Two-loop QCD anomalous dimensions of flavour-changing four-quark operatorswithin and beyond the Standard Model

We calculate the two-loop QCD anomalous dimension matrix (ADM) (<(gamma)ove r cap>)(NDR) in the NDR-MS scheme for all the flavour-changing four-quark d imension-six operators that are relevant in both the Standard Model and its extensions. Both current-current and penguin diagrams are included, Some o f our NDR-MS results for Delta F = 1 operators overlap with the previous ca lculations, but several others have never been published before. In the cas e of Delta F = 2 operators, our results are compatible with the ones obtain ed by Ciuchini et al. in the regularization-independent renormalization sch eme, bur differ from their NDR-MS results. In order to explain the differen ce, we calculate the ADM of Delta F = 2 operators again, extracting it From the ADM of Delta F = 1 operators. (C) 2000 Elsevier Science B.V. All right s reserved.