Decay of standard-model-like Higgs boson $h\to \mu \tau$ 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 $h_1^0\to \mu \tau ,e\tau$, 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 $h_1^0\to \mu \tau ,e\tau$ can reach values of ${10}^{-5}$ in the regions of parameter space satisfying the current experimental data of the decay $\mu \to e\gamma$. 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.

Figure 1

One-loop Feynman diagrams contributing to the decay $h_1^0\to e_a{e}_b$ in the unitary gauge. Here $V^{\pm }=W^{\pm },Y^{\pm }$.

Figure 2

$\mathrm{Br}(\mu \to e\gamma )$ (left) and $\mathrm{Br}(h_1^0\to \mu \tau )$ (right) as functions of $m_{H_2^{\pm }}$ with $k=500$.

Figure 3

$\mathrm{Br}(\mu \to e\gamma )$ (upper) and $\mathrm{Br}(h_1^0\to \mu \tau )$ (lower) as functions of $m_{H_2^{\pm }}$ with $k=5.5$ (left) and $k=9$ (right).

Figure 4

Density plots of $\mathrm{Br}(h_1^0\to \mu \tau )$ and contour plots of $\mathrm{Br}(\mu \to e\gamma )$ (black curves) as functions of $m_{H_2^{\pm }}$ and $z$, with $k=5.5$ (upper) and $k=9$ (lower).

Figure 5

Density plots of $\mathrm{Br}(h_1^0\to \mu \tau )$ and contour plots of $\mathrm{Br}(\mu \to e\gamma )$ (black curves) as functions of $m_{H_2^{\pm }}$ and $z$, with $k=5.5$, $z$ around 500 GeV, and different $m_Y$.