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

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 ${\sigma }_{\mathrm{tot}}$ and ${\sigma }_{\mathrm{inel}}$ 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 ${\sigma }_{\mathrm{tot}}$ 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 ${\sigma }_{\mathrm{tot}}$ and ${\sigma }_{\mathrm{inel}}$ measured by the TOTEM experiment at the LHC cms (center of mass) energy of $\sqrt{s}=7$ TeV, as well as those of ${\sigma }_{\mathrm{inel}}$ 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 ${\sigma }_{\mathrm{tot}}$ and ${\sigma }_{\mathrm{inel}}$ behave as ${\ln }^{2}s$, saturating the Froissart bound, (ii) the forward scattering amplitude becomes pure imaginary (iii) the ratio ${\sigma }_{\mathrm{inel}}/{\sigma }_{\mathrm{tot}}=0.509\pm 0.021$, compatible with the black disk value of 1/2, and (iv) proton interactions become flavor blind.

4 pages, 3 figures

References in corpus (3)

• Measurement of the proton-air cross-section at $\sqrt{s}=57$ TeV with the Pierre Auger Observatory
• Hadronic forward scattering: Predictions for the Large Hadron Collider and cosmic rays
• Forward hadronic scattering at 7 TeV: predictions for the LHC; an update

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