Extending the frontiers: Reconciling accelerator and cosmic rayp−pcross sections

We simultaneously fit a QCD-inspired parametrization of all accelerator data on forward proton-proton and antiproton-proton scattering amplitudes, together with cosmic ray data (using Glauber theory), to predict proton-air and proton-proton cross sections at energies near $\sqrt{s}\approx 30\hspace{0.5em}\mathrm{TeV}.$ The p-air cosmic ray measurements provide a strong constraint on the inclusive particle production cross section, as well as greatly reducing the errors on the fit parameters—in turn, greatly reducing the errors in the high-energy proton-proton and proton-air cross section predictions.