Signatures of an $S_3$-Orbifold Higgs Model

The lack of new physics at the LHC has sparked renewed interest in theories of neutral naturalness, in which the Standard Model partners required for naturalness carry no Standard Model charge. The Twin Higgs was the first of these theories to be introduced, but recent work has demonstrated it is only an isolated example in a large class of "orbifold Higgs" models. In this work we study an orbifold Higgs model resulting from the orbifold projection by the non-abelian group $S_3$. A model with multiple sectors uncharged under the SM emerges. Constraints are placed on the model from Higgs phenomenology and the prospects of finding evidence at colliders are discussed.