Higgs $\rightarrow$ $\mu\tau$ 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.