Single-Photon Z Decays and Small Neutrino Masses

We discuss some rare Z decay signatures associated with extensions of the Standard Model with spontaneous lepton number violation at the electroweak scale. We show that single-photon Z decays such as $Z \to \gamma H$ and $Z \to \gamma J J$ where H is a CP-even Higgs boson and J denotes the associated CP-odd Majoron may occur with branching ratios accessible to LEP sensitivities, even though the corresponding neutrino masses can be very small, as required in order to explain the deficit of solar neutrinos.