p-air production cross-section and uncorrelated mini-jets processes in   pp-scattering
  For the p-air production cross-section, we use a Glauber formalism which inputs the pp inelastic cross-section from a mini-jet model embedded in a single-channel eikonal expression, which provides the needed contribution of uncorrelated processes. It is then shown that current LO parton density functions for the pp mini-jet cross-sections, with a rise tempered by collinearity induced by soft gluon re-summation, are well suited to reproduce recent cosmic ray results. By comparing results for GRV, MRST72 and MSTW parametrizations, we estimate the uncertainty related to the low-x behavior of these densities. 
D.A. Fagundes, A. Grau, G. Pancheri, Y.N. Srivastava and O.   Shekhovtsova
hep-ph