Résumé
Phys.Lett. B612 (2005) 29-35 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$Z_2 \times Z_2$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.