The width difference $Delta Gamma$ among the two mass eigenstates of the $B_s$-$bar B_s$ system is measured with a precision of 7%. The theory prediction has a larger uncertainty which mainly stems from unknown perturbative higher-order QCD corrections. I discuss the subset of next-to-next-to-leading order diagrams proportional to $alpha_s^2, N_f$, where $N_f=5$ is the number of quark flavours. The results are published in [1].
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