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

Abstract

We compute the decay rate of the Standard Model Higgs boson to bottom quarks to order $\alpha {\alpha }_s$. We apply the optical theorem and calculate the imaginary part of three-loop corrections to the Higgs boson propagator using asymptotic expansions in appropriately chosen mass ratios. The corrections of order $\alpha {\alpha }_s$ are of the same order of magnitude as the $\mathcal{O}({\alpha }_s^3)$ QCD corrections but have the opposite sign.

Comments: 16 pages, 2 figures and 7 tables