Effective Hamiltonian for non-leptonic $|\Delta F| = 1$ decays at NNLO in QCD

By M. Gorbahn, U. Haisch. 2004

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Abstract We compute the effective Hamiltonian for non-leptonic | Δ 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 γ 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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c68c758f46b1b2fef68762d036327dbd2d945758

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Citations in the corpus

On the importance of NNLO QCD and isospin-breaking corrections in $$\varepsilon '/\varepsilon $$ (2019, methodology): “Much more difficult is the NNLO analysis of QCD penguin contributions which in addition to two-loop calculations requires three-loop anomalous dimension matrices [23, 24], obtained fortunately already in [45].”
Improved anatomy of ε′/ε in the Standard Model (2015, background): “The Wilson coefficients zi and yi have been calculated at the NLO level more than twenty years ago [10,11], and some pieces of NNLO corrections are also available [12–14].”