Leaks of CP violation in the real two-Higgs doublet model

TL;DR

This paper investigates CP violation leaks in the real two-Higgs doublet model by calculating complex three-loop diagrams, revealing an unavoidable divergence that challenges the model's consistency.

Contribution

It introduces a detailed three-loop calculation of the pseudoscalar tadpole in the real 2HDM, highlighting an inherent divergence linked to CP violation.

Findings

Discovery of an irremovable divergence in the scalar sector

Confirmation of cancellation of leading divergences through multiple derivations

Identification of CP violation transfer from quarks to scalars

Abstract

We discuss the $Z_2$ symmetric two Higgs doublet model with a real soft breaking term (real 2HDM). We explain in detail why it is not tenable to assume CP conservation in the scalar sector to keep the dimension two term real, while CP is violated by the dimension four Yukawa couplings. We propose the calculation of the infinite tadpole of the (would-be) pseudoscalar neutral scalar. We construct a simple toy model with the same flaws, where the unrenormalizable infinity is easier to calculate. We then turn our attention to the same tadpole in the real 2HDM. We spearhead this effort focusing on diagrams involving solely bare quantities. This involves hundreds of Feynman three-loop diagrams that could feed the CP violation from the quark into the scalar sector, and is only possible with state of the art automatic computation tools. Remarkably, some intermediate results agree when using three independent derivations, including the peculiar cancellation of the leading pole divergence due to a subtle interplay between masses and the Jarlskog invariant, which we calculate analytically. The calculation is not complete however, since the full two-loop renormalization of the real 2HDM is not yet available in the literature. Still, we argue convincingly that there is an irremovable infinity.