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

TL;DR

Recent experimental data from cosmic ray and LHC measurements support the theoretical prediction that the proton asymptotically behaves as a black disk of gluons at ultra-high energies, saturating the Froissart bound.

Contribution

The paper provides experimental evidence confirming the black disk model of the proton at asymptotic energies, extending previous theoretical predictions with new cosmic ray and collider data.

Findings

Proton behaves as a black disk at high energies.

Total and inelastic cross sections grow as ln^2s, saturating the Froissart bound.

The forward scattering amplitude becomes purely imaginary.

Abstract

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.