The Production of Prompt Cosmic Ray Muons and Neutrinos

The cross section of the charm hadroproduction is calculated in the diagrams with O(αs2) by the quark-parton model. By solving the diffusion equations including this differential cross section with respect to the charm energy, the energy spectrum of the prompt cosmic ray muons, decay products of produced D-mesons, in atmosphere is evaluated. Similarly the energy spectrum of the prompt neutrinos is given. Since these spectra have about unity larger exponent in the power forms than that of conventional spectra from π and K decays, it is shown that the prompt components exceed to conventional ones above 750 TeV for muons and 150 TeV for muon neutrinos in the vertical direction at sea-level. So the prompt components are detectable in a huge apparatus such as DUMAND.