Direct Higgs-top CP-phase measurement with $t\bar{t}h$ at the 14 TeV LHC and 100 TeV FCC

The study of the Higgs boson's properties is a cornerstone of the LHC and future collider programs. In this paper, we examine the potential to directly probe the Higgs-top interaction strength and CP-structure in the $t\bar t h$ channel with the Higgs boson decaying to bottom-quark pairs and top-quarks in the di-leptonic mode. We adopt the BDRS algorithm to tag the boosted Higgs and exploit the $M_2$-assisted reconstruction to compute observables sensitive to the CP-phase at the $t\bar{t}$ rest frame, where the new physics sensitivity can be enhanced. Performing a side-band analysis at the LHC to control the continuum $t\bar{t}b\bar{b}$ background, we find that the Higgs-top strength and CP-phase can be probed up to $\delta\kappa_t\lesssim 20\%$ and $| \alpha | \lesssim 36^\circ$ at 95% CL, respectively. We also derive that a similar analysis at a 100 TeV future collider could further improve the precision to $\delta\kappa_t\lesssim 1\%$ and $| \alpha| \lesssim 1.5^\circ$, where the CP-odd observables play a crucial role, boosting the sensitivity on the CP-phase.