CP violation in charged Higgs decays in the MSSM

In the MSSM with complex parameters loop corrections to the decays $H^+ \to t \bar{b}$ and $H^- \to \bar{t} b$ with $t \to b W$ and $W \to l \nu$ lead to CP-violating asymmetries: a decay rate asymmetry, a forward-backward asymmetry and an energy asymmetry. We derive explicit formulas for them and perform a detailed numerical analysis. We study the dependence on the parameters and the phases involved. In particular, the influence of the running Yukawa coupling is taken into account. The decay rate asymmetry can go up to 25%, the forward-backward and the energy asymmetry up to 10%.