Scaling laws of elastic proton-proton scattering differential cross sections

TL;DR

This paper investigates the universal scaling properties of elastic proton-proton scattering cross sections across a wide energy range, revealing a consistent bump-to-dip ratio and proposing a family of scaling laws that constrain scattering amplitude models.

Contribution

It identifies a universal property of the bump-to-dip ratio in elastic pp scattering and introduces a family of scaling laws at LHC energies, advancing understanding of scattering amplitude parametrizations.

Findings

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

A family of scaling laws describes elastic pp scattering at high energies.

Scaling laws impose constraints on scattering amplitude models.

Abstract

We show that elastic scattering $pp \to pp $ differential cross sections as function of the four-momentum transfer square $|t|$ have a universal property, such that the ratio of bump-to-dip positions is constant from the energies of the ISR to the LHC, from tens of GeV and up to the TeV scale. We explore this property to compare the geometrical scaling observed at the ISR with the recently proposed scaling law at the LHC. We argue that, at the LHC, within present experimental uncertainties, there is in fact a family of scaling laws. We discuss the constraints that the scaling laws impose on the parametrization of the elastic $pp\to pp$ scattering amplitude.