Confronting solutions to the atmospheric neutrino anomaly involving large angle $ u_{mu} to u_e$ oscillations with SuperKamiokande and CHOOZ

Neutrino oscillation scenarios involving large angle $ u_{mu} to u_e$ oscillations are disfavoured in the parameter range $Delta m^2/eV^2 >~ 10^{-3}$ by recent results from the CHOOZ reactor-based $bar{ u}_e$ disappearance experiment. For this reason we extend our previous work on up-down asymmetries for various oscillation scenarios by computing up-down asymmetries and the R ratio for the entire conceivable range $10^{-4} - 10^{-1} eV^2$ of $Delta m^2$. Matter effects in the Earth play a crucial role. We perform a $chi^2$ fit to the data. We find that, because of the matter effect, the three-flavour maximal mixing model provides a reasonable fit to SuperKamiokande and CHOOZ data provided that the relevant $Delta m^2$ is in the range $4 times 10^{-4} ~< Delta m^2/eV^2 ~< 1.5 times 10^{-3}$.