Studying possible CP-violating Higgs couplings through top-quark pair productions at muon colliders

We study possible anomalous CP-violating Higgs couplings to mu mu-bar and t t-bar fully model-independent way through top-quark pair productions at muon colliders. Assuming additional non-standard neutral Higgs bosons, whose couplings with top-quark and muon are expressed in the most general covariant form, we carry out analyses of effects which they are expected to produce via CP-violating asymmetries and also the optimal-observable (OO) procedure under longitudinal and transverse muon polarizations. We find the measurement of the asymmetry for longitudinal beam polarization could be useful to catch some signal of CP violation, and an OO analysis might also be useful if we could reduce the number of unknown parameters with a help of other experiments and if the size of the parameters is at least O(1) ~ O(10).