Decay of standard-model-like Higgs boson h → μ τ in a 3-3-1 model with inverse seesaw neutrino masses

By adding new gauge singlets of neutral leptons, the improved versions of the 3-3-1 models with right-handed neutrinos have been recently introduced in order to explain recent experimental neutrino oscillation data through the inverse seesaw mechanism. We prove that these models predict promising signals of lepton-flavor-violating decays of the standard-model-like Higgs boson ${h}_{1}^{0}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\tau},e\ensuremath{\tau}$, which are suppressed in the original versions. One-loop contributions to these decay amplitudes are introduced in the unitary gauge. Based on a numerical investigation, we find that the branching ratios of the decays ${h}_{1}^{0}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\tau},e\ensuremath{\tau}$ can reach values of ${10}^{\ensuremath{-}5}$ in the regions of parameter space satisfying the current experimental data of the decay $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$. The value of ${10}^{\ensuremath{-}4}$ appears when the Yukawa couplings of leptons are close to the perturbative limit. Some interesting properties of these regions of parameter space are also discussed.