Measuring single-top-associated Higgs production at the HL-LHC

Precision measurements of top-associated Higgs production are an important ingredient to unravel the $\mathcal{CP}$ nature of the Higgs boson. In this work, we constraint the $\mathcal{CP}$ nature of the top-Yukawa coupling taking into account all relevant inclusive and differential Higgs boson measurements. Based upon this fit, we show that it is crucial to disentangle single- and di-top-associated Higgs production for tightening indirect constraints on a $\mathcal{CP}$-odd top-Yukawa coupling in the future. In this context, we propose an analysis strategy for measuring $tH$ production at the HL-LHC without relying on assumptions about the Higgs $\mathcal{CP}$ character.