Sensitivity to primary composition and hadronic models from average   shape of high energy cosmic ray shower profiles
  The concept of Universal Shower Profile is used to characterize the average behavior of high energy cosmic rays. The shape variables contain important information about composition. They are independent of the primary cross-section by construction, but affected by other hadronic parameters, like multiplicity. The two variables give access to the average nuclear mass of the sample and their compatibility serves as a test of hadronic models. 
Sofia Andringa, Ruben Concei\c{c}\~ao, Francisco Diogo and M\'ario   Pimenta
hep-ph astro-ph.HE