Uncertainties in Atmospheric Neutrino Fluxes

An evaluation of the principal uncertainties in the computation of neutrino fluxes produced in cosmic ray showers in the atmosphere is presented. The neutrino flux predictions are needed for comparison with experiment to perform neutrino oscillation studies. The paper concentrates on the main limitations which are due to hadron production uncertainties. It also treats primary cosmic ray flux uncertainties, which are at a lower level. The absolute neutrino fluxes are found to have errors of around 15% in the neutrino energy region important for contained events underground. Large cancellations of these errors occur when ratios of fluxes are considered, in particular, the $\nu_\mu/\bar{\nu}_\mu$ ratio below $E_\nu=1$ GeV, the $(\nu_\mu+\bar{\nu}_\mu)/(\nu_e+\bar{\nu}_e)$ ratio below $E_\nu=10$ GeV and the up/down ratios above $E_\nu=1$ GeV are at the 1% level. A detailed breakdown of the origin of these errors and cancellations is presented.