A CP-conserving multi-Higgs model without real basis

Understand

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.