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Unitarity Saturation In P-P Scattering

The properties of soft p-p scattering amplitudes at the TeV-scale are studied so as to identify the impact of s and t channel unitarity screenings on their behavior at exceedingly high energies and determine the rate at which they approach the bounds implied by unitarity saturation. I shall examine the relevant high energy soft cross section features, as well as, the corresponding behavior of the coupled phenomenological models aiming to reproduce this data.\\ My conclusion is that p-p black body saturation is not attained up to 100 TeV. More over, I do not expect that saturation will be attained at energies that can be investigated experimentally.