Total Hadronic Cross Section Data and the Froissart-Martin Bound

TL;DR

This paper analyzes high-energy hadronic total cross section data, especially recent 7 TeV results, testing the Froissart-Martin bound and exploring whether the cross section rise exceeds the squared logarithm, which remains an open question.

Contribution

It introduces a flexible parametrization of the cross section with a free exponent and compares fits across different energy datasets, highlighting the potential for a rise faster than the squared logarithm.

Findings

Exponent consistent with 2 up to 1.8 TeV

Exponent exceeds 2 when including 7 TeV data

Faster-than-log-squared rise does not violate unitarity

Abstract

The energy dependence of the total hadronic cross section at high energies is investigated with focus on the recent experimental result by the TOTEM Collaboration at 7 TeV and the Froissart-Martin bound. On the basis of a class of analytical parametrization with the exponent $\gamma$ in the leading logarithm contribution as a free parameter, different variants of fits to $pp$ and $\bar{p}p$ total cross section data above 5 GeV are developed. Two ensembles are considered, the first comprising data up to 1.8 TeV, the second also including the data collected at 7 TeV. We shown that in all fit variants applied to the first ensemble the exponent is statistically consistent with $\gamma$ = 2. Applied to the second ensemble, however, the same variants yield $\gamma$'s above 2, a result already obtained in two other analysis, by U. Amaldi \textit{et al}. and by the UA4/2 Collaboration. As recently discussed by Ya. I. Azimov, this faster-than-squared-logarithm rise does not necessarily violate unitarity. Our results suggest that the energy dependence of the hadronic total cross section at high energies still constitute an open problem.