Higgs $\to$ $\mu \tau$ as an indication for $S_4$ flavor symmetry

Lepton flavor violating Higgs decays can arise in flavor symmetry models where the Higgs sector is responsible for both the electroweak and the flavor symmetry breaking. Here we advocate an $S_4$ three-Higgs-doublet model where tightly constrained flavor changing neutral currents are suppressed by a remnant $Z_3$ symmetry. A small breaking of this $Z_3$ symmetry can explain the $2.4\sigma$ excess of Higgs decay final states with a $\mu \tau$ topology reported recently by CMS if the new neutral scalars are light. The model also predicts sizable rates for lepton flavor violating Higgs decays in the $e\tau$ and $e\mu$ channels because of the unifying $S_4$ flavor symmetry.

Figure 1

One-Loop diagrams contributing to $l\to l^{\prime }\gamma$. Since $|y_{ll}|\gg |y_{l^{\prime }{l}^{\prime }}|$, the left diagram is the dominating one.

Figure 2

Parameter values leading to $|y_{\mu \tau }|$ required by CMS data on $h\to \mu \tau$ in brown (68% C.L.) and yellow (95% C.L.) for (a) positive and (b) negative $\theta$. Parameter regions shaded in blue are allowed by $\mathrm{Br}(\mu \to e\gamma )<5.7\times {10}^{-13}$. Solid (dashed) lines mark the $1\sigma (3\sigma )$ intervals of $|y_{\mu \tau }|$, where both regions overlap. Overlap occurs for $0.01\lesssim \theta \lesssim 0.09$, $126\mathrm{GeV}\lesssim m_H\lesssim 204\mathrm{GeV}$ (68% C.L.) and $-0.08\lesssim \theta \lesssim -0.01$, $127\mathrm{GeV}\lesssim m_H\lesssim 190\mathrm{GeV}$ (68% C.L.) allowing us to explain the excess in $h\to \mu \tau$ and at the same time to comply with the tight bound on $\mathrm{Br}(\mu \to e\gamma )(m_{\eta }=200\mathrm{GeV})$.

Figure 3

One-loop Feynman diagrams in the unitary gauge contributing to the $h\to \gamma \gamma$ decay.

Figure 4

The ratio $R_{\gamma \gamma }$ as a function of the charged Higgs masses $m_{{\varphi }_s^{\pm }}$ ($s=a,b$) for $a_{htt}=1$. The horizontal lines are the $R_{\gamma \gamma }$ experimental values given by CMS and ATLAS, which are equal to $1.14_{-0.23}^{+0.26}$ and $1.17\pm 0.27$, respectively [49, 50].

Figure 5

One-loop Feynman diagrams contributing to the $T$ parameter.

Figure 6

One-loop Feynman diagrams contributing to the $S$ parameter.

Figure 7

The $\mathrm{\Delta }S\text{−}\mathrm{\Delta }T$ plane, where the ellipses denote the experimentally allowed region at 95% C.L. taken from [58, 59, 60]. The origin $\mathrm{\Delta }S=\mathrm{\Delta }T=0$ corresponds to the SM value, with $m_h=125.5\mathrm{GeV}$ and $m_t=176\mathrm{GeV}$. Figures (a), (b) and (c) correspond to two different sets of values for the masses of the neutral non-SM Higgs bosons, as indicated. The mass $m_{{\varphi }_{(a,b)}^{\pm }}$ of the charged Higgs bosons varies between $130\mathrm{GeV}\le m_{{\varphi }_{(a,b)}^{\pm }}\le 196\mathrm{GeV}$ [Fig. 7], $600\mathrm{GeV}\le m_{{\varphi }_{(a,b)}^{\pm }}\le 672\mathrm{GeV}$ [Fig. 7], $925\mathrm{GeV}\le m_{{\varphi }_{(a,b)}^{\pm }}\le 990\mathrm{GeV}$ [Fig. 7]. The lines originating in the center of the plot and running up towards the ellipses correspond to the obtained values of the $\mathrm{\Delta }T$ and $\mathrm{\Delta }S$ parameters in our model, as the charged Higgs boson masses are varied in the aforementioned ranges.