Three Dirac neutrinos

Abstract

The consequences of imposing an exact L_e+L_τ−L_μ 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_e+L_τ−L_μ symmetry is avoided. The L_e+L_τ−L_μ 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 (~10⁻¹¹ μB) magnetic moment for the electron neutrino.