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SUSY-QCD corrections to the MSSM $h^0 b \bar b$ vertex in the decoupling limit

We analyze the supersymmetric (SUSY) QCD contribution to the $h^0 b \bar{b}$ coupling at one loop in the Minimal Supersymmetric Model (MSSM) in the decoupling limit. Analytic expressions in the large SUSY mass region are derived and the decoupling behavior of the corrections is examined in various limiting cases, where some or all of the SUSY mass parameters become large. We show that in the decoupling limit of large SUSY mass parameters and large CP-odd Higgs mass, the $h^0 b \bar b$ coupling approaches its Standard Model value at one loop. However, the onset of decoupling is delayed when $\tanβ$ is large. In addition, the one-loop SUSY-QCD corrections decouple if the masses of either the bottom squarks or the gluino are separately taken large; although the approach to decoupling is significantly slower in the latter case.