Three Dirac neutrinos

The consequences of imposing an exact L<SUB>e</SUB>+L<SUB>τ</SUB>−L<SUB>μ</SUB> symmetry on a 6×6 matrix describing neutrino masses are discussed. The presence of right-handed neutrinos avoids the need of introducing any SU(2) Higgs triplet. Hence the conflict with the CERN LEP data on the Z width found in earlier models with L<SUB>e</SUB>+L<SUB>τ</SUB>−L<SUB>μ</SUB> symmetry is avoided. The L<SUB>e</SUB>+L<SUB>τ</SUB>−L<SUB>μ</SUB> symmetry provides an interesting realization of a recent proposal of Glashow to accommodate the 17-keV Dirac neutrino in the SU(2)×U(1) theory. All the neutrinos in this model are Dirac particles. The solar-neutrino problem can be solved in an extension of the model which generates a large (~10<SUP>−11</SUP> μB) magnetic moment for the electron neutrino