Scaling of the elastic proton-proton cross-section

TL;DR

This paper investigates the scaling behavior of elastic proton-proton scattering cross-sections across ISR and LHC energies, revealing constant ratios and proposing new scaling laws based on observed properties.

Contribution

It introduces new scaling laws for elastic $pp$ scattering based on observed constant ratios of bump to dip positions over a wide energy range.

Findings

The ratio of bump to dip positions remains constant across energies.

Geometric scaling observed at ISR energies.

New scaling laws proposed for LHC energies.

Abstract

We discuss scaling properties of the elastic $pp$ cross-section both at the ISR and the LHC. We observe that the ratio of bump to dip positions of the differential cross-section $d\sigma_{\rm el}/dt$ is constant over a wide energy range. We next study the consequences of this property, including geometric scaling at the ISR and new scaling laws at the LHC.