We present a model with A4 × U(1)PQ lepton flavor symmetry which explains the origin of the lepton flavor structure and also solves the strong CP problem. Standard model gauge singlet fields, so-called “flavons”, charged under the A4 × U(1)PQ symmetry are introduced and are coupled with the lepton and the Higgs sectors. The flavon vacuum expectation values (VEVs) trigger spontaneous breaking of the A4 × U(1)PQ symmetry. The breaking pattern of the A4 accounts for the tri-bimaximal neutrino mixing and the deviation from it due to the non-zero θ13 angle, and the breaking of the U(1)PQ gives rise to a pseudo-Nambu-Goldstone boson, axion, whose VEV cancels the QCD θ term. We investigate the breaking of the A4 × U(1)PQ symmetry through an analysis on the scalar potential and further discuss the properties of the axion in the model, including its decay constant, mass and coupling with photons. It is shown that the axion decay constant is related with the right-handed neutrino mass through the flavon VEVs. Experimental constraints on the axion and their implications are also studied.
Beyond Standard Model Discrete Symmetries Global Symmetries Neutrino Physics
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