Status of SM calculations of b > s transitions

Abstract

We report recent progress in SM calculations of $b \to s$ transitions. We discuss the first NNLL prediction of the $\bar B \to X_s \gamma$ branching ratio, including important additional subtleties due to non-perturbative corrections and logarithmically-enhanced cut effects, and also recent results on the inclusive mode $\bar B \to X_s \ell^+ \ell^-$. Moreover, new results on the corresponding exclusive modes are reviewed. Finally, we comment on the present status of the so-called $B \to K \pi$ puzzle in hadronic $b \to s$ transitions