$B$−$\bar{B}$ mixing: decay matrix at high precision

I review the status of the Standard-Model prediction of the width difference $\Delta$$\Gamma$$_s$ among the two $B$$_s$ meson eigenstates. Ongoing effort addresses three-loop QCD corrections, corresponding to the next-to-next-to-leading order of QCD. With an improved theoretical precision of the ratio $\Delta$$\Gamma$$_s$/$\Delta$$M$$_s$, where $\Delta$$M$$_s$ denotes the mass difference in the $B$$_s$-$\bar{B}$s system, one can probe new physics in $\Delta$$M$$_s$ without sensitivity to |$V$$_{cb}$|, whose value is currently controversial.