Signs of universality in the behavior of elastic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si8.svg"> <mml:mi mathvariant="italic">pp</mml:mi> </mml:math> scattering cross-sections at high energies

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 $σ_{\mathrm{el} }(s)$. We observed that the value of the fundamental ratio $(m_{π^{\mathrm{0}}}/m_{p}) $, the minimum value of the ratio $ (σ_{\mathrm{el}}/σ_{\mathrm{tot}})$, and some other quantities are determined by the roots of the equation $ (9\,x^{2}+4\,\sqrt{2}\,x-1)=0 $.