Confronting solutions to the atmospheric neutrino anomaly involving large angle $ν_μ \to ν_e$ oscillations with SuperKamiokande and CHOOZ

Neutrino oscillation scenarios involving large angle $\nu_{\mu} \to \nu_e$ oscillations are disfavoured in the parameter range $\Delta m^2/eV^2 \stackrel{>}{\sim} 10^{-3}$ by recent results from the CHOOZ reactor-based $\overline{\nu}_e$ 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 $4 \times 10^{-4} \stackrel{<}{\sim} \Delta m^2/eV^2 \stackrel{<}{\sim} 1.5 \times 10^{-3}$.