Experimental Confirmation that the Proton is Asymptotically a Black Disk

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.