CP violation in charged Higgs boson decays in the MSSM with complex parameters

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Supersymmetric loop contributions can lead to different decay rates of H+→ t b and H-→ b t. We calculate the decay rate asymmetry δᶜP = Γ(H+→ t b)-Γ(H-→ b t)Γ(H+→ t b)+Γ(H-→ b t) at next-to-leading order in the MSSM with complex parameters. We analyse the parameter dependence of δᶜP with emphasis on the phases of Aₜ and Ab. It turns out that the most important contribution comes from the loop with stop, sbottom, and gluino. If this contribution is present, δᶜP can go up to 10-15%.