Fast neutrino decay in the minimal seesaw model

Neutrino decay in the minimal seesaw model containing three right-handed neutrinos and a complex SU(2)×U(1) singlet Higgs field in addition to the standard model fields is considered. A global horizontal symmetry ${\mathrm{U}\mathrm{}\left(1\right)\mathrm{}}_H$ is imposed, which on spontaneous breaking gives rise to a Goldstone boson. This symmetry is chosen in a way that makes (a) the contribution of heavy (≤ MeV) Majorana neutrinos to the neutrinoless double-$\beta$-decay amplitude vanish and (b) allows the heavy neutrino to decay to a lighter neutrino and the Goldstone boson. It is shown that this decay can occur at a rate much faster than in the original Majoron model even if one does not introduce any additional Higgs fields as is done in the literature. The possibility of describing the 17-keV neutrino in this minimal seesaw model is investigated. While most of the cosmological and astrophysical constraints on the 17-keV neutrino can be satisfied in this model, the laboratory limits coming from neutrino oscillations cannot be easily met. An extension that removes this inadequacy and offers a consistent description of the 17-keV neutrino is discussed.