CP Violation in the General Two-Higgs-Doublet Model: a Geometric View

TL;DR

This paper provides a geometric framework to analyze CP violation in the general Two-Higgs-Doublet Model, offering basis-independent conditions for explicit and spontaneous CP violation.

Contribution

It introduces a geometric approach using gauge invariant functions to characterize CP properties in the THDM, enabling basis-independent analysis.

Findings

Derived basis-independent conditions for explicit CP violation.

Established criteria for spontaneous CP violation in the THDM.

Linked CP transformations to reflections in a geometric space.

Abstract

We discuss the CP properties of the potential in the general Two-Higgs-Doublet Model (THDM). This is done in a concise way using real gauge invariant functions built from the scalar products of the doublet fields. The space of these invariant functions, parametrising the gauge orbits of the Higgs fields, is isomorphic to the forward light cone and its interior. CP transformations are shown to correspond to reflections in the space of the gauge invariant functions. We consider CP transformations where no mixing of the Higgs doublets is taken into account as well as the general case where the Higgs basis is not fixed. We present basis independent conditions for explicit CP violation which may be checked easily for any THDM potential. Conditions for spontaneous CP violation, that is CP violation through the vacuum expectation values of the Higgs fields, are also derived in a basis independent way.