Three-flavor atmospheric neutrino anomaly

We investigate the indications of flavor oscillations that come from the anomalous flavor composition of the atmospheric neutrino flux observed in some underground experiments. We study the information coming from the neutrino-induced $\mu$-like and $e$-like events both in the sub-GeV energy range (Kamiokande, IMB, Fr{\'e}jus, and NUSEX experiments) and in the multi-GeV energy range (Kamiokande experiment). First we analyze all the data in the limits of pure $\nu_\mu\leftrightarrow\nu_\tau$ and $\nu_\mu\leftrightarrow\nu_e$ oscillations. We obtain that $\nu_\mu\leftrightarrow\nu_e$ oscillations provide a better fit, in particular to the multi-GeV data. Then we perform a three-flavor analysis in the hypothesis of dominance of one neutrino square mass difference, $m^2$, implying that the neutrino mixing is parametrized by two angles, $(\psi,\,\phi)\in[0,\,\pi/2]$. We explore the space $(m^2,\,\psi,\,\phi)$ exhaustively, and find the regions favored by the oscillation hypothesis. The results are displayed in a form suited to the comparison with other flavor oscillation searches at accelerator, reactor, and solar $\nu$ experiments. In the analysis, we pay particular attention to the earth matter effects, to the correlation of the uncertainties, and to the symmetry properties of the oscillation probability.