CP Violation in Tau Slepton Pair Production at Muon Colliders

We discuss in detail signals for CP violation in the Higgs boson and tau-slepton sectors through the production processes $\mu^+\mu^- \to \tilde{\tau}_i^- \tilde{\tau}_j^+$, where $i,j=1,2$ label the two $\tau$ slepton mass eigenstates in the minimal supersymmetric standard model. We assume that the soft breaking parameters of third generation sfermions contain CP violating phases, which induce CP violation in the Higgs sector through quantum corrections. We classify all the observables for probing CP violation in the Higgs boson and $\tau$ slepton sectors. These observables depend on the initial muon beam polarization, where we include transverse polarization states. If the heavy Higgs bosons can decay into tau slepton pairs, a complete determination of the CP properties of the neutral Higgs boson and $\tau$--slepton systems is possible. The interference between the Higgs boson and gauge boson contributions could also provide a powerful method for probing CP violation, if transversely polarized muon beams are available. We show in detail how to directly measure CP violation in the tau slepton system, under the assumption that the neutral Higgs mixing angles are determined through the on--shell production of the neutral Higgs bosons.