Universal properties of elastic pp cross section from the ISR to the LHC

TL;DR

This paper investigates the consistent ratio of bump to dip positions in elastic proton-proton scattering across energies from the ISR to the LHC, highlighting geometric scaling and its implications for scattering parameters.

Contribution

It demonstrates that the ratio of bump to dip positions remains constant over a wide energy range, extending geometric scaling concepts to LHC energies.

Findings

The bump to dip position ratio is constant from ISR to LHC energies.

Geometric scaling applies at LHC energies as previously thought at ISR.

Implications for the $ ho$ parameter and cross section ratios are discussed.

Abstract

We explore the phenomenology of the property that the ratio of bump to dip {\em positions} of the elastic differential $pp$ cross section is constant over the energy range from the ISR to the LHC. We review the old idea of geometric scaling at the ISR and argue that it also holds at the LHC. We discuss its consequences for the $\rho$ parameter and for the ratio of bump to dip cross section {\em values}.