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

TL;DR

This paper explores how generalized CP symmetries influence the two-Higgs-doublet model, revealing new symmetry classes, their implications for parameter space, and connections to Higgs family symmetries.

Contribution

It identifies three classes of generalized CP symmetries in the two-Higgs-doublet model and links two of these to specific scalar potential symmetries and Higgs family symmetries.

Findings

Two classes constrain the scalar potential to special parameter regions.

A basis-invariant quantity distinguishes between Z_2 and U(1) symmetries.

Standard CP symmetry can generate all identified models.

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.