$B_s \to \mu^+ \mu^-$ in the SM and $\bar{B}\to X_s \gamma$ in the 2HDM at NNLO in QCD

Abstract

In this contribution the QCD next-to-next-to-leading order (NNLO) matching coefficients to the branching ratio $B_s \to \mu^+ \mu^-$ in the Standard Model (SM) and to $\bar{B}\to X_s \gamma$ in the Two Higgs Doublet Model (2HDM) are discussed. In both cases a three-loop matching between the full and effective theory was performed, which leads to a significant reduction of the scale uncertainty.