Abstract
We use the high-energy predictions of a QCD-inspired parametrization of all accelerator data on forward proton-proton and antiproton-proton scattering amplitudes, along with Glauber theory, to predict proton-air cross sections at energies near $\sqrt{s}\ensuremath{\approx}30\mathrm{TeV}$. The parametrization of the proton-proton cross section incorporates analyticity and unitarity and demands that the asymptotic proton is a black disk of soft partons. By comparing with the $p$-air cosmic ray measurements, our analysis results in a constraint on the inclusive particle production cross section.
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