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

We calculate the two-loop QCD anomalous dimension matrix (ADM) (<(gamma)over cap>)(NDR) in the NDR-MS scheme for all the flavour-changing four-quark dimension-six operators that are relevant in both the Standard Model and its extensions. Both current-current and penguin diagrams are included, Some of our NDR-MS results for Delta F = 1 operators overlap with the previous calculations, but several others have never been published before. In the case of Delta F = 2 operators, our results are compatible with the ones obtained by Ciuchini et al. in the regularization-independent renormalization scheme, bur differ from their NDR-MS results. In order to explain the difference, 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 rights reserved.