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) (γ̂)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 ∆F = 1 operators overlap with the previous calculations, but several others have never been published before. In the case of ∆F = 2 operators, our results are compatible with the ones obtained by Ciuchini et al. in the RegularizationIndependent renormalization scheme, but differ from their NDR–MS results. In order to explain the difference, we calculate the ADM of ∆F = 2 operators again, extracting it from the ADM of ∆F = 1 operators.