We make new predictions of ${\sigma }_{p-\mathrm{air}}^{\mathrm{prod}}$, the proton-air inelastic production cross section, at $pp$ center-of-mass energies $0.1\lesssim \sqrt{s}\lesssim 100\mathrm{TeV}$, using high-energy predictions from a saturated Froissart bound parametrization of accelerator data on forward $\overline{p}p$ and $pp$ scattering amplitudes, together with Glauber theory. The parametrization of the $\overline{p}p$ and $pp$ cross sections incorporates analyticity constraints and unitarity, allowing accurate extrapolations to ultrahigh energies. Our predictions are in excellent agreement with available cosmic-ray extensive air shower measurements, both in magnitude and in energy dependence.

• Received 21 May 2007

DOI:https://doi.org/10.1103/PhysRevD.76.111503