We study a seesaw model with A 4 flavor symmetry and the physics phenomenological consequences. After symmetry breaking, the model leads to the neutrino mixing matrix that satisfies the current data of neutrino oscillation experiments. We then study how the low energy CP violation parameter, J CP , associates with the Dirac CP violation phase δ. We also study the high energy CP violation associate with the decay of heavy right handed neutrino in leptogenesis process in order to explain the observed baryon asymmetry of the Universe, η B . Numerically, we find a correlation between J CP and η B through the high energy phases. It is shown that our prediction for J CP , and hence for the Dirac CP violating phase δ, for some high energy fixed parameters can be constrained by the current data of η B .

An extension of the two Higgs doublet model including inverse seesaw neutrinos and neutral Higgs bosons was constructed based on the A4 symmetry in order to explain the recent neutrino oscillation data. This model can distinguish two well-known normal and inverted order schemes of neutrino data once both the effective masses mβ in tritium beta decays and 〈m〉 in the neutrinoless double beta decay are observed. The lepton flavor violating decays of the charged leptons eb → eaγ, μ → 3e, the Standard model-like Higgs boson decays h → ebea, and the μ-e conversions in some nuclei are generated from loop corrections. The experimental data of the branching ratio Br(μ → eγ, 3e) predict that the upper bounds of Br(τ → μγ, eγ) and Br(h → eaeb) are much smaller than the planned experimental sensitivities. In contrast, the μ-e conversions are the promising signals for experiments.