Constraining pion interactions at very high energies by cosmic ray data
  We demonstrate that a substantial part of the present uncertainties in model predictions for the average maximum depth of cosmic ray-induced extensive air showers is related to very high energy pion-air collisions. Our analysis shows that the position of the maximum of the muon production profile in air showers is strongly sensitive to the properties of such interactions. Therefore, the measurements of the maximal muon production depth by cosmic ray experiments provide a unique opportunity to constrain the treatment of pion-air interactions at very high energies and to reduce thereby model-related uncertainties for the shower maximum depth. 
Sergey Ostapchenko and Marcus Bleicher
hep-ph astro-ph.HE