The Hilbert Series and the Flavor Invariants of the 3HDM

Abstract

We perform a systematic study of invariant operators in the three-Higgs-doublet model (3HDM). We compute the closed-form multigraded Hilbert series associated with the global symmetry group of the theory. In addition, we construct explicit expressions for the corresponding invariant operators up to cubic order in the couplings. As a phenomenological application, we further organize the invariants up to quadratic order in the field content into CP-even and CP-odd combinations. For the special case of invariants involving no $27$ representations, our results are complete to all orders.

35 pages

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