Multi-Higgs models with CP symmetries of increasingly high order

TL;DR

This paper explores multi-Higgs-doublet models with higher-order CP symmetries like CP8 and CP16, revealing new CP-conserving structures and potential dark matter candidates protected by exotic CP charges.

Contribution

It extends the concept of CP-symmetry beyond CP4 to higher orders, constructing renormalizable potentials with CP8 and CP16 symmetries without accidental symmetries.

Findings

Higher-order CP symmetries lead to new CP-charge classifications.

Neutral scalars can serve as dark matter candidates protected by exotic CP.

Models with CP8 and CP16 exhibit distinctive mass spectra and interactions.

Abstract

When building CP-symmetric models beyond the Standard Model, one can impose CP-symmetry of higher order. This means that one needs to apply the CP-transformation more than two times to get the identity transformation, but still the model is perfectly CP-conserving. A multi-Higgs-doublet model based on CP-symmetry of order 4, dubbed CP4, was recently proposed and its phenomenology is being explored. Here, we show that the construction does not stop at CP4. We build examples of renormalizable multi-Higgs-doublet potentials which are symmetric under CP8 or CP16, without leading to any accidental symmetry. If the vacuum conserves CP-symmetry of order 2k, then the neutral scalars become CP-eigenstates, which are characterized not by CP-parities but by CP-charges defined modulo 2k. One or more lightest states can be the dark matter candidates, which are protected against decay not by the internal symmetry but by the exotic CP. We briefly discuss their mass spectra and interaction patterns for CP8 and CP16.