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NLO supersymmetric QCD corrections to the $t \bar b H^-$ associated production at hadron colliders

We present the next-to-leading order QCD corrected total cross sections and the distributions of the transverse momenta of the final anti-bottom-quark, top-quark and charged Higgs-boson for the processes of $p\bar p/pp \to t\bar b H^-+X$ in the minimal supersymmetric standard model(MSSM) at the Tevatron and the LHC. We find that the NLO QCD corrections significantly modify the leading-order distributions of the transverse momenta of final particles($p_T^b$, $p_T^t$ and $p_T^{H^-}$), and the total NLO QCD corrections reduce the dependence of the cross section on the renormalization and factorization scales, especially the NLO QCD corrected cross sections at the LHC are nearly independent of these scales. Our results show that the relative correction is obviously related to $m_{H^-}$ and $\tanβ$, and the total NLO QCD relative corrections can be beyond -50% at the Tevatron and approach -40% at the LHC in our chosen parameter space.