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In the two-Higgs-doublet model (THDM), generalized-CP transformations (Formula: see text where X is unitary) and unitary Higgs-family transformations (φ i →U ij φ j ) have recently been examined in a series of papers. In terms of gauge-invariant bilinear functions of the Higgs fields φ i , the Higgs-family transformations and the generalized-CP transformations possess a simple geometric description. Namely, these transformations correspond in the space of scalar-field bilinears to proper and improper rotations, respectively. In this formalism, recent results relating generalized CP transformations with Higgs-family transformations have a clear geometric interpretation. We will review what is known regarding THDM symmetries, as well as derive new results concerning those symmetries, namely how they can be interpreted geometrically as applications of several CP transformations.
Ferreira et al. (Sun,) studied this question.