Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD

Details Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD

2004-11-04

arxiv.org/abs/hep-ph/0411071v5

Nucl.Phys.B713:291-332,2005

Physics

High Energy Physics

High Energy Physics - Phenomenology

46 pages, 6 figures; typos in Eqs. (27) and (37) corrected (thanks to Guido Bell and Diego Guadagnoli for pointing them out) a

Scientific paper

10.1016/j.nuclphysb.2005.01.047

We compute the effective hamiltonian for non-leptonic |Delta F| = 1 decays in the standard model including next-to-next-to-leading order QCD corrections. In particular, we present the complete three-loop anomalous dimension matrix describing the mixing of current-current and QCD penguin operators. The calculation is performed in an operator basis which allows to consistently use fully anticommuting gamma_5 in dimensional regularization at an arbitrary number of loops. The renormalization scheme dependences and their cancellation in physical quantities is discussed in detail. Furthermore, we demonstrate how our results are transformed to a different basis of effective operators which is frequently adopted in phenomenological applications. We give all necessary two-loop constant terms which allow to obtain the three-loop anomalous dimensions and the corresponding initial conditions of the two-loop Wilson coefficients in the latter scheme. Finally, we solve the renormalization group equation and give the analytic expressions for the low-energy Wilson coefficients relevant for non-leptonic B meson decays beyond next-to-leading order in both renormalization schemes.

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