Prompt Atmospheric Neutrinos and Muons: Dependence on the Gluon Distribution Function

We compute the next-to-leading order QCD predictions for the vertical flux of atmospheric muons and neutrinos from decays of charmed particles, for different PDF’s ~MRS-R1, MRS-R2, CTEQ-4M and MRST! and different extrapolations of these at a small partonic momentum fraction x. We find that the predicted fluxes vary up to almost two orders of magnitude at the largest energies studied, depending on the chosen extrapolation of the PDF’s. We show that the spectral index of the atmospheric leptonic fluxes depends linearly on the slope of the gluon distribution function at very small x. This suggests the possibility of obtaining some bounds on this slope in ‘‘neutrino telescopes,’’ at values of x not reachable at colliders, provided the spectral index of atmospheric leptonic fluxes could be determined.