Master Formulae for Delta F=2 NLO-QCD Factors in the Standard Model and Beyond
Andrzej J. Buras, Sebastian Jager, Joerg Urban
Abstract
We present analytic formulae for the QCD renormalization group factors relating the Wilson coefficients Ci(mut) and Ci(mu), with mut = O(mt) and mu < mut, of the Delta F=2 dimension six four-quark operators Qi in the Standard Model and in all of its extensions. Analogous analytic formulae for the QCD factors relating the matrix elements <Qi(2 GeV)> and <Qi(muK)> with muK < 2GeV are also presented. The formulae are given in the NDR scheme. The strongest renormalization-group effects are found for the operators with the Dirac structures (1 - gamma5)*(1 + gamma5) and (1 - gamma5)*(1 - gamma5). We calculate the matrix elements < K0|Qi|K0> in the NDR scheme using the lattice results in the LRI scheme. We give expressions for the mass differences Delta MK and Delta MB and the CP-violating parameter epsilonK in terms of the non-perturbative parameters Bi and the Wilson coefficients Ci(mut). The latter summarize the dependence on new physics contributions.
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