Contribution of heavy neutrinos to decay of standard-model-like Higgs boson $h\rightarrow \mu\tau$ in a 3-3-1 model with additional gauge singlets.

In the framework of the improved version of the 3-3-1 models with right-handed neutrinos, which is added to the Majorana neutrinos as new gauge singlets, the recent experimental neutrino oscillation data is completely explained through the inverse seesaw mechanism. We show that the major contributions to $Br(\mu\rightarrow e\gamma)$ are derived from corrections at 1-loop order of heavy neutrinos and bosons. But, these contributions are sometime mutual destructive, creating regions of parametric spaces where the experimental limits of $Br(\mu\rightarrow e\gamma)$ are satisfied. In these regions, we find that $Br(\tau\rightarrow \mu\gamma)$ can achieve values of $10^{-10}$ and $Br(\tau\rightarrow e\gamma)$ may even reach values of $10^{-9}$ very close to the upper bound of the current experimental limits. Those are ideal areas to study lepton-flavor-violating decays of the standard model -like Higgs boson ($h_1^0$). We also pointed out that the contributions of heavy neutrinos play an important role to change $Br(h_1^0\rightarrow \mu\tau)$, this is presented through different forms of mass mixing matrices ($M_R$) of heavy neutrinos. When $M_R \sim diag(1,1,1)$, $Br(h_1^0\rightarrow \mu\tau)$ can get a greater value than the cases $M_R \sim diag(1,2,3)$ and $M_R \sim diag(3,2,1)$ and the largest that $Br(h_1^0\rightarrow \mu\tau)$ can reach is very close $10 ^{-3}$.