The electron neutrino mass, double beta decay and cosmology

The Lubimov et al. experiment suggests a nonzero ν_e mass in the 20-45 eV range, while neutrinoless double beta decay experiments set upper limits between 2 and 10 eV if the ν_e is an unmixed Majorana particle. Together, these imply that the ν_e is either a Dirac neutrino or that it is a mixture of Majorana mass eigenstates which cancel in the double beta decay amplitude. We consider the laboratory and cosmological constraints on the latter possibility and show that it is ruled out except for two small regions of parameter space unless new physics is invoked to allow a fast invisible decay or annihilation channel for the heavy neutrino. Surprisingly, the cosmological constraints are often stronger if the heavy neutrino is mainly an SU₂×U₁ singlet than if it has normal weak interactions. Implications for the recently reported 17 keV neutrino are also discussed.