Energy spectra of gamma rays, electrons, and neutrinos produced at proton-proton interactions in the very high energy regime

Abstract

We present new parameterizations of energy spectra of secondary particles, $\ensuremath{\pi}$ mesons, gamma rays, electrons, and neutrinos produced in inelastic proton-proton collisions. The simple analytical approximations based on simulations 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 formulas 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 $\ensuremath{\pi}$-meson production.