Atmospheric and Solar Neutrinos with a Heavy Singlet

We follow a minimalistic approach to neutrino masses, by introducing a single heavy singlet $N$ into the standard model (or supersymmetric standard model) with a heavy Majorana mass $M$, which couples as a single right-handed neutrino in a Dirac fashion to leptons, and induces a single light see-saw mass $m_{\nu}\sim 5\times 10^{-2} eV$, leaving two neutrinos massless. This trivial extension to the standard model may account for the atomospheric neutrino data via $\nu_{\mu}\to \nu_{\tau}$ oscillations with near maximal mixing angle $\theta_{23}\sim \pi/4$ and $\Delta m_{\mu \tau}^2 \sim 2.5\times 10^{-3} eV^2$. In order to account for the solar neutrino data the model is extended to SUSY GUT/ string-inspired type models which can naturally yield an additional light tau neutrino mass $m_{\nu_{\tau}}\sim few \times 10^{-3} eV$ leading to $\nu_{e L}\to (\cos \theta_{23}{\nu}_{\mu L} -\sin \theta_{23}{\nu}_{\tau L})$ oscillations with $\Delta m_{e1}^2\sim 10^{-5} eV^2$ and a mixing angle $\sin^2 2 \theta_1 \approx 10^{-2}$ in the correct range for the small angle MSW solution to the solar neutrino problem. The model predicts $\nu_{e L}\to (\sin \theta_{23}{\nu}_{\mu L} +\cos \theta_{23}{\nu}_{\tau L})$ oscillations with a similar angle but a larger splitting $\Delta m_{e2}^2 \sim 2.5\times 10^{-3} eV^2 $.