Where is the black disc limit?

Abstract

By using realistic models for elastic hadron scattering, we demonstrate that at present accelerator energies the s-channel unitarity bound is safe, not to be reached before $10^5$ GeV, while the black disc limit is saturated around 6 TeV. By increasing the energy, a larger transparency of the scattered particles near the center, surrounded by a black ring, is expected. Unitarity effects are incorporated and their effects are studied both in a phenomenological and formal, analytical way.