  The Higgs-gluon interaction is crucial for LHC phenomenology. To improve the
constraints on the CP structure of this coupling, we investigate Higgs
production with two jets using machine learning. In particular, we exploit the
CP sensitivity of the so far neglected phase space region that differs from the
typical vector boson fusion-like kinematics. Our results suggest that
significant improvements in current experimental limits are possible. We also
discuss the most relevant observables and how CP violation in the Higgs-gluon
interaction can be disentangled from CP violation in the interaction between
the Higgs boson and massive vector bosons. Assuming the absence of CP-violating
Higgs interactions with coloured beyond-the-Standard-Model states, our
projected limits on a CP-violating top-Yukawa coupling are stronger than more
direct probes like top-associated Higgs production and limits from a global
fit.
