Improved SUSY QCD corrections to Higgs boson decays into quarks and squarks

We improve the calculation of the supersymmetric $O(\alpha_s)$ QCD corrections to the decays of Higgs bosons into quarks and squarks in the Minimal Supersymmetric Standard Model. In the on-shell renormalization scheme these corrections can be very large, which makes the perturbative expansion unreliable. This is especially serious for decays into bottom quarks and squarks for large $\tan\beta$. Their corrected widths can even become negative. We show that this problem can be solved by a careful choice of the tree-level Higgs boson couplings to quarks and squarks, in terms of the QCD and SUSY QCD running quark masses, running trilinear couplings $A_q$, and on-shell left-right mixing angles of squarks. We also present numerical results for the corrected partial decay widths for the large $\tan\beta$ case.