Mass Matrix Ansatz for Degenerate Neutrinos Consistent with Solar and Atmospheric neutrino Data

Abstract

We suggest mass matrices for neutrinos and charged leptons that can explain solar and atmospheric neutrino data. The resulting flavor mixing matrix $V_{\nu}$ has a property that $(V_{\nu})_{13}=0$, thus making $\nu_e \leftrightarrow \nu_{\mu}$ and $\nu_{\mu} \leftrightarrow \nu_{\tau}$ oscillations to be effectively a two-channel problem. Phenomenological consequences of the lepton mass matrix ansatze are consistent with the current data on various type of neutrino oscillation experiments except the LSND measurement. %and that three neutrinos are almost degenerate in mass. Three neutrinos, being almost degenerate with $\sum | m_{\nu_i} | \lesssim 1 $ eV, can be a part of hot dark matter without any conflict with the constraint from neutrinoless double beta decay experiments. The $\nu_{\mu} \leftrightarrow \nu_{\tau}$ oscillation, $\sin^2{2\theta_{\mu \tau}}$, is predicted to be 0.86-0.97 with $\Delta m^2_{\mu \tau}\simeq 2 \times 10^{-3} {eV}^2$, which is consistent with the atmospheric neutrino data and can be tested further at the planned MINOS and K2K experiments searching for $\nu_{\mu} \to \nu_{\tau}$ oscillation.