Geometrical CP violation from non-renormalisable scalar potentials

TL;DR

This paper investigates how non-renormalisable scalar potentials with specific discrete symmetries can preserve geometrical CP violation in multi-Higgs models, extending the understanding of symmetry and vacuum structure.

Contribution

It demonstrates that non-renormalisable terms consistent with Delta(27) or Delta(54) symmetries can maintain geometrical CP violation in three-Higgs-doublet models.

Findings

Non-renormalisable terms can preserve the CP-violating vacuum.

Geometrical CP violation is robust against higher-order corrections.

Symmetry constraints ensure stability of the vacuum structure.

Abstract

We consider in detail the non-renormalisable scalar potential of three Higgs doublets transforming as an irreducible triplet of Delta(27) or Delta(54). We start from a renormalisable potential that spontaneously leads to a vacuum with CP-violating phases independent of arbitrary parameters - geometrical CP violation. Then we analyse to arbitrarily high order non-renormalisable terms that are consistent with the symmetry and we demonstrate that inclusion of non-renormalisable terms in the potential can preserve the geometrical CP-violating vacuum.