The energy dependence of the ratio of elastic to total cross section in $pp$ and $\bar{p}p$ collisions

TL;DR

This paper analyzes how the ratio of elastic to total cross sections in proton-proton and antiproton-proton collisions depends on energy, providing models and estimates up to ultra-high energies relevant for colliders and cosmic rays.

Contribution

It introduces phenomenological analytic functions that accurately describe the energy dependence of the cross section ratio across a wide energy range, including ultra-high energies up to 10 PeV.

Findings

The ratio increases with energy and approaches asymptotic behavior.

Onset of the asymptotic region is indicated at energies above 5-10 PeV.

Models provide estimates for future collider and cosmic ray experiments.

Abstract

The paper presents the phenomenological analysis of the energy dependence for the ratio of elastic to total cross section in proton-proton and antiproton-proton scattering. The analytic functions based on the study of low- and high-energy experimental data for various scattering parameters provide the quantitative description of energy dependence of the ratio with statistically acceptable qualities in wide range of collision energy $\sqrt{s} \geq 3$ GeV in the case of the separate datasets for $pp$, $\bar{p}p$ collisions and at $\sqrt{s} \geq 5$ GeV for the joined experimental data ensemble. Based on the fit results the estimations are derived for the ratio of elastic to total cross section in $pp$ scattering at various $\sqrt{s}$ up to energy frontier $\sqrt{s}=10$ PeV which can be useful for present and future hadron colliders as well as for cosmic ray measurements at ultra-high energies. The indication is observed for onset of the asymptotic region at $\sqrt{s} \gtrsim 5-10$ PeV for the ratio of cross sections under consideration.