The ΔI = 1/2 rule in the chiral limit

We discuss the matching between long-distance and short-distance at next-to-leading in 1/N_c and show how the scheme-dependence from the two-loop renormalization group running can be treated. We then use this method to study the three O(p²) terms contributing to non-leptonic kaon decays, namely the usual octet and 27-plet derivative terms as well as the weak mass term using the Extended Nambu Jona-Lasinio model as the low energy approximation. We also discuss subtleties in the momentum routing in the low energy theory and a problem in separating factorizable and non-factorizable contributions from the Q₆ operator in the chiral limit. We update our earlier results on the B_K parameter as well.