New experimental evidence that the proton develops asymptotically into a black disk

Recently, the Auger group has extracted the proton-air cross section from observations of air showers produced by cosmic ray protons (and nuclei) interacting in the atmosphere and converted it into measurements of the total and inelastic $pp$ cross sections $\sigma_{\rm tot}$ and $\sigma_{\rm inel}$ at the super-LHC energy of 57 TeV. Their results reinforce our earlier conclusions that the proton becomes a black disk at asymptotic energies, a prediction reached on the basis of sub-LHC $\pbar p$ and $pp$ measurements of $\sigma_{\rm tot}$ and $\rho$, the ratio of the real to the imaginary part of the forward scattering amplitude [M. M. Block and F. Halzen, Phys. Rev. Lett. {\bf 107}, 212002 (2011)]. The same black disk description of the proton anticipated the values of $\sigma_{\rm tot}$ and $\sigma_{\rm inel}$ measured by the TOTEM experiment at the LHC cms (center of mass) energy of $\sqrt s=7$ TeV, as well as those of $\sigma_{\rm inel}$ measured by ALICE, ATLAS and CMS, as well as the ALICE measurement at 2.76 TeV. All data are consistent with a proton that is asymptotically a black disk of gluons: (i) both $\sigma_{\rm tot}$ and $\sigma_{\rm inel}$ behave as $\ln^2s$, saturating the Froissart bound, (ii) the forward scattering amplitude becomes pure imaginary (iii) the ratio $\sigma_{\rm inel}/\sigma_{\rm tot}=0.509 \pm 0.021$, compatible with the black disk value of 1/2, and (iv) proton interactions become flavor blind.