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We compute the decay rate of the Standard Model Higgs boson to bottom quarksto order $\alpha\alpha_s$. We apply the optical theorem and calculate theimaginary part of three-loop corrections to the Higgs boson propagator usingasymptotic expansions in appropriately chosen mass ratios. The corrections oforder $\alpha\alpha_s$ are of the same order of magnitude as the ${\calO}(\alpha_s^3)$ QCD corrections but have the opposite sign.

$Gamma(H\to b\bar{b})$ to order $\alpha\alpha_s$