Two-loop anomalous dimension matrix for ΔS = 1 weak non-leptonic decays. (II) O( ααs)

Abstract

We calculate the 10×10 two-loop anomalous dimension matrix to order O( αα s) in the dimensional regularization scheme with anticommuting γ 5 (NDR) which is necessary for the extension of the ΔS = 1 weak hamiltonian involving electroweak penguins beyond the leading logarithmic approximation. We demonstrate how a direct calculation of penguin diagrams involving γ 5 in closed fermion loops can be avoided thus allowing a consistent calculation of two-loop anomalous dimensions in the simplest renormalization scheme with anticommuting γ 5 in D dimensions. We give the necessary one-loop finite terms which allow us to obtain the corresponding two-loop anomalous dimension matrix in the HV scheme with non-anticommuting γ 5.