Scaling properties of elastic pp cross-section

TL;DR

This paper investigates the universal scaling property of the elastic proton-proton cross-section across different energies, revealing a consistent ratio in the bump-to-dip position and proposing a family of scaling laws at the LHC.

Contribution

It introduces a universal property of the elastic pp cross-section and compares geometric scaling at ISR energies with proposed LHC scaling laws.

Findings

The bump-to-dip position ratio remains constant across ISR to LHC energies.

A family of scaling laws is consistent with current LHC experimental uncertainties.

Geometric scaling at ISR differs from the proposed LHC scaling law.

Abstract

We show that the elastic differential $pp$ cross-section has a unique universal property that the ratio of bump-to-dip position is constant from the energies of the ISR to the LHC. We explore this property to compare Geometric Scaling present at the ISR with the recently proposed scaling law at the LHC. We argue that at the LHC, within present experimental uncertainties, there is fact a family of scaling laws.