Smallness of Leptonic θ 13 and Discrete Symmetry

The leptonic mixing angle θ 13 is known to be small. If it is indeed tiny, the simplest explanation is that charged leptons mix only in the µ − τ sector and neutrinos only in the 1 − 2 sector. We show that this pattern may be explained by the discrete symmetry Z 2 × Z 2 of a complete Lagrangian, which has 2 Higgs doublets and 2 Higgs triplets (or 2 heavy right-handed singlet neutrinos). In the case of Higgs triplets, the Majorana neutrino masses are arbitrary, whereas in the case of heavy singlet neutrinos, an inverted hierarchy is predicted. Lepton-Flavor-Violation effects, present only in the µ − τ sector, are analyzed in detail: the LFV τ-decay rates are predicted below the present bounds by a few orders of magnitude, whereas LFV Higgs decays could allow for a direct test of the model.