Decay widths of the neutral CP-even MSSM Higgs bosons in the Feynman-diagrammatic approach

In the Minimal Supersymmetric Standard Model (MSSM) we incorporate the Higgs-boson propagator corrections, evaluated up to two-loop order, into the prediction of Gamma(h --> f (f) over bar) and BR(h --> f (f) over bar) for f = b, c, tau. The propagator corrections consist of the full one-loop contribution, including the effects of non-vanishing external momentum, and corrections of O(alpha alpha(s)) at the two-loop level. The results are supplemented with the dominant one-loop QED corrections and final state QCD corrections from both gluons and gluinos. The effects of the two-loop propagator corrections and of the one-loop gluino contributions are investigated in detail. Our results are compared with the result obtained within the renormalization group approach. Agreement within 10% is found for most parts of the MSSM parameter space.