Investigation of the Role of Elastic Unitarity in High-Energy Scattering: Gribov's Theorem and the Froissart Bound

We re-examine V. Gribov's theorem of 1960 according to which the total cross-section cannot approach a finite non-zero limit with, at the same time, a diffraction peak having a finite slope. We are very close to proving by an explicit counter-example that elastic unitarity in the elastic region is an essential ingredient of the proof. By analogy, we raise the question of the saturation of the Froissart-Martin bound, for which no examples incorporating elastic unitarity exist at the present time.