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

A bstract 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: tth t t ¯ h, tbhμν, and tt h t t ¯ hν ν ¯ with h bb h → b b ¯ and semileptonic top decays. At different energies, different processes dominate the cross section, providing complementary information. At and above an energy of O (10) 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 tt h t t ¯ hν ν ¯ 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 O (50\%) O 50 % statistical uncertainty at 1 σ, 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 tth t t ¯ h process the azimuthal angle between the t+t t + t ¯ plane and the initial state muon+Higgs plane shows good discrimination for ξ = ±0. 1 π. For the tbhμν and tt h t t ¯ hν ν ¯ processes, the operator proportional to (p_ pₕ) p → μ × p → h · pₜ p → t is sensitive to the sign of CP phase ξ. From these observables, we construct asymmetry parameters that show good distinction between different values and signs of the CP violating angle.