Analysis of O(p^2) Corrections to <pi pi|Q_{7,8}|K>

The one-loop corrections to K->pi and K->2pi matrix elements of the electroweak penguin operator are calculated. General next-to-leading order relations between the K->pi and K->2pi amplitudes are obtained. The fractional shift Delta_2 = 0.27 ± 0.27 is found for the O(p^2) corrections to a recent chiral determination of <(pi pi){I=2}|Q{7,8}|K^0>. We explain why the sign for Delta_2 is opposite to that expected from unitarization approaches based on the Omnes equation. We perform a background-field, heat-kernel determination of the divergent one-loop amplitudes for a general class of (V-A)x(V+A) operators.