Asymptotic regimes for hadron diffractive scatterings and coulomb interaction. Arguments for the black disk mode

TL;DR

This paper analyzes the interplay of hadron and Coulomb interactions in proton-proton scattering across a wide energy range, comparing black disk and resonant disk models, and argues against the resonant disk mode based on experimental data.

Contribution

It provides a comparative analysis of hadron and Coulomb interactions in different asymptotic regimes using the $K$-matrix technique, highlighting differences in impact parameter space.

Findings

The real part of the hadronic amplitude concentrates on the disk boundary at high energies.

A shoulder in the differential cross-section at around 10 TeV supports the black disk mode.

Absence of the shoulder at 8 TeV challenges the resonant disk model.

Abstract

Comparative analysis of the interplay of hadron and Coulomb interactions in $pp^\pm$ scattering amplitudes is performed in a broad energy interval, $\sqrt{s}=1-10^6$ TeV, for two extreme cases: for the asymptotic interactions of hadrons in black disk and resonant disk modes. The interactions are discussed in terms of the $K$-matrix function technique. In the asymptotic regime the real part of the hadronic amplitude is concentrated in both cases on the boundary of the disks in the impact parameter space but the LHC energy region is not asymptotic for the resonant disk mode that lead to a specific interplay of hadronic and coulombic amplitudes. For the $pp$ scattering at $\sqrt{s}\sim 10$ TeV an interplay of the hadron and Coulomb interactions in the resonant disk modes is realized in a shoulder in $d\sigma_{el}/d{\bf q}^2$ at ${\bf q}^2\sim 0.0025-0.0075$ GeV$^2$. The absence of such a shoulder in the data at 8 TeV can be considered as an argument against the resonant disk mode.