Parametrizations of Inclusive Cross Sections for Pion Production in   Proton-Proton Collisions
  Accurate knowledge of cross sections for pion production in proton-proton collisions finds wide application in particle physics, astrophysics, cosmic ray physics and space radiation problems, especially in situations where an incident proton is transported through some medium, and one requires knowledge of the output particle spectrum given the input spectrum. In such cases accurate parametrizations of the cross sections are desired. In this paper we review much of the experimental data and compare to a wide variety of different cross section parametrizations. In so doing, we provide parametrizations of neutral and charged pion cross sections which provide a very accurate description of the experimental data. Lorentz invariant differential cross sections, spectral distributions and total cross section parametrizations are presented. 
Steve R. Blattnig, Sudha R. Swaminathan, Adam T. Kruger, Moussa Ngom,   and John W. Norbury