Corrections to the Hadronic Matrix Elements of Q 6 and Q 8 in K → ππ Decays ∗

We calculate long-distance contributions to the amplitudes A(K0 → 2π, I) induced by the gluon and the electroweak penguin operators Q6 and Q8, respectively. We use the 1/Nc expansion within the effective chiral lagrangian for pseudoscalar mesons. In addition, we adopt a modified prescription for the identification of meson momenta in the chiral loop corrections in order to achieve a consistent matching to the short-distance part. Our approach leads to an explicit classification of the loop diagrams into non-factorizable and factorizable, the scale dependence of the latter being absorbed in the low-energy coefficients of the effective theory. Along these lines we calculate the one-loop corrections to the O(p0) term in the chiral expansion of both operators. In the numerical results, we obtain moderate corrections to B (1/2) 6 and a substantial reduction of B (3/2) 8 . This work was supported in part by the Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF), 057D093P(7), Bonn, FRG, and DFG Antrag PA-10-1.