Hadron collisions at ultrahigh energies: black disk or resonant disk modes?

TL;DR

This paper explores two possible high-energy behaviors of hadronic scattering amplitudes, the black disk and resonant disk modes, and discusses their implications for cross section growth at ultrahigh energies.

Contribution

It introduces and compares the black disk and resonant disk modes as potential descriptions of hadronic scattering at energies above 100 TeV.

Findings

At LHC energies, the profile function reaches the black disk limit.

Two scenarios are proposed: black disk mode with fixed T(b) and increasing radius, and resonant disk mode with T(b) approaching 2.

Resonant disk mode predicts different growth rates for inelastic cross sections.

Abstract

The analysis of current ultrahigh energy data for hadronic total cross sections and diffractive scattering cross sections points to a steady growth of the optical density with energy for elastic scattering amplitudes in the impact parameter space, $b$. At LHC energy the profile function of the $pp$-scattering amplitude, $T(b)$, reaches the black disk limit at small $b$. Two scenarios are possible at larger energies, $\sqrt{s}\ga 100$ TeV. First, the profile function gets frozen in the black disk limit, $T(b)\simeq 1$ while the radius of the black disk $R_{black\;disk}$ is increasing with $\sqrt s$, providing $\sigma_{tot}\sim \ln^2s$, $\sigma_{el}\sim \ln^2s$, $\sigma_{inel}\sim \ln^2s$. In another scenario the profile function continues to grow at $\sqrt{s}\ga 100$ TeV approaching the maximal value, $T(b)\simeq 2$, that means the resonant disk mode. We discuss features of the resonant disk mode when the disk radius, $R_{resonant\;disk}\,$, increases providing the growth of the total and elastic cross sections $\sigma_{tot}\sim \ln^2s$, $\sigma_{el}\sim \ln^2s$, but a more slow increase of inelastic cross section, $\sigma_{inel}\sim \ln s$.