QCD corrections to $B$-meson mixing at two loops and beyond

We report on the updated theoretical predictions for the width difference $\Delta {\Gamma }_s$ and the flavor-specific CP asymmetry $a_{fs}^s$ in the $B_s-{\overline{B}}_s$ mixing. Working at leading power in the Heavy Quark Expansion we evaluated all previously unknown two-loop contributions to this observable, which marks an important step in the task of reducing uncomfortably
large scale uncertainties stemming from uncalculated QCD corrections.
Our new the Standard-Model prediction for the ratio of the width and mass differences in the $\overline{MS}$ scheme reads $\Delta {\Gamma }_s/\Delta M_s=(5.20\pm 0.69)\cdot {10}^{-3}$.