Uncertainties in Atmospheric Muon-Neutrino Fluxes Arising from Cosmic-Ray Primaries

We present an updated calculation of the uncertainties on the atmospheric muon-neutrino flux arising from cosmic-ray primaries. For the first time, we include recent measurements of the cosmic-ray primaries collected since 2005. We apply a statistical technique that allows the determination of correlations between the parameters of the GSHL primary-flux parametrisation and the incorporation of these correlations into the uncertainty on the muon-neutrino flux. We obtain an uncertainty related to the primary cosmic rays of around $(5\text{--}15)\%$, depending on energy, which is about a factor of two smaller than the previously determined uncertainty. The hadron production uncertainty is added in quadrature to obtain the total uncertainty on the neutrino flux, which is reduced by $\approx 5\%$. To take into account an unexpected hardening of the spectrum of primaries above energies of $100$ $\text{GeV}$ observed in recent measurements, we propose an alternative parametrisation and discuss its impact on the neutrino flux uncertainties.