Causality in the Pion-Proton Scattering

Dispersion relations applicable to particles with mass and charge have been used for analyzing pion-proton scattering data. In these relations, experimental values of the total cross sections for ${\pi }^{+}$ and ${\pi }^{-}$ from 0 to 1.9 Bev were used to calculate the real part of the forward scattering amplitudes, and these were compared with the results of phase-shift analyses. With suitable choice of the pion-nucleon coupling constant, good agreement can be obtained for the phase-shift solutions with a resonant behavior for ${\alpha }_{33}$.