Black disk radius constrained by unitarity

TL;DR

The paper demonstrates that the high-energy behavior of elastic proton-proton scattering must follow a Froissart-like growth pattern to satisfy unitarity, linking the growth of the interaction radius with the increase in cross section.

Contribution

It establishes that a Froissart-like radius growth is the only consistent high-energy behavior for elastic scattering under unitarity constraints.

Findings

Froissart-like behavior ensures unitarity at high energies.

Large Rapidity Gap events require maximal cross section growth.

Interaction radius must grow as c*log(s) to satisfy unitarity.

Abstract

We argue that if the elastic proton-proton cross section increases with energy, the Froissart-like high energy behaviour of the elastic amplitude (which corresponds to a `black disk' of radius $R(s)=c\ln s-\beta\ln(\ln s)$) is the only possibility to satisfy the unitarity equation at each value of the impact parameter, $b$. Otherwise the cross section of events with Large Rapidity Gaps grows faster than the total cross section at the same $b$. That is, these `gap' events require {\it maximal} growth of the high-energy (asymptotic) cross section and of the interaction radius $R(s)$ in order to be consistent with unitarity.