Geometric picture of generalized-CP and Higgs-family transformations in the two-Higgs-doublet model

TL;DR

This paper provides a geometric framework for understanding generalized-CP and Higgs-family transformations in the two-Higgs-doublet model, revealing their correspondence to rotations in a bilinear scalar-field space.

Contribution

It introduces a geometric interpretation of these transformations as rotations and improper rotations, clarifying their relationship in the scalar-field bilinear space.

Findings

Higgs-family transformations correspond to proper rotations.

Generalized-CP transformations correspond to improper rotations.

The geometric picture simplifies understanding of symmetry relations.

Abstract

In the two-Higgs-doublet model (THDM), generalized-CP transformations (phi_i--> X_{ij} phi_j^* where X is unitary) and unitary Higgs-family transformations (phi_i--> U_{ij} phi_j) have recently been examined in a series of papers. In terms of gauge-invariant bilinear functions of the Higgs fields phi_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.