Total Hadronic Cross Section Data 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 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.

20 pages, 10 figures, introduction extended and general references added to match editorial style, to appear in the Brazilian Journal of Physics

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Cited by in corpus (8)

• On the rise of proton-proton cross-sections at high energies
• A study on analytic parametrizations for proton-proton cross-sections and asymptotia
• Leading components in forward elastic hadron scattering: Derivative dispersion relations and asymptotic uniqueness
• Hadronic total cross sections at high energy and the QCD spectrum
• Bounds on the rise of total cross section from LHC7 and LHC8 data
• An updated analysis on the rise of the hadronic total cross-section at the LHC energy region
• Froissart Bound, Diffraction Scattering of Hadrons and Scaling at Asymptotic Energies
• Analyticity Properties of Scattering Amplitude in Theories with Compactified Space Dimensions: The Proof of Dispersion Relations