The size seems to matter or where lies the “asymptopia”?

Abstract

We discuss an apparent correlation between the onset of the rising regime for the total cross-sections and the slowdown of the rise of the forward slopes with energy. It is shown that even at highest energies achieved with the large hadron collider (LHC) the proper sizes of the colliding protons comprise the bulk of the interaction region. This seems to witness that the “asymptopia” — a hypothetical “truly asymptotic” regime — lies at energies no less than [Formula: see text] (100 TeV). In the course of reasoning, we also discuss the question of the dependence of the effective sizes of hadrons in collision on the type of their interaction.