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

Abstract

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.

16 pages, 2 figures

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• Strong Enhancement of ${\epsilon }^{\prime }/\epsilon$ Through Final State Interactions
• Dispersive calculation of B_7^{3/2} and B_8^{3/2} in the chiral limit
• Renormalization Group Invariant Matrix Elements of DS = 2 and DI = 3/2 Four-Fermion Operators without Quark Masses

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