Anomalous Dimension Matrix for Radiative and Rare Semileptonic B Decays up to Three Loops

Abstract

We compute the complete O(alphas^2) anomalous dimension matrix relevant for the b to s gamma, b to s gluon and b to s l+l- transitions in the standard model and some of its extensions. For radiative decays we confirm the results of Misiak and Munz, and of Chetyrkin, Misiak and Munz. The O(alphas^2) mixing of four-quark into semileptonic operators is instead a new result and represents one of the last missing ingredients of the next-to-next-to-leading-order analysis of rare semileptonic B meson decays.

Comments: 26 pages, 2 figures; a few typos fixed, version to appear in NPB