Smallness of Leptonic $\hat{I}{¸}_{13}$ and Discrete Symmetry

Abstract

The leptonic mixing angle $\hat{I}{¸}_{13}$ is known to be small. If it is indeed tiny, the simplest explanation is that charged leptons mix only in the $\hat{I}¼-\ddot{I}„$ 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 $\hat{I}¼-\ddot{I}„$ sector, are analyzed in detail: the LFV $\ddot{I}„$-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.

12 pages, several clarifications and references added