AN UPDATED ANALYSIS ON THE RISE OF THE HADRONIC TOTAL CROSS-SECTION AT THE LHC ENERGY REGION

A forward amplitude analysis on pp and (p) over barp 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 (sigma(tot)) is parametrized as ln(gamma)(s/s(h)), where gamma and s(h) are free real fit parameters. Singly-subtracted derivative dispersion relations are used to connect sigma(tot) and the rho parameter (rho) in an analytical way. Different fit procedures are considered, including individual fits to sigma(tot) data, global fits to sigma(tot) and rho data, constrained and unconstrained data reductions. The results favor a rise of the sigma(tot) faster than the log-squared bound by Froissart and Martin at the LHC energy region. The parametrization for sigma(tot) is extended to fit the elastic cross-section (sigma(el)) data with satisfactory results. The analysis indicates an asymptotic ratio sigma(el)/sigma(tot) 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 gamma and s(h) is presented. The discussion confronts the 2002 prediction of sigma(tot) 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.