Two-Loop ${\cal O}(α_s^2)$ Correction to the $H\to b\bar b$ Decay Rate Induced by the Top Quark

We present the two-loop QED and QCD corrections to the $f\bar fH$ Yukawa coupling that are induced by the exchange of a virtual photon or gluon, respectively, with a heavy-fermion loop inserted. As an application, we study the corresponding $\O(\alpha_s^2M_H^2/m_t^2)$ correction to the $H\to b\bar b$ decay rate.