Probing the CP structure of the top quark Yukawa at the future muon collider

We study the top-Higgs coupling with a CP violating phase at a future multi-TeV muon collider. We focus on processes that are directly sensitive to the top quark Yukawa coupling. At different energies, different processes dominate the cross section, providing complementary information. At and above an energy of O(10) TeV, vector boson fusion processes dominate. As we show, in the Standard Model there is destructive interference in the vector boson fusion processes between the top quark Yukawa and Higgs-gauge boson couplings. A CP-violating phase changes this interference, and the cross section measurement is very sensitive to the size of the CP-violating angle. Although we find that the cross sections are measured to 50% statistical uncertainty at 1-sigma, a 10 and 30 TeV muon collider can bound the CP-violating angle to 9.0 and 5.4 degrees, respectively. However, cross section measurements are insensitive to the sign of the CP-violating angle. To determine that the coupling is truly CP violating, observables sensitive to CP-violation must be measured. We investigate several possible CP violating observables, we construct asymmetry parameters that show good distinction between different values and signs of the CP violating angle.