Hyperchargeless triplet Majoron model

We study the general conditions to maintain the scale of the lepton-number-breaking vacuum expectation value at the electroweak scale. It is shown that the only possibilities are if the main component of the resulting Majoron is a hyperchargeless complex triplet or a neutral singlet. Models with a hyperchargeless triplet, even though phenomenologically more interesting, seem to be very difficult to build because they like to break charge conservation. However, we have found a particular extension, by adding an additional neutral singlet, that solves this problem. The model can give a Majorana mass to the neutrinos in the eV range, μ→eγ can proceed with branching ratios at the verge of the present experimental limit and there are no additional decay modes of the $Z^0$ into invisible particles.