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 reno
rmalization group running can be treated. We then use this method to study
the three O(p(2)) terms contributing to non-leptonic kaon decays, namely th
e usual octet and 27-plet derivative terms as well as the weak mass term us
ing 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 contribution
s from the Q(6) operator in the chiral limit. We update our earlier results
on the B-K parameter as well.