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

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 $.