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

We describe a critical test of the pion-nucleon forward dispersion relations up to the highest energies practical at the Brookhaven alternating-gradient synchrotron involving a precise measurement of both the real and imaginary parts of the $\ensuremath{\pi}\ensuremath{-}N$ scattering amplitude. We find that the predictions of the $\ensuremath{\pi}\ensuremath{-}N$ forward dispersion relations are in good agreement with the experiment up to at least 20 BeV/c.