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

Supersymmetric loop contributions can lead to different decay rates of H+\to t\bar b and H-\to b\bar t. We calculate the decay rate asymmetry \delta^CP = \frac{\Gamma(H+\to t\bar b)-\Gamma(H-\to b\bar t)}{{\Gamma(H+\to t\bar b)+\Gamma(H-\to b\bar t)} at next-to-leading order in the MSSM with complex parameters. We analyse the parameter dependence of \delta^CP with emphasis on the phases of A_t and A_b. It turns out that the most important contribution comes from the loop with stop, sbottom, and gluino. If this contribution is present, \delta^CP can go up to 10-15% for tan(beta)~10, and to ~5% for large values of tan(beta).