Electroweak penguin contributions to non-leptonic ΔF=1 decays at NNLO

We calculate the corrections to the Z0-penguin and electroweak box diagrams relevant for non-leptonic ΔF=1 decays with F=S,B. This calculation provides the complete and corrections (αW=α/sin2θW) to the Wilson coefficients of the electroweak penguin four quark operators relevant for non-leptonic K- and B-decays. We argue that this is the dominant part of the next-next-to-leading (NNLO) contributions to these coefficients. Our results allow us to reduce considerably the uncertainty due to the definition of the top quark mass present in the existing NLO calculations of non-leptonic decays. The NNLO corrections to the coefficient of the color singlet (V−A)⊗(V−A) electroweak penguin operator Q9 relevant for B-decays are generally moderate, amount to a few percent for the choice mt(μt=mt) and depend only weakly on the renormalization scheme. Larger NNLO corrections with substantial scheme dependence are found for the coefficients of the remaining electroweak penguin operators Q7, Q8 and Q10. In particular, the strong scheme dependence of the NNLO corrections to C8 allows us to reduce considerably the scheme dependence of C8〈Q8〉2 relevant for the ratio ε′/ε.