Smallness of Leptonic ${\theta }_{13}$ and Discrete Symmetry

Abstract

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.

arXiv comment12 pages, several clarifications and references added

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Cited by in corpus (6)

• The Unique Horizontal Symmetry of Leptons
• Neutrino Mass Matrix from S_4 Symmetry
• Hybrid Seesaw Neutrino Masses with A_4 Family Symmetry
• 125 GeV Higgs decay with lepton flavor violation in the $\mu \nu$SSM
• Common origin of θ_{13} and Δm^2_{12} in a model of neutrino mass with quaternion symmetry
• Higgs boson decays with lepton flavor violation in the $B-L$ symmetric SSM