On the rise of proton-proton cross-sections at high energies

TL;DR

This paper analyzes the increasing trend of proton-proton cross sections at high energies using empirical fits, revealing a rise faster than the Froissart bound and confirming unitarity constraints.

Contribution

It introduces a flexible analytical parametrization with a free exponent for the logarithmic rise, fitting extensive data and deriving asymptotic ratios consistent with unitarity and recent theoretical predictions.

Findings

Cross sections increase faster than log-squared bound

Asymptotic ratios for elastic/total and inelastic/total are 1/3 and 2/3

Empirical fits agree with unitarity and recent theories

Abstract

The rise of the total, elastic and inelastic hadronic cross sections at high energies is investigated by means of an analytical parametrization, with the exponent of the leading logarithm contribution as a free fit parameter. Using derivative dispersion relations with one subtraction, two different fits to proton-proton and antiproton-proton total cross section and rho parameter data are developed, reproducing well the experimental information in the energy region 5 GeV - 7 TeV. The parametrization for the total cross sections is then extended to fit the elastic (integrated) cross section data in the same energy region, with satisfactory results. From these empirical results we extract the energy dependence of several physical quantities: inelastic cross section, ratios elastic/total, inelastic/total cross sections, ratio total-cross-section/elastic-slope, elastic slope and optical point. All data, fitted and predicted, are quite well described. We find a statistically consistent solution indicating: (1) an increase of the hadronic cross sections with the energy faster than the log-squared bound by Froissart and Martin; (2) asymptotic limits 1/3 and 2/3 for the ratios elastic/total and inelastic/total cross sections, respectively, a result in agreement with unitarity. These indications corroborate recent theoretical arguments by Ya. I. Azimov on the rise of the total cross section.