$A_4 \times U(1)_{PQ}$ Model for the Lepton Flavor Structure and the Strong $CP$ Problem

Understand

We present a model with $A_4 \times U(1)_{PQ}$ 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 $A_4 \times U(1)_{PQ}$ symmetry are introduced and are coupled with the lepton and the Higgs sectors.
• The flavon vacuum expectation values (VEVs) trigger spontaneous breaking of the $A_4 \times U(1)_{PQ}$ symmetry.
• The breaking pattern of the $A_4$ accounts for the tri-bimaximal neutrino mixing and the deviation from it due to the non-zero $\theta_{13}$ angle, and the breaking of the $U(1)_{PQ}$ gives rise to a pseudo-Nambu-Goldstone boson, axion, whose VEV cancels the QCD $\theta$ term.