QCD and SUSY-QCD corrections to the Three-Body Decay of the Charged Higgs Boson

The ${\cal O}(\alpha_s)$ QCD corrections to the three-body decay width of the charged Higgs $\Gamma$($H^+\to W^+b\bar{b}$) are discussed in the MSSM model. Our calculations indicate that the standard QCD corrections to the three-body decay mode raise the width by about 12% and the supersymmetric QCD corrections(due to $\tilde{g}, \tilde{t}, \tilde{b}$ exchanges) can be comparable to or even larger than the standard QCD corrctions in some regions of the supersymmetric parameter space. This is mainly due to the effect of large left-right mixing of stop($\tilde{t}$). It could significantly affect the phenomenology of the $H^+$ search.