$B_s\to μ^+μ^-$ and $\bar{B} \to X_s γ$ to NNLO

In this contribution, the recent calculation of next-to-next-to-leading order QCD and next-to-leading order electroweak corrections to the decay $B_s\to μ^+μ^-$ is reviewed, and a detailed discussion of the uncertainty of the theory prediction is provided. Furthermore, we discuss the status of the next-to-next-to-leading order QCD corrections to $\bar{B} \to X_s γ$.

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