Experimental Test of the Pion-Nucleon Forward Dispersion Relations at High Energies

The small-angle differential scattering cross sections of protons for pions have been measured to high precision at the Brookhaven AGS. The range of incident momenta was 8-20 GeV/c for ${\ensuremath{\pi}}^{+}$, and 8-26 GeV/c for ${\ensuremath{\pi}}^{\ensuremath{-}}$. The real part of the pion-nucleon forward scattering amplitude was determined by observing its interference with the known Coulomb amplitude. Combining these results with precision measurements of pion-proton total cross sections over this energy range provided a critical test of the predictions of the forward dispersion relations. The results demonstrate the validity of the dispersion relations up to at least 20 GeV/c laboratory momentum. The predictions of charge independence are also verified by comparing these experimental measurements with forward charge-exchange scattering cross sections. Furthermore, if microscopic causality is violated, this occurs at "distances" less than ${10}^{\ensuremath{-}15}$ cm.