Experimental Confirmation that the Proton is Asymptotically a Black Disk

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 $\text{sigin}$ and $\text{sigtot}$, the inelastic and total cross sections for $pp$ and $\bar{p}p$ interactions, saturate the Froissart bound of ${\ln }^{2}s$, ii) when $s\rightarrow \infty$,theratio$\sigin/\sigtot$isexperimentallydeterminedtobe$0.509\pm 0.021$, consistent with the value 0.5 required by black disk at infinite energies, and iii) when $s\to \mathrm{\infty }$, 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.