Quark and lepton mass effects and the observational constraints on the high energy neutrino cross sections

The cross sections of neutrino-nucleon scattering at high energies are evaluated with quark masses at next-to-leading order in strong interaction corrections. We compare the results with two kinds of schemes for treating the heavy quarks, the fixed flavor number scheme and the variable flavor number scheme for muon neutrino-nucleon interaction, and discuss which scheme is more relevant. The optimized parton distribution functions (PDF) for the flavor number schemes are also evaluated. The tau mass, much larger than the muon mass, suppresses the cross sections at low energies. We calculate the tau neutrino and antineutrino cross sections including the lepton mass corrections with low Q-extrapolated structure functions. Uncertainties due to the factorization scale, PDF choice, and the momentum transfer cutoff for the structure functions are also discussed with total theoretical errors. At ultra high energies (UHE), the same cross sections can be used for all flavors. We applied our evaluated cross sections to estimate the UHE neutrino event rates from lunar detection. The effective lunar aperture depends on the frequency and the minimum detectable electric field. We evaluate the effective aperture for a range of inputs. The event rates for both neutrino and cosmic rays are calculated in the standard model and compared with the enhanced neutrino-nucleon cross section for mini-black hole production. Lunar detection of UHE neutrino fluxes in the standard model will be challenging because low event rates are predicted.