The $S3$ Symmetric Model with a Dark Scalar

We study the $S3$ symmetric extension of the Standard Model in which all the irreducible representations of the permutation group are occupied by $SU(2)$ scalar doublets, one of which is taken as inert and can lead to dark matter candidates. We perform a scan over parameter space probing points against physical constraints ranging from unitarity tests to experimental Higgs searches limits. We find that the latter constraints severely restrict the parameter space of the model. For acceptable points we compute the value of the relic density of the dark scalar candidates and find that it has a region for low dark matter masses which complies with the Higgs searches bounds and lies within the experimental Planck limit. For masses $\gtrsim 80$ GeV the value of the relic density is below the Planck bound, and it reaches values close to it for very heavy masses $\sim 5$ TeV. In this heavy mass region, this opens the interesting possibility of extending the dark sector of the model with additional particles.