Neutrino Oscillations in the Framework of Three-Generation Mixings with Mass Hierarchy

We have analyzed the results of reactor and accelerator neutrino oscillation experiments in the framework of a general model with mixing of three neutrino fields and a neutrino mass hierarchy that can accommodate the results of the solar neutrino experiments. It is shown that $\nu_\mu \leftrightarrows \nu_e$ oscillations with $0.6 \le \Delta m^2 \le 100 \, \mathrm{eV}^2$ and amplitude larger than $2 \times 10^{-3}$ are not compatible with the existing limits on neutrino oscillations if the non-diagonal elements of the mixing matrix $\left| U_{e3} \right|$ and $\left| U_{\mu3} \right|$ are small. Thus, if the excess of electron events recently observed in the LSND experiment is due to $\nu_\mu \leftrightarrows \nu_e$ oscillations, the mixing in the lepton sector is basically different from the CKM mixing of quarks. If this type of mixing is realized in nature, the observation of $\nu_\mu \leftrightarrows \nu_e$ oscillations would not influence $\nu_\mu \leftrightarrows \nu_\tau$ oscillations that are being searched for in the CHORUS and NOMAD experiments.