Comprehensive fits to high energy data for $\sigma$, $\rho$, and $B$ and the asymptotic black-disk limit

TL;DR

This paper analyzes high-energy proton and antiproton scattering data to show that at very high energies, the scattering behaves like a black disk, with specific ratios approaching theoretical limits.

Contribution

It provides comprehensive fits to scattering data up to 57 TeV, demonstrating the black-disk limit behavior in forward scattering amplitudes at high energies.

Findings

The ratio of elastic to total cross section approaches 1/2.

The parameter 8πB/σ_total approaches 1.

Data supports the black-disk scattering model at high energies.

Abstract

We demonstrate that the entirety of the data on proton--proton and antiproton--proton forward scattering between 6 GeV and 57 TeV center-of-mass energy is sufficient to show that $\sigma_{\rm elas}/\sigma_{\rm tot} \rightarrow 1/2$, and that $8\pi B/\sigma_{\rm tot}\rightarrow 1$ at very high energies, where $B$ the forward slope parameter for the differential elastic scattering cross sections. The relations demonstrate convincingly that the asymptotic $pp$ and $\bar{p}p$ scattering amplitudes approach those of scattering from a black disk. This result obviously has implications for any new physics that modifies the forward scattering amplitudes.