On the effects of (partial) quenching on penguin contributions to K-> pi pi

TL;DR

This paper investigates how partial quenching in QCD affects penguin operator contributions to K-> pi pi decays, revealing new operators and systematic errors in lattice calculations.

Contribution

It extends the analysis of quenched effects on penguin operators to K-> pi pi amplitudes, identifying new low-energy constants and systematic uncertainties.

Findings

New penguin-like operators appear in (partially) quenched QCD.

Systematic errors due to quenching artifacts are quantified.

A recipe for determining new low-energy constants is provided.

Abstract

Recently, we pointed out that chiral transformation properties of strong penguin operators change in the transition from unquenched to (partially) quenched QCD. As a consequence, new penguin-like operators appear in the (partially) quenched theory, along with new low-energy constants, which should be interpreted as a quenching artifact. Here, we extend the analysis to the contribution of the new low-energy constants to the K^0 -> pi^+ pi^- amplitude, at leading order in chiral perturbation theory, and for arbitrary (momentum non-conserving) kinematics. Using these results, we provide a detailed discussion of the intrinsic systematic error due to this (partial) quenching artifact. We also give a simple recipe for the determination of the leading-order low-energy constant parameterizing the new operators in the case of strong $LR$ penguins.