Extended analysis of the"penguin"part of $K\to\pi\pi$ amplitude

We make an attempt to clarify the role of the annihilation or ”penguin” mode in the description of the K → ππ decay within the Standard Model. The attention is concentrated on new operators in the effective ∆ S = 1 Hamiltonian and the violation of factorization for mesonic matrix elements of the local four-quark operators. We propose a regular method to evaluate the mesonic matrix elements of K → ππ transitions based on studying three-point correlators via QCD sum rules using the chiral effective theory as an underlying low-energy model for strong interaction. Matrix elements of the QCD penguin operator are calculated within this approach. The total ”penguin” contribution is found to be relatively large that improves the theoretical description of the ∆ I = 1 / 2 rule in non-leptonic kaon decays.