CP violation in 2HDM and EFT: the ZZZ vertex

TL;DR

This paper investigates CP violation in the ZZZ vertex within the two-Higgs doublet model and its effective field theory limit, identifying the order of operators responsible for CP violation and their suppression factors.

Contribution

It provides a detailed calculation of the ZZZ vertex form factor in 2HDM and clarifies the operator dimension at which CP violation appears in the effective theory.

Findings

The form factor $f_4^Z$ is computed at one loop in a general gauge.

CP violation in the ZZZ vertex is suppressed by high-dimensional operators in the EFT.

CP violation appears only at dimension-12 operators in the decoupling limit.

Abstract

We study the CP violating ZZZ vertex in the two-Higgs doublet model, which is a probe of a Jarlskog-type invariant in the extended Higgs sector. The form factor $f_4^Z$ is evaluated at one loop in a general $R_\xi$ gauge and its magnitude is estimated in the realistic parameter space. Then we turn to the decoupling limit of the two-Higgs doublet model, where the extra scalars are heavy and the physics can be described by the Standard Model supplemented by higher-dimensional operators. The leading operator contributing to $f_4^Z$ at one loop is identified. The CP violating ZZZ vertex is not generated in the effective theory by dimension-8 operators, but instead arises only at the dimension-12 level, which implies an additional suppression by powers of the heavy Higgs mass scale.