Saturation Effects in Hadronic Cross Sections
  We compute total and differential elastic cross sections of high-energy hadronic collisions in the loop-loop correlation model that provides a unified description of hadron-hadron, photon-hadron, and photon-photon reactions. The impact parameter profiles of pp and gamma*p collisions are calculated. For ultra-high energies the hadron opacity saturates at the black disc limit which tames the growth of the hadronic cross sections in agreement with the Froissart bound. We compute the impact parameter dependent gluon distribution of the proton xG(x,Q^2,b) and find gluon saturation at small Bjorken x. These saturation effects manifest S-matrix unitarity in hadronic collisions and should be observable in future cosmic ray and accelerator experiments at ultra-high energies. The c.m. energies and Bjorken x at which saturation sets in are determined and LHC and THERA predictions are given. 
Arif I. Shoshi, Frank D. Steffen