Effects of (partial) quenching on penguin contributions toK→ππ

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 penguinlike 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 of the contribution of the new low-energy constants to the $K^0\to {\pi }^{+}{\pi }^{-}$ amplitude, at leading order in chiral perturbation theory, and for arbitrary (momentum nonconserving) 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 parametrizing the new operators in the case of strong LR penguins operators.