameters quite accurately. These are found to be in complete agreement with high-energy analyses. We are also able to see that in the forward direction, only $\rho$-meson exchange is allowed to a very good approximation. The evaluation of low-energy parameters and the prediction of forward pion charge-exchange scattering are also discussed. A criterion is given relating the validity of the "interference" model to the behavior of the general sum rule.