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

We improve the calculation of the supersymmetric script O sign(α_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 β. 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 β case.