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, 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.