1208.3456 (D. A. Fagundes et al.)

On the rise of the proton-proton cross-sections at high energies    [PDF]

D. A. Fagundes, M. J. Menon, P. V. R. G. Silva

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. Making use of derivative dispersion relations with one subtraction, two different fits to proton-proton and antiproton-proton total cross section and rho parameter data are developed, leading to a good reproduction of 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 quite good results. From these empirical results we extract the dependence on the energy 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, including in the latter case the estimations of the total cross sections from cosmic-ray experiments. We conclude that, once the TOTEM Collaboration results for the total and elastic cross sections at 7 TeV are confirmed, our analysis indicates: (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.

View original: http://arxiv.org/abs/1208.3456