Exploring central opacity and asymptotic scenarios in elastic hadron scattering

Abstract

In the absence of a global description of the experimental data on elastic and soft diffractive scattering from the first principles of QCD, model-independent analyses may provide useful phenomenological insights for the development of the theory in the soft sector. With that in mind, we present an empirical study on the energy dependence of the ratio $X$ between the elastic and total cross sections; a quantity related to the evolution of the hadronic central opacity. The dataset comprises all the experimental information available on proton-proton and antiproton-proton scattering in the c.m. energy interval 5 GeV - 8 TeV. Generalizing previous works, we discuss four model-independent analytical parameterizations for $X$, consisting of sigmoid functions composed with elementary functions of the energy and three distinct asymptotic scenarios: either the standard black disk limit or scenarios above or below that limit. Our two main conclusions are the following: (1) although consistent with the experimental data, the black disk does not represent an unique solution; (2) the data reductions favor a semi-transparent scenario, with asymptotic average value for the ratio $\bar{X}$ = 0.30 $\pm$ 0.12. In this case, within the uncertainty, the asymptotic regime may already be reached around 1000 TeV. We present a comparative study of the two scenarios, including predictions for the inelastic channel (diffraction dissociation) and the ratio associated with the total cross-section and the elastic slope. Details on the selection of our empirical ansatz for $X$ and physical aspects related to a change of curvature in this quantity at 80 - 100 GeV, indicating the beginning of a saturation effect, are also presented and discussed.

41 pages, 10 figures, 13 tables; references [31], [90] and some misprints corrected

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• The Tsallis entropy and the BKT-like phase transition in the impact parameter space for $pp$ and $\bar{p}p$ collisions
• Analytization of elastic scattering amplitude
• Pomeron pole plus grey disk model: real parts, inelastic cross sections and LHC data
• Eikonal model analysis of elastic proton-proton collisions at 52.8 GeV and 8 TeV
• Hollowness effect and entropy in high energy elastic scattering
• Inelastic cross sections, overlap functions and Cq moments from ISR to LHC energies in proton interactions
• Energy evolution of the overlap functions: increasing ratio of ${\sigma }_{el}(s)/{\sigma }_{tot}(s)$ and black ring emergence
• Increasing effective intensity of soft strong interactions
• Parton Distribution Functions properties of the statistical model
• Will protons become gray at 13 TeV and 100 TeV?
• 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