Proton-proton cross-sections: the interplay between density and radius

TL;DR

This paper presents a simple model explaining the growth of proton-proton cross-sections at high energies through density increase and radial expansion, successfully fitting data from ISR to LHC and proposing a mechanism for cosmic ray energies.

Contribution

It introduces a model combining density saturation and radial expansion to explain high-energy pp cross-section growth, aligning with experimental data.

Findings

Model reproduces all available pp data from ISR to LHC.

Proposes a two-mechanism growth involving density saturation and radial expansion.

Suggests a transition to geometric scaling at very high energies.

Abstract

We argue that there are two mechanisms responsable for the growth of high energy cross-sections - \sigma_{tot} and \sigma_{el}, say - in pp collisions. One is by the increase of matter \emph{density}, resulting in the black disk saturation. The other is by exclusively radial expansion affecting the periphery of the overlap area. Within this simple model we can reproduce all available data in pp from ISR to LHC. In order to achieve a fast growth in the very high energy cosmic ray energies, we propose a fast black disk saturation followed by the dominance of geometric scaling (GS).