Low energy phenomena of the lepton sector in an $A_4$ symmetry model with heavy inverse seesaw neutrinos

An extension of the two Higgs doublet model including inverse seesaw neutrinos and neutral Higgs bosons was constructed based on the $A_4$ 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 $m_{\beta}$ in tritium beta decays and $\langle m\rangle$ in the neutrinoless double beta decay are observed. The lepton flavor violating decays of the charged leptons $e_b\rightarrow e_a\gamma$, $\mu\rightarrow3e$, the Standard model-like Higgs boson decays $h\rightarrow e_be_a$, and the $\mu$-e conversions in some nuclei arise from loop corrections. The experimental data of the branching ratio Br$(\mu\rightarrow e\gamma, 3e)$ predicts that the upper bounds of Br$(\tau \rightarrow \mu\gamma,e\gamma)$ and Br$(h\rightarrow e_{a}e_b)$ are much smaller than the planned experimental sensitivities. In contrast, the $\mu$-e conversions are the promising signals for experiments.