Exploring central opacity and asymptotic scenarios in elastic hadron scattering

TL;DR

This study analyzes the energy dependence of the ratio between elastic and total cross sections in hadron scattering, suggesting a semi-transparent asymptotic scenario and indicating the possible onset of saturation effects around 80-100 GeV.

Contribution

It introduces four model-independent parameterizations for the ratio, exploring different asymptotic scenarios and providing new insights into the central opacity evolution in hadron scattering.

Findings

The black disk limit is not the only solution consistent with data.

Data favor a semi-transparent scenario with an asymptotic ratio around 0.30.

The asymptotic regime may be reached near 1000 TeV.

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.