Bounds on the rise of total cross section from LHC7 and LHC8 data

Recent measurements of the proton proton total cross section sigma(tot) at 7 and 8 TeV by the TOTEM and ATLAS Collaborations are characterized by some discrepant values: the TOTEM data suggest a rise of the cross section with the energy faster than the ATLAS data. Attempting to quantify these different behaviors, we develop new analytical fits to sigma(tot) and rho data from (p) over barp and pp scattering in the energy region 5 GeV-8 TeV. The dataset comprises all the accelerator data below 7 TeV and we consider three ensembles by adding: either only the TOTEM data (T), or only the ATLAS data (A), or both sets (T + A). For the purposes, we use our previous RRPL gamma parametrization for sigma(tot) (s), consisting of two Reggeons (RR), one critical Pomeron (P) and a leading log-raised-to-gamma (L gamma) contribution (with gamma as a free fit parameter), analytically connected to rho(s) through singly-subtracted derivative dispersion relations and energy scale fixed at the physical threshold. The data reductions with ensembles T and A present good agreement with the experimental data analyzed and cannot be distinguished on statistical grounds. The quality of the fit is not as good with ensemble T + A. The fit results provide gamma similar to 2.3 +/- 0.1 (T), 2.0 +/- 0.1 (A), 2.2 +/- 0.2 (T + A), with x(2)/DOF similar to 1.07 (T), 1.09 (A), 1.14 (T + A), suggesting extrema bounds for gamma given by 1.9 and 2.4. Fits with gamma = 2 (fixed) are also developed and discussed. (C) 2017 Elsevier B.V. All rights reserved.