Rising cross sections in QCD and the cosmic-ray data

Novel features of the QCD-implied growth of the total cross sections are discussed. Specifically, Lipatov's QCD Pomeron is a series of poles above unity, so that the center of gravity of the QCD Pomeron---the effective intercept---moves to higher j with rising energy. The higher the energy the steeper is the predicted rate of growth of the cross section, until unitarity enforces saturation of the growth rate and the onset of the Froissart asymptotics at extremely high energies. We demonstrate that the QCD-predicted rapid rise of the p(p\ifmmode\bar\else\textasciimacron\fi{})p total cross section agrees perfectly with the recent CERN Sp\ifmmode\bar\else\textasciimacron\fi{}pS datum on the phase of the p\ifmmode\bar\else\textasciimacron\fi{}-p forward amplitude. Further evidence for the QCD-predicted rise of the total cross section comes from the published Akeno and Fly's Eye data on the extensive air showers. Our principal observation is that in view of the unitarity-enforced slope--cross-section correlation one can determine proton-proton inelastic cross section from the proton-air absorption cross section to a very high accuracy. The published Fly's Eye result ${\ensuremath{\sigma}}_{\mathrm{abs}(\mathrm{p}}$-air)=540\ifmmode\pm\else\textpm\fi{}40 mb corresponds to ${\ensuremath{\sigma}}_{\mathrm{in}(\mathrm{p}\mathrm{\ensuremath{-}}\mathrm{p}{)=113}_{\mathrm{\ensuremath{-}}15}^{+16}}$ mb and ${\ensuremath{\sigma}}_{\mathrm{tot}(\mathrm{p}\mathrm{\ensuremath{-}}\mathrm{p}{)=164}_{\mathrm{\ensuremath{-}}27}^{+32}}$ mb. All of the previous determinations of ${\ensuremath{\sigma}}_{\mathrm{tot}(\mathrm{p}\mathrm{\ensuremath{-}}\mathrm{p}}$) from ${\ensuremath{\sigma}}_{\mathrm{abs}(\mathrm{p}}$-air) have grossly underestimated ${\ensuremath{\sigma}}_{\mathrm{tot}(\mathrm{p}\mathrm{\ensuremath{-}}\mathrm{p}}$). We present predictions for Fermilab Tevatron, \ensuremath{\surd}s =1.8 TeV, and Superconducting Super Collider, \ensuremath{\surd}s =40 TeV, energies. We give a functional form of correlation of the scaling violations in proton-air collisions with ${\ensuremath{\sigma}}_{\mathrm{abs}(\mathrm{p}}$-air), allowance for which could greatly improve the reliability of determination of ${\ensuremath{\sigma}}_{\mathrm{abs}(\mathrm{p}}$-air) from data on extensive air showers.