Decays of CP-even Higgs bosons $H \rightarrow l_il_j$ in a 3-3-1 model with neutral leptons

The 3-3-1 model with neutral leptons contains four CP-even Higgs bosons when some constraints are imposed on the Higgs potential. Two Higgs bosons of this type are identified with the corresponding ones in the Two-Higgs-Doublet model (2HDM), an other being more massive does not couple with similar particles contained in the Standard Model (SM). The remaining particle is assumed to have no lepton-flavor-violating couplings. The contributions at one-loop order to $\mathrm{\Gamma}(\mathrm{H}\rightarrow l_il_j)$$(H \equiv h^0_1,h^0_2,h^0_3)$ come mainly from neutral leptons leading them to depend very strongly on mass of charged Higgs boson, masses and the mixing matrix ($V^L_{ab}$) of the neutral leptons. The numerical investigated results of $\mathrm{\Gamma}(\mathrm{H}\rightarrow l_il_j)$ in the spatial regions satisfying the experimental limit of lepton-flavor-violating decays of charged leptons (cLFV) indicate that the signal of SM-like Higgs boson ($\mathrm{\Gamma}(h^0_1\rightarrow l_il_j)$) approaches the upper bound of the experimental limit and $\mathrm{\Gamma}(\mathrm{H}\rightarrow l_il_j)$ can take large values in the case of $V^L_{ab} = U^L_{ab}(\pi/4,\pi/4,-\pi/4)$ and smaller in the case of $V^L_{ab} = U^L_{ab}(\pi/4,0,0)$. Further, some distinct properties of $\mathrm{\Gamma}(h^0_2\rightarrow l_il_j)$ and $\mathrm{\Gamma}(h^0_3\rightarrow l_il_j)$ are also discussed.