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Directly Probing the CP-structure of the Higgs-Top Yukawa at HL-LHC and Future Colliders

Constraining the Higgs boson properties is a cornerstone of the LHC program and future colliders. In this Snowmass contribution, we study the potential to directly probe the Higgs-top CP-structure via the $t\bar{t}h$ production at the HL-LHC, 100 TeV FCC and muon colliders. We find the limits on the CP phase ($α$) at 95% CL are $|α| \lesssim 36^\circ$ with dileptonic $t\bar t (h\to b\bar b) $ and $|α| \lesssim 25^\circ$ with combined $t\bar t (h\to γγ) $ at the HL-LHC. The 100 TeV FCC brings a significant improvement in sensitivity with $|α| \lesssim 3^\circ$ for the dileptonic $t\bar t (h\to b\bar b) $, due to the remarkable gain in the signal cross-section and the increased luminosity. At future muon colliders, we find that the bounds with semileptonic $t\bar t (h\to b\bar b) ν\barν$ are $|α| \lesssim 9^\circ$ for 10 TeV and $|α| \lesssim 3^\circ$ for 30 TeV, respectively.