QCD corrections to the decay $H^+ \to t \bar{b}$ in the Minimal Supersymmetric Standard Model

We present a complete calculation of the QCD corrections (of the order $\alpha_s$) to the width of the decay $H^+ \to t \bar{b}$ within the Minimal Supersymmetric Standard Model. We find that the QCD corrections are quite important, and that the supersymmetric QCD corrections (due to gluino, stop and sbottom exchange) can be comparable to or even larger than the standard QCD corrections in a large region of the supersymmetric parameter space. This is mainly due to the effect of large left-right mixings of stop and sbottom. This could significantly affect the phenomenology of the $H^+$ search.