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-quark 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 long-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 B̂_K is 0.77 ± 0.05 ± 0.05.