Two – Loop Anomalous Dimension Matrix for ∆ S = 1 Weak Non - Leptonic Decays II : O ( αα s ) ∗

We calculate the 10 × 10 two–loop anomalous dimension matrix to order O(ααs) in the dimensional regularization scheme with anticommuting γ5 (NDR) which is necessary for the extension of the ∆S = 1 weak Hamiltonian involving electroweak penguins beyond the leading logarithmic approximation. We demonstrate, how a direct calculation of penguin diagrams involving γ5 in closed fermion loops can be avoided thus allowing a consistent calculation of two–loop anomalous dimensions in the simplest renormalization scheme with anticommuting γ5 in D dimensions. We give the necessary one–loop finite terms which allow to obtain the corresponding two–loop anomalous dimension matrix in the HV scheme with non–anticommuting γ5. ∗Supported by the German Bundesministerium für Forschung und Technologie under contract 06 TM 732 and by the CEC Science project SC1-CT91-0729.