The decays $\nu _H \rightarrow \nu_L \gamma$ and $\nu_H \rightarrow \nu_L e^+ e^-$ of massive neutrinos

Abstract

If, as recently reported by the Super-Kamiokande collaboration, the neutrinos are massive, the heaviest one, $\nu_H$ , would not be stable and, though chargeless, could in particular decay into a lighter neutrino $\nu_L$ and a photon by quantum loop effects. The corresponding rate is computed in the standard model with massive Dirac neutrinos as a function of the neutrino masses and mixing angles. The lifetime of the decaying neutrino is estimated to be $\approx 10^{44}$ years for a mass $\approx 5\times 10^{-2}$ eV. Before the mass range arising from present experiments on neutrino oscillations is definitively settled, it is still motivating to study the $\nu_H \rightarrow \nu_L e^+ e^-$ decay; if kinematically possible, it occurs at tree level and its one-loop radiative corrections get enhanced by a large logarithm of the electron mass acting as an infrared cutoff. Thus the $\nu_H \rightarrow \nu_L e^+ e^-$ decay largely dominates the $\nu_H \rightarrow \nu_L \gamma$ one by several orders of magnitude, corresponding to a lifetime $\approx 10^{-2}$ year for a mass of $\approx 1.1$ MeV.