Sensitivity to $\mathcal{CP}$-violating effective couplings in the top-Higgs sector

The observed baryon asymmetry of the Universe requires new sources of charge-parity ($\mathcal{CP}$) violation beyond those in the Standard Model. In this work, we investigate $\mathcal{CP}$-violating effects in the top-Higgs sector using the Standard Model Effective Field Theory (SMEFT) framework. Focusing on top-pair production in association with a Higgs boson and single top-Higgs associated production at the LHC, we study $\mathcal{CP}$ violation in the top-Higgs Yukawa coupling and other Higgs and top interactions entering these processes. By analysing $\mathcal{CP}$-sensitive differential observables and asymmetries, we provide direct constraints on $\mathcal{CP}$-violating interactions in the top-Higgs sector. Our analysis demonstrates how combining $t\bar{t}h$ and $thj$ production can disentangle the real and imaginary components of the top-Yukawa coupling, offering valuable insights into potential sources of $\mathcal{CP}$ violation. The sensitivity of these observables to SMEFT operators provides model-independent constraints on the parameter space, advancing the search for new physics in the top-Higgs sector.