Analysis of an extended scalar sector with $S_3$ symmetry

We investigate the scalar potential of a general $S_3$-symmetric three-Higgs-doublet model. The outcome of our analysis does not depend on the fermionic sector of the model. We identify a decoupling limit for the scalar spectrum of this scenario. In view of the recent LHC Higgs data, we show our numerical results only in the decoupling limit. Unitarity and stability of the scalar potential demand that many new scalars must be lurking below 1 TeV. We provide numerical predictions for $h\to \gamma \gamma$ and $h\to Z \gamma$ signal strengths which can be used to falsify the theory.