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The $\mathcal{CP}$ structure of the Higgs boson in its coupling to theparticles of the Standard Model is amongst the most important Higgs bosonproperties which have not yet been constrained with high precision. In thisstudy, all relevant inclusive and differential Higgs boson measurements fromthe ATLAS and CMS experiments are used to constrain the $\mathcal{CP}$-natureof the top-Yukawa interaction. The model dependence of the constraints isstudied by successively allowing for new physics contributions to the couplingsof the Higgs boson to massive vector bosons, to photons, and to gluons. In themost general case, we find that the current data still permits a significant$\mathcal{CP}$-odd component in the top-Yukawa coupling. Furthermore, weexplore the prospects to further constrain the $\mathcal{CP}$ properties ofthis coupling with future LHC data by determining $tH$ production ratesindependently from possible accompanying variations of the $t\bar t H$ rate.This is achieved via a careful selection of discriminating observables. At theHL-LHC, we find that evidence for $tH$ production at the Standard Model ratecan be achieved in the Higgs to diphoton decay channel alone.

Indirect $\mathcal{CP}$ probes of the Higgs-top-quark interaction: current LHC constraints and future opportunities