Smallness of leptonic θ13 and discrete symmetry

The leptonic mixing angle θ13 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 Z2×Z2 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.