Probing the MSSM Higgs boson sector with explicitCPviolation through third generation fermion pair production at muon colliders

Abstract

We perform a systematic study of the production of a third-generation fermion pair, ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\rightarrow}f\overline{f}$ for $f={\ensuremath{\tau}}^{\ensuremath{-}},$ b, and t in the minimal supersymmetric standard model (MSSM) with explicit $\mathrm{CP}$ violation, which is induced radiatively by soft trilinear interactions related to squarks of the third generation. We classify all the observables for probing the $\mathrm{CP}$ 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 the $\mathrm{CP}$ 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 $\mathrm{CP}$ 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 $\mathrm{CP}$ property of the lightest Higgs boson. We give a detailed numerical analysis to show how the radiatively induced $\mathrm{CP}$ violation in the Higgs sector of the MSSM can be measured.