Two-Loop $ O(\alpha_sG_Fm_t^2)$ Correction to the $H\to b\bar b$ Decay Rate

We present the two-loop ${\cal O}(\alpha_sG_Fm_t^2)$ correction to the $b\bar b$ decay rate of the Stan\-dard-Model Higgs boson, assuming that the $t$ quark is much heavier than the Higgs boson. Apart from the universal correction connected with the renormalizations of the wave function and the vacuum expectation value of the Higgs field, this involves vertex corrections specific to the presence of beauty in the final state. We calculate the latter by means of a low-energy theorem. All would-be mass singularities related to the $b$ quark can be absorbed into the running Higgs-bottom Yukawa coupling. It turns out that the total ${\cal O}(\alpha_sG_Fm_t^2)$ correction screens the leading high-$m_t$ behaviour of the one-loop result by 71\% to 75\% for $M_H$ between 60~GeV and $2M_W$.