Smallness of leptonic θ13 and discrete symmetry

The leptonic mixing angle theta(13) is known to be small. If it is indeed tiny, the simplest explanation is that charged leptons mix only in the mu-tau sector and neutrinos only in the 1-2 sector. We show that this pattern may be explained by the discrete symmetry Z(2) x 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 mu-tau sector, are analyzed in detail: the LFV tau-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. (c) 2005 Elsevier B.V. All rights reserved.