Phenomenology of the Neutrino-Mass-Giving Higgs Triplet and the Low-Energy Seesaw Violation of Lepton Number

Small realistic Majorana neutrino masses can be generated via a Higgs triplet $(\xi^{++}, \xi^+, \xi^0)$ without having energy scales larger than $M_*={\cal O}(1)$ TeV in the theory. The large effective mass scale $\Lambda$ in the well-known seesaw neutrino-mass operator $\Lambda^{-1} (LL\Phi\Phi)$ is naturally obtained with $\Lambda\sim M_*^2/\mu,$ where $\mu$ is a {\it small} scale of lepton-number violation. In theories with large extra dimensions, the smallness of $\mu$ is naturally obtained by the mechanism of ``shining'' if the number of extra dimensions $n\ge 3.$ We study here the Higgs phenomenology of this model, where the spontaneous violation of lepton number is treated as an external source from extra dimensions. The observable decays $\xi^{++} \to l_i^+l_j^+$ will determine directly the magnitudes of the $\{ij\}$ elements of the neutrino mass matrix. The decays $\xi^+ \to W^+ J^0$ and $\xi^0 \to Z J^0$, where $J^0$ is the massless Goldstone boson (Majoron), are also possible, but of special importance is the decay $\xi^0 \to J^0 J^0$ which provides stringent constraints on the allowed parameter space of this model. Based on the current neutrino data, we also predict observable rates of $\mu-e$ conversion in nuclei.