# Approaching robust EFT limits for CP-violation in the Higgs sector

## TL;DR

This paper develops methods to improve constraints on CP-violation in the Higgs sector using effective field theory, addressing degeneracies and disentangling contributions, and demonstrates the potential of future collider measurements.

## Contribution

It introduces combined measurement strategies and a perturbative validation approach to robustly constrain CP-violating operators in Higgs interactions.

## Key findings

- Degeneracies can be lifted by combining specific Higgs production measurements.
- Exploiting the top-quark threshold enhances analysis sensitivity.
- High-statistics future collider data enables perturbatively robust constraints.

## Abstract

Constraining CP-violating interactions in effective field theory (EFT) of dimension six faces two challenges. Firstly, degeneracies in the multi-dimensional space of Wilson coefficients have to be lifted. Secondly, quadratic contributions of CP-odd dimension six operators are difficult to disentangle from squared contributions of CP-even dimension six operators and from linear contributions of dimension eight operators. Both of these problems are present when new sources of CP-violation are present in the interactions between the Higgs boson and heavy strongly-interacting fermions. We show that degeneracies in the Wilson coefficients can be removed by combining measurements of Higgs-plus-two-jet production via gluon fusion with measurements of top-pair associated Higgs production. In addition, we demonstrate that the sensitivity of the analysis can be improved by exploiting the top-quark threshold in the gluon fusion process. Finally, we substantiate a perturbative argument about the validity of EFT by comparing the quadratic and linear contributions from CP-odd dimension six operators and use this to show explicitly that high statistics measurements at future colliders enable the extraction of perturbatively robust constraints on the associated Wilson coefficients.