Experimental Confirmation that the Proton is Asymptotically a Black Disk

TL;DR

Recent high-energy measurements at the LHC and Auger suggest that protons behave as black disks at asymptotic energies, saturating the Froissart bound and becoming fully absorptive, with implications for QCD and glueball mass.

Contribution

The paper provides experimental confirmation that protons asymptotically behave as black disks, supporting theoretical predictions and connecting high-energy scattering data with QCD insights.

Findings

Proton cross sections saturate the Froissart bound at high energies.

The ratio of inelastic to total cross section approaches 0.5, indicating black disk behavior.

Forward scattering amplitude becomes purely imaginary at asymptotic energies.

Abstract

Although experimentally accessible energies can not probe `asymptopia', recent measurements of` inelastic $pp$ cross sections at the LHC at 7000 GeV and by Auger at 57000 GeV allow us to conclude that: i) both $\sigin$ and $\sigtot$, the inelastic and total cross sections for $pp$ and $\bar p p$ interactions, saturate the Froissart bound of $\ln^2 s$, ii) when $s\rightarrow \infty$, the ratio $\sigin/\sigtot$ is experimentally determined to be $0.509\pm 0.021$, consistent with the value 0.5 required by black disk at infinite energies, and iii) when $s\rightarrow \infty$, the forward scattering amplitude becomes purely imaginary, another requirement for the proton to become a totally absorbing black disk. Experimental verification of the hypotheses of analyticity and unitarity over the center of mass energy range $6\le \sqrt s\le 57000$ GeV are discussed. In QCD, the black disk is naturally made of gluons; our results suggest that the lowest-lying glueball mass is $2.97\pm 0.03$ GeV.