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

TL;DR

This paper calculates one-loop O(p^2) corrections to electroweak penguin operators in K decays, revealing a significant fractional shift and providing insights into the sign discrepancy with unitarization expectations.

Contribution

It provides the first detailed calculation of O(p^2) corrections to K->pi and K->2pi matrix elements of Q_{7,8} operators, including a background-field heat-kernel analysis.

Findings

Fractional shift Delta_2 = 0.27 ± 0.27 for O(p^2) corrections.

Opposite sign for Delta_2 compared to unitarization predictions.

General NLO relations between K->pi and K->2pi amplitudes derived.

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.