Smallness of Leptonic $θ_{13}$ and Discrete Symmetry

Details Smallness of Leptonic $θ_{13}$ and Discrete Symmetry Smallness of Leptonic $θ_{13}$ and Discrete Symmetry

2004-12-01

arxiv.org/abs/hep-ph/0412018v2

Phys.Lett. B612 (2005) 29-35

Physics

High Energy Physics

High Energy Physics - Phenomenology

12 pages, several clarifications and references added

Scientific paper

10.1016/j.physletb.2005.03.006

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.

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