Lepton-number violation with quasi-Dirac neutrinos

We investigate lepton-number violation in weak interactions with massive Dirac neutrinos. In the framework of a simple $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_L\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ electroweak model we find that neutrinos naturally acquire only Dirac masses at tree level, and for an odd number of lepton families, one neutrino remains massless. After a spontaneous breakdown of symmetry we find that the SU(2)×U(1) effective theory has lepton-number-violating currents which couple to the standard gauge bosons. Flavorconserving $\left|\Delta l\right|=2\mathrm{}$ processes such as neutrinoless double-$\beta$ decay are forbidden in the simplest model, but processes such as ${\mu }^{-}+(A, Z)\to e^{+}+(A, Z-2)$ and $K^{-}\to {\pi }^{+}{e}^{-}{\mu }^{-}$ are allowed.