A study on analytic parametrizations for proton-proton cross-sections and asymptotia

Abstract

A comparative study on some representative parametrizations for the total and elastic cross-sections as a function of energy is presented. The dataset comprises pp and \bar{p}p scattering in the c.m energy interval 5 GeV-8 TeV. The parametrization for the total cross-section at low and intermediate energies follows the usual reggeonic structure (non-degenerate trajectories). For the leading high-energy pomeron contribution, we consider three distinct analytic parametrizations: either a power (P) law, or a log-squared (L2) law or a log-raised-to-gamma (Lgamma) law, where the exponent gamma is treated as a real free fit parameter. The parametrizations are also extended to fit the elastic (integrated) cross-section data in the same energy interval. Our main conclusions are the following: the data reductions with the logarithmic laws show strong dependence on the unknown energy scale involved, which is treated here either as a free parameter or fixed at the energy threshold; the fit results with the P law, the L2 law (free scale) and the Lgamma law (fixed scale and exponent gamma above 2) are all consistent within their uncertainties and with the experimental data up to 7 TeV, but they partially underestimate the high-precision TOTEM measurement at 8 TeV; once compared with these results, the L2 law with fixed scale is less consistent with the data and, in the case of a free scale, this pomeron contribution decreases as the energy increases below the scale factor (which lies above the energy cutoff); in all cases investigated, the predictions for the asymptotic ratio between the elastic and total cross-sections, within the uncertainties, do not exceed the value 0.430 (therefore, below the black-disc limit) and the results favor rational limits between 1/3 and 2/5. We are led to conclude that the rise of the hadronic cross-sections at the highest energies still constitutes an open problem.

40 pages, minor corrections, matches the published version

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Cited by in corpus (15)

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• $pp$ and $\bar{p}p$ total cross sections and elastic scattering
• Using the Tsallis distribution for hadron spectra in $pp$ collisions: Pions and quarkonia at $\sqrt{s}$ = 5--13000 GeV
• Soft Pomerons and the Forward LHC Data
• Exploring central opacity and asymptotic scenarios in elastic hadron scattering
• Forward Elastic Scattering and Pomeron Models
• Leading components in forward elastic hadron scattering: Derivative dispersion relations and asymptotic uniqueness
• Nonlinear effects and the behavior of total hadronic and photonic cross sections
• Bounds on the rise of total cross section from LHC7 and LHC8 data
• Asymptotic Behaviour of Pion--Pion Total Cross-Sections
• Can Froissart Bound Explain Hadron Cross-Sections at High Energies?
• Updating an empirical analysis on the proton's central opacity and asymptotia
• An investigation on the leading and subleading high-energy behavior of hadron-hadron total cross sections using a best-fit analysis of hadronic scattering data
• Pomeron Physics at the LHC