Signs of universality in the behavior of elastic $\text{pp}$ 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 $\text{pp}$ 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 $(m_{{\pi }^0}/m_p)$, the minimum value of the ratio $({\sigma }_{\mathrm{el}}/{\sigma }_{\mathrm{tot}})$, and some other quantities are determined by the roots of the equation $(9x^2+4\sqrt{2}x-1)=0$.

Comments: 11 pages, 3 figures