Breaking the Barriers - Uniting Accelerator and Cosmic Ray p-p Cross   Sections
  We make a QCD-inspired parameterization of all accelerator data on forward proton-proton and antiproton-proton scattering amplitudes. Using vector dominance and the additive quark model, we show that the same parameters also fit gamma p and gamma gamma interactions. Using the high energy predictions of our model, along with Glauber theory, we calculate proton-air cross sections at energies near sqrt s approx 30 TeV. The comparisons of p-air cosmic ray measurements with our QCD model predictions provide a strong constraint on the inclusive particle production cross section. 
M. M. Block, F. Halzen, G. Pancheri, and T. Stanev