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 $\Delta m_{23}^2\sim m_{{\nu }_3}^2\sim 2.5\times 10^{-3}e{V}^2$. 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.

Comments: 18 pages, Latex. References to bi-maximal mixing fixed