Title: Predicting Total and Elastic Cross Sections at the LHC


Using 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), we make a global fit to predict proton-air and proton-proton cross sections at ultra-high energies. The p-air cosmic ray measurements greatly reduce the errors on the fit parameters, in turn enabling us to greatly reduce the errors in predicting nucleon-nucleon cross sections at the LHC. The model uses an eikonal formulation that allows us to test the validity of factorization theorems for nucleon-nucleon, and collisions. For example, we show that factorization theorem, , holds if the opacity of the eikonal is independent of whether the reaction is , or . Using factorization theorems, we present experimental evidence for the additive quark model and vector meson dominance in high energy , and collisions.