D. A. Fagundes, M. J. Menon, P. V. R. G. Silva
The rise 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 possible qualitative saturation of the Froissart-Martin bound. Based on a class of analytical parametrization with the exponent 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 one with data up to 1.8 TeV and the second one by adding the data at 7 TeV. It is shown that in all fit variants the exponent is statistically consistent with the value 2 in the former case, but above 2 in the latter case, as already indicated in two other analysis by U. Amaldi et al. and by the UA4/2 Collaboration. This increase faster than the logarithm squared is not necessarily related to violation of unitarity, as recently discussed by Ya. I. Azimov, and suggests that the rise of the total cross section may still constitute an open problem.
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http://arxiv.org/abs/1112.4704
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