Group-theoretic restrictions on generation of CP-violation in multi-Higgs-doublet models

TL;DR

This paper proves that in multi-Higgs-doublet models, the presence or absence of explicit CP-violation due to a symmetry group G directly determines the possibility of spontaneous CP-violation, confirming a longstanding conjecture.

Contribution

The paper establishes a general proof that symmetry group G's restrictions on CP-violation in multi-Higgs-doublet models are universally linked for any number of doublets.

Findings

If G prevents explicit CPV, it also prevents spontaneous CPV.

If G allows explicit CPV, it allows spontaneous CPV.

The proof applies to any rephasing symmetry group G and any number of doublets.

Abstract

It has been known since decades that imposing a symmetry group G on the scalar sector of multi-Higgs-doublet models has consequences for CP-violation. In all examples of two- and three-Higgs-doublet models equipped with symmetries, one observes the following intriguing property: if G prevents explicit CP-violation (CPV), at least in the neutral Higgs sector, then it also prevents spontaneous CPV, and if G allows explicit CPV, then it allows for spontaneous CPV. One is led to conjecture that this is a general phenomenon. In this paper, we prove this conjecture for any rephasing symmetry group G and any number of doublets.