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 $m_ν\sim 5\times 10^{-2} eV$, leaving two neutrinos massless. This trivial extension to the standard model may account for the atomospheric neutrino data via $ν_μ\to ν_τ$ oscillations with near maximal mixing angle $θ_{23}\sim π/4$ and $Δm_{μτ}^2 \sim 2.5\times 10^{-3} eV^2$. 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 $m_{ν_τ}\sim few \times 10^{-3} eV$ leading to $ν_{e L}\to (\cos θ_{23}ν_{μL} -\sin θ_{23}ν_{τL})$ oscillations with $Δm_{e1}^2\sim 10^{-5} eV^2$ and a mixing angle $\sin^2 2 θ_1 \approx 10^{-2}$ in the correct range for the small angle MSW solution to the solar neutrino problem. The model predicts $ν_{e L}\to (\sin θ_{23}ν_{μL} +\cos θ_{23}ν_{τL})$ oscillations with a similar angle but a larger splitting $Δm_{e2}^2 \sim 2.5\times 10^{-3} eV^2 $.