Extending the Frontiers - Reconciling Accelerator and Cosmic Ray p-p   Cross Sections
  We simultaneously fit a QCD-inspired parameterization 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 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. 
M. M. Block, F. Halzen, T. Stanev