Bi-Maximal Neutrino Mixing in the MSSM with a Single Right-Handed Neutrino

Abstract

We discuss neutrino masses in the framework of a minimal extension of the minimal supersymmetric standard model (MSSM) consisting of an additional single right-handed neutrino superfield $N$ with a heavy Majorana mass $M$, which induces a single light see-saw mass $m_{ν_3}$ leaving two neutrinos massless at tree-level. This trivial extension to the MSSM may account for the atomospheric neutrino data via $ν_μ\to ν_τ$ oscillations by assuming a near maximal mixing angle $θ_{23}\sim π/4$ and taking $Δm_{23}^2 \sim m_{ν_3}^2 \sim 2.5\times 10^{-3} eV^2$. In order to account for the solar neutrino data we appeal to one-loop radiative corrections involving internal loops of SUSY particles, which we show can naturally generate an additional light neutrino mass $m_{ν_{2}}\sim 10^{-5} eV$ again with near maximal mixing angle $θ_{12}\sim π/4$. The resulting scheme corresponds to so-called ``bi-maximal'' neutrino mixing involving ``just-so'' solar oscillations.