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

Recent measurements of the proton-proton total cross section σtot 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 σtot and ρ data from pp and p¯p 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 RRPLγ parametrization for σtot(s), consisting of two Reggeons (RR), one critical Pomeron (P) and a leading log-raised-to-gamma (Lγ) contribution (with γ as a free fit parameter), analytically connected to ρ(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 γ∼2.3±0.1 (T), 2.0±0.1 (A), 2.2±0.2 (T+A), with χ2/DOF∼1.07 (T), 1.09 (A), 1.14 (T + A), suggesting extrema bounds for γ given by 1.9 and 2.4. Fits with γ=2 (fixed) are also developed and discussed.