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

We calculate the O(alpha(s)) corrections to the Z(0)-penguin and electrowea k box diagrams relevant for non-leptonic Delta F = 1 decays with F = S, B. This calculation provides the complete O(alpha(W)alpha(s)) and O(alpha(W)al pha(s)sin(2)theta(w)m(t)(2)) corrections (alpha(W)= alpha/sin(2)theta(W)) t o the Wilson coefficients of the electroweak penguin four quark operators r elevant for non-leptonic K- and B-decays. We argue that this is the dominan t part of the next-next-to-leading (NNLO) contributions to these coefficien ts. Our results allow us to reduce considerably the uncertainty due to the definition of the top quark mass present in the existing NLO calculations o f non-leptonic decays. The NNLO corrections to the coefficient of the color singlet (V - A) x (V - A) electroweak penguin operator Q(9) relevant for B -decays are generally moderate, amount to a few percent for the choice m(t) (mu(t) = m(t)) and depend only weakly on the renormalization scheme. Larger NNLO corrections with substantial scheme dependence are found for the coef ficients of the remaining electroweak penguin operators Q(7), Q(8), and Q(1 0). In particular, the strong scheme dependence of the NNLO corrections to C-8 allows us to reduce considerably the scheme dependence of C-8[Q(8)](2) relevant for the ratio epsilon'/epsilon. (C) 2000 Elsevier Science B.V. All rights reserved.