Probing the MSSM Higgs Boson Sector with Explicit CP Violation through Third Generation Fermion Pair Production at Muon Colliders

We perform a systematic study of the production of a third-generation fermion-pair, $\mu^+\mu^-\to f\bar{f}$ for $f=\tau^-,b$, and t in the minimal supersymmetric standard model (MSSM) with explicit CP violation, which is induced radiatively by soft trilinear interactions related to squarks of the third generation. We classify all the observables for probing the CP property of the Higgs bosons constructed by the initial muon beam polarization along with the unpolarized final fermions and with the final-fermion polarization configuration of equal helicity, respectively. The observables allow for complete determination of CP property of the neutral Higgs bosons. The interference between the Higgs boson and gauge boson contributions also could provide a powerful method for the determination of the CP property of two heavy Higgs bosons in the top-quark pair production near the energy region of the Higgs-boson resonances. For the lightest Higgs-boson mass there is no sizable interference between scalar and vector contributions for the determination of the CP property of the lightest Higgs boson. We give a detailed numerical analysis to show how the radiatively-induced CP violation in the Higgs sector of the MSSM can be measured.