Master Formulae for Delta F=2 NLO-QCD Factors in the Standard Model and Beyond
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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