Signs of universality in the behavior of elastic $\textit{pp}$ scattering cross-sections at high energies

TL;DR

The paper analyzes high-energy proton-proton scattering cross-sections, suggesting a universal behavior driven by the rapid increase of inelastic cross-sections and their ratios, linked to fundamental physical constants.

Contribution

It introduces a phenomenological model connecting cross-section ratios to roots of a specific quadratic equation, highlighting universal features in high-energy pp scattering.

Findings

Inelastic cross-section increases rapidly with energy.

The ratio of elastic to total cross-section approaches a universal value.

Key ratios are determined by roots of a quadratic equation.

Abstract

We give a phenomenological analysis of the behavior of inelastic, elastic and total cross-sections of the high energy $\textit{pp}$ interaction. In particular, we argue that the universal picture of behavior of cross-sections and their ratios is a consequence of the rapid increase of inelastic cross-section with energy and its large value compared to $\sigma_{\mathrm{el} }(s)$. We observed that the value of the fundamental ratio $(m_{\pi^{\mathrm{0}}}/m_{p}) $, the minimum value of the ratio $ (\sigma_{\mathrm{el}}/\sigma_{\mathrm{tot}})$, and some other quantities are determined by the roots of the equation $ (9\,x^{2}+4\,\sqrt{2}\,x-1)=0 $.