The Two-Loop Anomalous Dimension Matrix for ΔS=1 Weak Non-Leptonic Decays I: O( α 2 s )
Andrzej J. Buras, Matthias Jamin, Markus E. Lautenbacher, Peter H. Weisz
Abstract
We calculate the two-loop
10×10
anomalous dimension matrix
O(
α
2
s
)
involving current-current operators, QCD penguin operators, and electroweak penguin operators especially relevant for
ΔS=1
weak non-leptonic decays, but also important for
ΔB=1
decays. The calculation is performed in two schemes for
γ
5
: the dimensional regularization scheme with anticommuting
γ
5
(NDR), and in the 't Hooft-Veltman scheme. We demonstrate how a direct calculation of diagrams involving
γ
5
in closed fermion loops can be avoided thus allowing a consistent calculation in the NDR scheme. The compatibility of the results obtained in the two schemes considered is verified and the properties of the resulting matrices are discussed. The two-loop corrections are found to be substantial. The two-loop anomalous dimension matrix
O(
α
e
α
s
)
, required for a consistent inclusion of electroweak penguin operators, is presented in a subsequent publication.