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We discuss in detail signals for CP violation in the Higgs boson andtau-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. Weassume that the soft breaking parameters of third generation sfermions containCP violating phases, which induce CP violation in the Higgs sector throughquantum corrections. We classify all the observables for probing CP violationin the Higgs boson and $\tau$ slepton sectors. These observables depend on theinitial muon beam polarization, where we include transverse polarizationstates. If the heavy Higgs bosons can decay into tau slepton pairs, a completedetermination of the CP properties of the neutral Higgs boson and$\tau$--slepton systems is possible. The interference between the Higgs bosonand gauge boson contributions could also provide a powerful method for probingCP violation, if transversely polarized muon beams are available. We show indetail how to directly measure CP violation in the tau slepton system, underthe assumption that the neutral Higgs mixing angles are determined through theon--shell production of the neutral Higgs bosons.Comment: 38 pages, 9 figures Including 7 eps ones. A figure to show the  dependence on tan(beta) and the mass parameters of the sfermion sectors and a  reference added. To appear in Phys. Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>CP</mml:mi></mml:math>violation in tau slepton pair production at muon colliders

CPviolation in tau slepton pair production at muon colliders