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

Abstract

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 $pp$ and $\bar{p}p$ 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 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 $\gamma \sim 2.3\pm 0.1$ (T), $2.0\pm 0.2$ (A), $2.1\pm 0.2$ (T+A), with ${\chi }^2/\mathrm{DOF}\sim 1.07$ (T), $1.09$ (A), $1.14$ (T+A), suggesting extrema bounds for $\gamma$ given by 1.8 and 2.4. Fits with $\gamma =2$ (fixed) are also developed and discussed.

14 pages, 3 figures, 6 tables, one appendix added (discussing some TOTEM data at 8 TeV), minor corrections, few comments added. Matches version accepted for publication in Nucl. Phys. A

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Cited by in corpus (8)

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• Elastic and diffractive scattering in the LHC era
• Leading components in forward elastic hadron scattering: Derivative dispersion relations and asymptotic uniqueness
• Corrections to the Elastic Proton-Proton Analyzing Power Parametrization at High Energies
• Diffractive excitation in $pp$ and $pA$ collisions at high energies
• A model of diffractive excitation in $pp$ collisions at high energies
• Analytic components for the hadronic total cross-section: Fractional calculus and Mellin transform