Atmospheric and Solar Neutrinos with a Heavy Singlet

Abstract

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 $\Delta m_{\mu \tau }^2\sim 2.5\times 10^{-3}e{V}^2$. 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 ${\nu }_{eL}\to (\cos {\theta }_{23}{\nu }_{\mu L}-\sin {\theta }_{23}{\nu }_{\tau L})$ oscillations with $\Delta m_{e1}^2\sim 10^{-5}e{V}^2$ 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 ${\nu }_{eL}\to (\sin {\theta }_{23}{\nu }_{\mu L}+\cos {\theta }_{23}{\nu }_{\tau L})$ oscillations with a similar angle but a larger splitting $\Delta m_{e2}^2\sim 2.5\times 10^{-3}e{V}^2$.

Comments: 10 pages, Latex. Expanded discussion of mixing angles mainly in an Appendix