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 $σ_{\mathrm{el} }(s)$. 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 $.

Figures (3)

• Figure 1: Cross-sections for pp collisions as a function of total center-of-mass energy $\sqrt{s}$. The experimental data for $\sigma_{\mathrm{tot}}(s)$ and $\sigma_{\mathrm{el}}(s)$ are from [21-23], lines represent a fit according to the form: $\sigma_{\mathrm{el,tot}}=C_{2} x^{2}+C_{1} x+C_{0}+C_{4} e^{-x} , \, x=\ln(\sqrt{s})$. Inelastic cross-section and $\Delta$ are given by $\sigma_{\mathrm{inel}}=(\sigma_{\mathrm{tot}}-\sigma_{\mathrm{el}})$ and $\Delta=(\sigma_{\mathrm{inel}}-\sigma_{\mathrm{el}})=(\sigma_{\mathrm{tot}}-2\,\sigma_{\mathrm{el}})$ both for data and for fits.
• Figure 2: The elastic to total cross-section ratio for pp collisions as a function of energy $\sqrt{s}$. The experimental data for $\sigma_{\mathrm{el}}$ and $\sigma_{\mathrm{tot}}$ are from Refs. [21--23], including the $\bar{p}$p data at $\sqrt{s}=546$ and 1800 GeV [21]. The line represents a ratio of the fits for $\sigma_{\mathrm{el}}$ and $\sigma_{\mathrm{tot}}$ (see Fig. 1 ).
• Figure 3: Ratio of the real to imaginary part of the elastic pp scattering amplitude in the forward direction as a function of energy $\sqrt{s}$ (the experimental data are from Refs. [21--22], including the $\bar{p}$p data at $\sqrt{s}=546$ and 1800 GeV [21]). The line represents a fit according to the form: $\rho=(a_{0} +a_{1}x+(a_{2} +a_{3}x) e^{-x})/ \sigma_{\mathrm{tot}},\, x=\ln(\sqrt{s})$, where the fit from Fig. 1 was used for $\sigma_{\mathrm{tot}}$.