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

Q. Ho-Kim; B. Machet; X.Y. Pham

doi:doi:10.1007/s100520000292

EPJ

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2023 Impact factor 4.2

Particles and Fields

Eur. Phys. J. C 13, 117-123
DOI 10.1007/s100520000292

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

Q. Ho-Kim¹ - B. Machet^2,3^, - X.Y. Pham^2,3

¹ Department of Physics, Université Laval (Québec), Sciences and Engineering Building, Sainte Foy, QC G1K7P4, Canada
² Laboratoire de Physique Théorique et Hautes Energies, LPTHE tour 16/1 $^{er}\!$ étage, Université P. et M. Curie, BP 126,
4 place Jussieu, 75252 Paris Cedex 05, France
³ Universités Pierre et Marie Curie (Paris 6) et Denis Diderot (Paris 7), Unité associée au CNRS UMR 7589, Paris, France

Received: 19 August 1999 / Published online: 3 February 2000 - © Springer-Verlag 2000

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.