Two--Loop Anomalous Dimension Matrix for ΔS=1 Weak Non-Leptonic Decays II: O( α e α s )
Abstract
We calculate the
10×10
two--loop anomalous dimension matrix to order $\ord(\alpha_e \alpha_s)$ 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 to obtain the corresponding two--loop anomalous dimension matrix in the HV scheme with non--anticommuting
γ
5
.