Energy Dependence of the Ratio of the Elastic-to-Total Cross Sections for Proton—Proton and Antiproton—Proton Collisions

Abstract

The results obtained from a phenomenological analysis of the ratio of the elastic-to-total cross sections for proton-proton (pp) and antiproton-proton ($(\bar pp)$) scattering as a function of energy are presented. Analytic functions proposed on the basis of studying low- and high-energy experimental data for various scattering parameters make it possible to obtain a statistically acceptable quantitative description of the energy dependence of this ratio over a broad energy region of $\sqrt s \ge 3$ GeV for individual samples of pp and $\bar pp$ collisions and over the region of $\sqrt s \ge 5$ GeV for a combined ensemble of experimental data. On the basis of the resulting approximations, the ratio of the elastic-to-total cross sections for pp collisions are estimated at various values of $\sqrt s$ up to an ultrahigh energy of $\sqrt s = 10$ PeV. The resulting estimates may prove to be useful for experiments at currently operating and future hadron colliders, as well as for measurements of ultrahigh-energy cosmic rays. An indication of the onset of the asymptotic region for the cross-section ratio in question is observed in the region of $\sqrt s \mathbin{\lower.3ex\hbox{$\buildrel>\over {\smash{\scriptstyle\sim}\vphantom{_x}}$}} 5 - 10$ PeV.