The Size Seems to Matter or Where Lies the "Asymptopia"?

TL;DR

The paper analyzes the relationship between proton sizes and scattering behaviors at high energies, suggesting the true asymptotic regime occurs at energies around 100 TeV, beyond current LHC capabilities.

Contribution

It introduces a correlation between cross-section growth and proton size effects, proposing the asymptotic regime lies at much higher energies than currently accessible.

Findings

Protons' proper sizes dominate the interaction region at LHC energies.

The asymptotic regime likely occurs at energies around 100 TeV.

Effective hadron sizes depend on interaction types.

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 LHC the proper sizes of the colliding protons comprise the bulk of the the interaction region. This seems to witness that the "asymptopia" - a hypothetical "truly asymptotic" regime - lies at energies no less than $\mathcal{O}$(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.