Generalized CP symmetries and special regions of parameter space in the two-Higgs-doublet model

Abstract

We consider the impact of imposing generalized CP symmetries on the Higgs sector of the two-Higgs-doublet model, and identify three classes of symmetries. Two of these classes constrain the scalar potential parameters to an exceptional region of parameter space which respects either a Z_2 discrete flavor symmetry or a U(1) symmetry. We exhibit a basis-invariant quantity that distinguishes between these two possible symmetries. We also show that the consequences of imposing these two classes of CP symmetry can be achieved by combining Higgs Family symmetries, and that this is not possible for the usual CP symmetry. We comment on the vacuum structure and on renormalization in the presence of these symmetries. Finally, we demonstrate that the standard CP symmetry can be used to build all the models we identify, including those based on Higgs Family symmetries.