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 ξ at a future multi-TeV muon collider. We focus on processes that are directly sensitive to the top quark Yukawa coupling: $t$$\overline{t}$$h$, $tbhμν$, and $t$$\overline{t}$$h$$v$$\overline{v}$ with $h$ → $b$$\overline{b}$ and semileptonic top decays. At different energies, different processes dominate the cross section, providing complementary information. At and above an energy of $\mathcal{O}$(10) TeV, vector boson fusion processes dominate. As we show, in the Standard Model there is destructive interference in the vector boson fusion processes $t$$\overline{t}$$h$$v$$\overline{v}$ and $tbhμν$ between the top quark Yukawa and Higgs-gauge boson couplings. A CP-violating phase changes this interference, and the cross section measurement is very sensitive to the size of the CP-violating angle. Although we find that the cross sections are measured to $\mathcal{O}$(50%) statistical uncertainty at 1σ, a 10 and 30 TeV muon collider can bound the CP-violating angle |ξ| ≲ 9.0° and |ξ| ≲ 5.4°, respectively. However, cross section measurements are insensitive to the sign of the CP-violating angle. To determine that the coupling is truly CP violating, observables sensitive to CP-violation must be measured. We find in the $t$$\overline{t}$$h$ process the azimuthal angle between the $t$ + $\overline{t}$ plane and the initial state muon+Higgs plane shows good discrimination for ξ = ±0.1π.