We summarize our recent proposals for probing the CP-odd iκ˜t¯γ5th interaction at the LHC and its projected upgrades directly using associated on-shell Higgs boson and top quark or top quark pair production. We first recount how to construct a CP-odd observable based on top quark polarization in Wb→th scattering with optimal linear sensitivity to κ˜. For the corresponding hadronic process pp→thj we then present a method of extracting the phase-space dependent weight function that allows to retain close to optimal sensitivity to κ˜. For the case of top quark pair production in association with the Higgs boson, pp→tt¯h, with semileptonically decaying tops, we instead show how one can construct manifestly CP-odd observables that rely solely on measuring the momenta of the Higgs boson and the leptons and b-jets from the decaying tops without having to distinguish the charge of the b-jets. Finally, we introduce machine learning (ML) and non-ML techniques to study the phase-space optimization of such CP-odd observables. We emphasize a simple optimized linear combination α·ω that gives similar sensitivity as the studied fully fledged ML models. Using α·ω we review sensitivity projections to κ˜ at HL-LHC, HE-LHC, and FCC-hh.
Some recent theoretical progress in Higgs boson and top quark physics at hadron colliders