A CP-conserving multi-Higgs model without real basis

TL;DR

This paper presents a unique three-Higgs-doublet model that is CP-conserving but lacks a real basis, challenging previous assumptions linking CP invariance to basis transformations.

Contribution

It provides the first counterexample to the belief that all CP-conserving multi-Higgs models have a real basis, revealing new phenomenological features.

Findings

Counterexample of a CP-conserving model without a real basis

Extra neutral Higgs bosons are 'half-odd' under generalized CP-symmetry

Challenges previous theorems on basis realness and CP invariance

Abstract

Models beyond the Standard Model (bSM) often involve elaborate Higgs sectors, which can be a source of CP-violation. It brings up the question of recognizing in an efficient way whether a model is CP-violating. There is a diffuse belief that the issue of explicit CP invariance can be linked to the existence of a basis in which all coefficients are real; with even a theorem proposed a decade ago claiming that the scalar sector of any multi-Higgs doublet model is explicitly CP-conserving if and only if all of its coefficients can be made real by a basis change. This is compounded by the fact that in all specific multi Higgs models considered so far, the calculations complied with this claim. Here, we present the first counterexample to this statement: a CP-conserving three-Higgs-doublet model for which no real basis exists. We outline the phenomenological consequences of this model, and notice that the extra neutral Higgs bosons are neither CP-even nor CP-odd but are "half-odd" under the generalized CP-symmetry of the model.