  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.
