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 $m_{\nu_3}$ leaving two neutrinos massless at tree-level. This trivial extension to the MSSM may account for the atomospheric neutrino data via $\nu_{\mu}\to \nu_{\tau}$ oscillations by assuming a near maximal mixing angle $\theta_{23}\sim \pi/4$ and taking $\Delta m_{23}^2 \sim m_{\nu_3}^2 \sim 2.5\times 10^{-3} eV^2$. 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 $m_{\nu_{2}}\sim 10^{-5} eV$ again with near maximal mixing angle $\theta_{12}\sim \pi/4$. The resulting scheme corresponds to so-called ``bi-maximal'' neutrino mixing involving ``just-so'' solar oscillations.