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An extension of the two Higgs doublet model including inverse seesawneutrinos and neutral Higgs bosons was constructed based on the $A_4$ symmetryin order to explain the recent neutrino oscillation data. This model candistinguish two well-known normal and inverted order schemes of neutrino dataonce both the effective masses $m_{\beta}$ in tritium beta decays and $\langlem\rangle$ in the neutrinoless double beta decay are observed. The lepton flavorviolating decays of the charged leptons $e_b\rightarrow e_a\gamma$,$\mu\rightarrow3e$, the Standard model-like Higgs boson decays $h\rightarrowe_be_a$, and the $\mu$-e conversions in some nuclei are generated from loopcorrections. The experimental data of the branching ratio Br$(\mu\rightarrowe\gamma, 3e)$ predict that the upper bounds of Br$(\tau \rightarrow\mu\gamma,e\gamma)$ and Br$(h\rightarrow e_{a}e_b)$ are much smaller than theplanned experimental sensitivities. In contrast, the $\mu$-e conversions arethe promising signals for experiments.

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