The rise of 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. Using derivative dispersion relations with one subtraction, two different fits to proton-proton and antiproton-proton total cross section and ρ parameter data are developed, reproducing well 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 satisfactory results. From these empirical results we extract the energy dependence of several physical quantities: inelastic cross section, ratios elastic/total, inelastic/total cross sections, ratio total-cross-section/elasticslope, elastic slope and optical point. All data, fitted and predicted, are quite well described. We find a statistically consistent solution indicating: (1) an increase of the hadronic cross sections with the energy faster than the logsquared 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 Azimov on the rise of the total cross section.

A forward amplitude analysis on pp andpp elastic scattering above 5 GeV is presented. The dataset includes the recent high-precision TOTEM measurements of the pp total and elastic (integrated) cross-sections at 7 TeV and 8 TeV. Following previous works, the leading high-energy contribution for the total cross-section (σtot) is parametrized as ln γ (s/s h ), where γ and s h are free real fit parameters. Singly-subtracted derivative dispersion relations are used to connect σtot and the rho parameter (ρ) in an analytical way. Different fit procedures are considered, including individual fits to σtot data, global fits to σtot and ρ data, constrained and unconstrained data reductions. The results favor a rise of the σtot faster than the log-squared bound by Froissart and Martin at the LHC energy region. The parametrization for σtot is extended to fit the elastic cross-section (σ el ) data with satisfactory results. The analysis indicates an asymptotic ratio σ el /σtot consistent with 1/3 (as already obtained in a previous work). A critical discussion on the correlation, practical role and physical implications of the parameters γ and s h is presented. The discussion confronts the 2002 prediction of σtot by the COMPETE Collaboration and the recent result by the Particle Data Group (2012 edition of the Review of Particle Physics). Some conjectures on possible implications of a fast rise of the proton-proton total cross-section at the highest energies are also presented.

A comparative study on some representative parametrizations for the total and elastic cross-sections as a function of energy is presented. The dataset comprises pp andpp scattering in the c.m energy interval 5 GeV -8 TeV. The parametrization for the total cross-section at low and intermediate energies follows the usual reggeonic structure (non-degenerate trajectories). For the leading high-energy pomeron contribution, we consider three distinct analytic parametrizations: either a power (P ) law, or a log-squared (L2) law or a log-raised-to-γ (Lγ) law, where the exponent γ is treated as a real free fit parameter. The parametrizations are also extended to fit the elastic (integrated) cross-section data in the same energy interval. Our main conclusions are the following: (1) the data reductions with the logarithmic laws show strong dependence on the unknown energy scale involved, which is treated here either as a free parameter or fixed at the energy threshold; (2) the fit results with the P law, the L2 law (free scale) and the Lγ law (fixed scale and exponent γ above 2) are all consistent within their uncertainties and with the experimental data up to 7 TeV, but they partially underestimate the high-precision TOTEM measurement at 8 TeV;(3) once compared with these results, the L2 law with fixed scale is less consistent with the data and, in the case of a free scale, this pomeron contribution decreases as the energy increases below the scale factor (which lies above the energy cutoff); (4) in all cases investigated, the predictions for the asymptotic ratio between the elastic and total cross-sections, within the uncertainties, do not exceed the value 0.430 (therefore, below the black-disc limit) and the results favor rational limits between 1/3 and 2/5. We are led to conclude that the rise of the hadronic cross-sections at the highest energies still constitutes an open problem, demanding further and detailed investigation.

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 γ in the leading logarithm contribution as a free parameter, different variants of fits to pp andpp 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 γ = 2. Applied to the second ensemble, however, the same variants yield γ's above 2, a result already obtained in two other analysis, by U. Amaldi 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. PACS numbers: 13.85.-t Hadron-induced high-and super-high-energy interactions, 13.85.Lg Total cross sections, 11.10.Jj Asymptotic problems and properties

In the absence of a global description of the experimental data on elastic and soft diffractive scattering from the first principles of QCD, model-independent analyses may provide useful phenomenological insights for the development of the theory in the soft sector. With that in mind, we present an empirical study on the energy dependence of the ratio X between the elastic and total cross sections; a quantity related to the evolution of the hadronic central opacity. The dataset comprises all the experimental information available on proton-proton and antiproton-proton scattering in the c.m energy interval 5 GeV -8 TeV. Generalizing previous works, we discuss four model-independent analytical parameterizations for X, consisting of sigmoid functions composed with elementary functions of the energy and three distinct asymptotic scenarios: either the standard black disk limit or scenarios above or below that limit. Our two main conclusions are the following: (1) although consistent with the experimental data, the black disk does not represent an unique solution; (2) the data reductions favor a semi-transparent scenario, with asymptotic average value for the ratioX = 0.30 ± 0.12. In this case, within the uncertainty, the asymptotic regime may already be reached around 1000 TeV. We present a comparative study of the two scenarios, including predictions for the inelastic channel (diffraction dissociation) and the ratio associated with the total cross-section and the elastic slope. Details on the selection of our empirical ansatz for X and physical aspects related to a change of curvature in this quantity at 80 -100 GeV, indicating the beginning of a saturation effect, are also presented and discussed.