Total Hadronic Cross-Section Data and the Froissart–Martin Bound

TLDR: In this paper, the energy dependence of the total hadronic cross section at high energies is investigated with focus on the recent experimental result by the Total Elastic and Diffractive Cross-section Measurement Collabora- tion at 7 TeV and the Froissart-Martin bound.

Abstract: The energy dependence of the total hadronic cross section at high energies is investigated with focus on the recent experimental result by the Total Elastic and Diffractive Cross-section Measurement Collabora- tion at 7 TeV and the Froissart-Martin bound. On the basis of a class of analytical parametrization with the exponent γ in the leading logarithm contribution as a free parameter, different variants of fits to pp and ¯ pp total cross-section data above 5 GeV are developed. Two ensembles are considered, the first comprising data up to 1.8 TeV and the second also including the data collected at 7 TeV. We show that in all fit variants applied to the first ensemble, the exponent is statis- tically consistent with γ = 2. Applied to the second ensemble, however, the same variants yield γ values above 2, a result already obtained in two other analysis, by Amaldi et al. and by the UA4/2 Collaboration. As recently discussed by 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 consti- tutes an open problem.