QCD CORRECTIONS TO HIGGS BOSON DECAYS

The two--loop ${\cal O}(\alpha_s G_F m_t^2)$ corrections to the $b\bar b$ decay rate of the Standard Model Higgs boson as well as its production via $e^+e^- \to ZH$ will be presented. These QCD corrections are obtained by using a low-energy theorem for light Higgs bosons compared to the top quark mass. The results yield strong screening effects of the ${\cal O}(G_F m_t^2)$ contributions. After that the two-loop QCD corrections to the $\gamma\gamma$ and gluonic decays of the Higgs bosons of the Standard Model and its minimal supersymmetric extension are discussed. While the corrections to the $\gamma\gamma$ decays remain small of ${\cal O}(\alpha_s)$ they are huge $\sim$ 50 -- 70 \% in the case of the gluonic decays.