Energy spectra of gamma-rays, electrons and neutrinos produced at   proton-proton interactions in the very high energy regime
  We present new parametrisations of energy spectra of secondary particles, $\pi$-mesons, gamma-rays, electrons and neutrinos, produced in inelastic proton-proton collisions. The simple analytical approximations based on imulations of proton-proton interactions using the public available SIBYLL code, provide very good accuracy for energy distributions of secondary products in the energy range above 100 GeV. Generally, the recommended analytical formulae deviate from the simulated distributions within a few percent over a large range of $x=E_i/E_p$ - the fraction of energy of the incident proton transferred to the secondaries. Finally, we describe an approximate procedure of continuation of calculations towards low energies, down to the threshold of $\pi$-meson production. 
S.R. Kelner, F.A. Aharonian, V.V. Bugayov