Phenomenology in the Zee model with the A₄ symmetry

The Zee model generates neutrino masses at the one-loop level by adding charged SU(2)_L-singlet and extra SU(2)_L-doublet scalars to the standard model of particle physics. We introduce the softly broken A ₄ symmetry to the Zee model as the origin of the nontrivial structure of the lepton flavor mixing. This model is compatible with the tribimaximal mixing which agrees well with neutrino oscillation measurements. Then, a sum rule m₁eiα₁₂+2m₂+3m₃eiα ₃₂=0 is obtained and it results in Δm312<0 and m₃ ≥1.8×10^-2eV. The effective mass |(M_ν) _ee| for the neutrinoless double beta decay is predicted as |(M _ν)_ee|≥1.7×10^-2eV. The characteristic particles in this model are SU(2)_L-singlet charged Higgs bosons sα+(α=ξ,η,ζ) which are made from a 3 representation of A₄. Contributions of sα± to the lepton flavor violating decays of charged leptons are almost forbidden by an approximately remaining Z₃ symmetry; only BR(τ→ēμ μ) can be sizable by the flavor changing neutral current interaction with SU(2)_L-doublet scalars. Therefore, sα± can easily be light enough to be discovered at the LHC with satisfying current constraints. The flavor structures of BR(sα-→ℓν) are also discussed.