Is the real two-Higgs-doublet model consistent?

TL;DR

This paper demonstrates that the real two-Higgs-doublet model is inconsistent under renormalization due to quark-induced divergent CP violation, which arises at seven loops and breaks certain symmetries.

Contribution

The study identifies the loop order at which divergent CP violation appears and explains the symmetry properties affecting its emergence in the model.

Findings

Divergent CP violation appears at seven loops in the model.

Symmetries suppress divergent CPV at six loops, but are broken at seven loops.

The parameter dependence of the divergent CPV is characterized.

Abstract

We provide strong evidence that the widely-studied real two-Higgs-doublet model is inconsistent under renormalization due to quark-induced divergent CP violation (CPV). We identify the necessary ingredients for the CPV to enter the renormalization-group equations based on symmetry proprieties of the divergent diagrams. We demonstrate that while these ingredients are present starting at six loops, the divergent CPV is zero at that order due to approximate symmetries. We show that these symmetries are broken at seven loops and determine the parameter dependence of the resulting divergent CPV.