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Two-Loop Anomalous Dimension Matrix for S=1 Weak Non-leptonic Decays (I). O(alpha 2s)

A. Buras
Matthias Jamin
Organization: Technical University, Munich
Department: Department of Physics
Markus E. Lautenbacher
Organization: Physics Department, Technical University, Munich
P. Weisz
Journal / Anthology

Nuclear Physics B
Year: 1993
Volume: 400
Page range: 37-74

We calculate the two loop 10x10 anomalous dimension matrix O(alpha 2s) involving current-current operators, QCD penguin operators, and electroweak penguin operators especially relevant for B=1 decays. The calculation is performed in two schemes for gamma 5: the dimensional regularization scheme with anticommuting gamma 5 (NDR), and in the 't Hooft-Veltman scheme. We demonstrate how a direct calculation of diagrams involving gamma 5 in closed fermion loops can be 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(alpha alpha s), required for a consistent inclusion of electroweak penguin operators, is presented in a subsequent publication.

*Science > Physics > Quantum Physics