CPviolation in tau slepton pair production at muon colliders

Abstract

We discuss in detail signals for $\mathrm{CP}$ violation in the Higgs boson and tau-slepton sectors through the production processes ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{i}^{\ensuremath{-}}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}}_{j}^{+},$ where $i,j=1,2$ label the two $\ensuremath{\tau}$ slepton mass eigenstates in the minimal supersymmetric standard model. We assume that the soft breaking parameters of third generation sfermions contain $\mathrm{CP}$ violating phases, which induce $\mathrm{CP}$ violation in the Higgs sector through quantum corrections. We classify all the observables for probing $\mathrm{CP}$ violation in the Higgs boson and $\ensuremath{\tau}$ 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 $\mathrm{CP}$ properties of the neutral Higgs boson and $\ensuremath{\tau}$-slepton systems is possible. The interference between the Higgs boson and gauge boson contributions could also provide a powerful method for probing $\mathrm{CP}$ violation, if transversely polarized muon beams are available. We show in detail how to measure $\mathrm{CP}$ violation directly 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.