Scheme dependence of weak matrix elements in the 1/N-c expansion

We show how the scheme- and scale-dependence of the short-distance operator product expansion with four-quark operators can be correctly accounted for in the framework of the 1/N-c-expansion once the hadronization of two-quar k currents has been fixed. We show formulas explicitly in the case of the B K-parameter. We then use them together with our earlier estimates of the lo ng-distance effects. We compare Chiral Perturbation Theory at Leading- and Next-to-Leading-Order with the ENJL model results in the chiral limit. Good matching between the long- and short-distance regimes is obtained and our final value for the physical scheme independent (B) over cap (K) is 0.77 +/ - 0.05 +/- 0.5.