The ΔI = 1/2 rule in the large-N limit

The large-N limit is used to obtain a consistent picture of the K → ππ matrix elements. It is confirmed that the dominant Q6 penguin matrix elements are enhanced by an order of magnitude compared to those of the current-current operators and that this result is consistent with chiral perturbation theory. An additional enhancement of the penguin contributions is identified with respect to standard estimates which comes from an incomplete GIM cancellation above the charm quark mass. Performing the short-distance analysis to first nontrivial order in 1/N its validity and simplicity is demonstrated. Encouraging results are obtained for A(K → ππ) amplitudes and it is pointed out that further improvements can be obtained through the inclusion of the low-energy evolution which necessarily must be done in a meson rather than a quark picture