Analysis of O(p(2)) corrections to <pi pi vertical bar Q(7,8)vertical bar K >

The one-loop corrections to K -->, pi and K --> 2 pi matrix elements of the electroweak penguin operator are calculated. General next-to-leading order relations between the K --> pi and k --> 2 pi amplitudes are obtained. The fractional shift Delta(2), = 0.27 +/- 0.27 is found for the O(p(2)) correc tions to a recent chiral determination of ((pi pi)(l=2)/Q(7.8)/K-0). We exp lain why the sign for Delta(2) is opposite to that expected from unitarizat ion approaches based on the Omnes equation. We perform a background-field, heat-kernel determination of the divergent one-loop amplitudes for a genera l class of (V - A)x(V + A) operators. (C) 2000 Elsevier Science B.V, All ri ghts reserved.