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The ${\cal O}(\alpha_s)$ QCD corrections to the three-body decay width of thecharged 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-bodydecay mode raise the width by about 12% and the supersymmetric QCDcorrections(due to $\tilde{g}, \tilde{t}, \tilde{b}$ exchanges) can becomparable to or even larger than the standard QCD corrctions in some regionsof the supersymmetric parameter space. This is mainly due to the effect oflarge left-right mixing of stop($\tilde{t}$). It could significantly affect thephenomenology of the $H^+$ search.Comment: 14 pages, 14figure

QCD and SUSY QCD corrections to the three-body decay of the charged Higgs boson