Problems with Atmospheric Neutrino Oscillations

The neutrino oscillation hypothesis does a poor job of representing the atmospheric neutrino anomaly. The anomaly is observed over 4 decades in path length and at least a factor of 30 in energy. This restricts the potential oscillation solutions to those with large amplitudes and mixing mass differences that are ruled out by other observations. The $\Delta m^{2}$ region in the range $10^{-4} - 10^{-2}$ leads to inconsistencies within the atmospheric neutrino data itself. The observed value of $R$ seems to be incompatible with the $\Delta m^{2}$ implied by recent results