By adding new gauge singlets of neutral leptons, the improved versions of the 3-3-1 models with righthanded 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 0 1 → μτ; eτ, 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 0 1 → μτ; eτ can reach values of 10 −5 in the regions of parameter space satisfying the current experimental data of the decay μ → eγ. The value of 10 −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.

The significance of new physics appearing in the loop-induced decays of neutral Higgs bosons into pairs of di-bosons γγ and Zγ will be discussed in the framework of the 3-3-1 models based on a recent work [1], where the Higgs sector becomes effectively the same as that in the Two Higgs Doublet models (2HDM) after the first symmetry breaking from SU (3) L scale into the electroweak scale. For large SU (3) L scale v 3 10 TeV, dominant one-loop contributions to the two decay amplitudes arise from only the single charged Higgs boson predicted by the 2HDM, leading to that experimental constraint on the signal strength µ 331 γγ of the Standard model like Higgs boson decay h → γγ will result in a strict upper bound on the signal strength µ 331 Zγ of the decay h → Zγ. For a particular model with lower v 3 around 3 TeV, contributions from heavy charged gauge and Higgs bosons may have the same order, therefore may give strong destructive or constructive correlations.As a by product, deviations from the SM prediction |µ 331 γγ − 1| ≤ 0.04 still allows |µ 331 Zγ − 1| to reach values near 0.1. We also show that there exists an CP-even neutral Higgs boson h 0 3 predicted by the 3-3-1 models, but beyond the 2HDM, has an interesting property that the branching ratio Br(h 0 3 → γγ) is very sensitive to the parameter β used to distinguish different 3-3-1 models. ¶ Corresponding author * Electronic address: hathanhhung@hpu2.edu.vn 1 arXiv:1907.06735v1 [hep-ph]

In the framework of the flipped 3-3-1 model introduced recently [R. M. Fonseca and M. Hirsch, J. High Energy Phys. 1608, 003 (2016)], the lepton-flavor-violating (LFV) decay $\mu \rightarrow 3e$ was predicted to have a large branching ratio (Br) close to the recent experimental limit. We will show that the Br of LFV decays of the standard-model-like (SM-like) Higgs boson decays (LFVHD) Br$(h\rightarrow e_ae_b)$ may also be large. Namely, Br$(h\rightarrow \mu\tau,e\tau)$ can reach values of $\mathcal{O}(10^{-4}){-}\mathcal{O}(10^{-5})$, which will reach the upcoming experimental sensitivities. On the other hand, for LFV decays of charged leptons (cLFV) $(e_b\rightarrow e_a\gamma)$, the branching ratios are well below experimental bounds.