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

Abstract

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