Supersymmetric Higgs boson decays into scalar quarks: QCD corrections

In supersymmetric theories, the decays of the neutral $\mathrm{CP}$-even and $\mathrm{CP}$-odd as well as the charged Higgs bosons into scalar quarks, in particular into top and bottom squarks, can be dominant if they are kinematically allowed. We calculate the QCD corrections to these decay modes in the minimal supersymmetric extension of the standard model, including all quark mass terms and squark mixing. These corrections turn out to be rather large, altering the decay widths by an amount which can be larger than 50%. The corrections can be either positive or negative, and depend strongly on the mass of the gluino. We also discuss the QCD corrections to the decays of heavy scalar quarks into light scalar quarks and Higgs bosons.