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.