Geometrical CP violation in multi-Higgs models

TL;DR

This paper introduces methods to identify calculable, parameter-independent phases in multi-Higgs models, leading to new candidates for geometrical CP violation that inherently violate CP, depending on scalar number and symmetry group.

Contribution

The paper develops novel methods to find geometrical CP violation phases and extends the proof that more than two scalars are necessary for such phenomena in non-renormalisable potentials.

Findings

Identified new geometrical CP violation candidates with CP-violating vacuum expectation values.

Established that the phases depend on the number of scalars and the discrete symmetry group.

Extended proof to non-renormalisable potentials confirming the requirement of more than two scalars.

Abstract

We introduce several methods to obtain calculable phases with geometrical values that are independent of arbitrary parameters in the scalar potential. These phases depend on the number of scalars and on the order of the discrete non-Abelian group considered. Using these methods we present new geometrical CP violation candidates with vacuum expectation values that must violate CP (the transformation that would make them CP conserving is not a symmetry of the potential). We also extend to non-renormalisable potentials the proof that more than two scalars are needed to obtain these geometrical CP violation candidates.