Bi-maximal neutrino mixing in the MSSM with a single right-handed neutrino

We discuss neutrino masses in the framework of a minimal extension of the m inimal supersymmetric standard model (MSSM) consisting of an additional sin gle 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 atomo spheric neutrino data via nu(mu) --> nu(tau) oscillations by assuming a nea r maximal mixing angle theta(23) similar to pi/4 and taking Delta m(23)(2) similar to m(nu 3)(2) similar to 2.5 x 10(-3) eV(2). In order to account fo r the solar neutrino data we appeal to one-loop radiative corrections invol ving internal loops of SUSY particles, which we show can naturally generate an additional light neutrino mass m(nu 2) similar to 10(-5) eV again with near maximal mixing angle theta(12) similar to pi/4. The resulting scheme c orresponds to so-called "bi-maximal" neutrino mixing involving "just-so" so lar oscillations. We predict that the decay tau --> e gamma should be obser ved in the near future. (C) 1998 Elsevier Science B.V. All rights reserved.