The order $O(\bar{\alpha }{\bar{\alpha }}_s)$ and $O({\bar{\alpha }}^2)$ corrections to the decay width of the neutral Higgs boson to the $\bar{b}b$ pair

We present the analytical expressions for the contributions of the order $O(\bar{\alpha }{\bar{\alpha }}_s)$ and $O({\bar{\alpha }}^2)$ corrections to the decay width of the Standard Model Higgs boson into the $\bar{b}b$-pair. The numerical value of the mixed QED and QCD correction of order $O(\bar{\alpha }{\bar{\alpha }}_s)$ is comparable with the previously calculated terms in the perturbative series for $\mathrm{\Gamma }(H^0\to \bar{b}b)$.