Ε′k/εk in the Chiral Limit Using Large Nc

∆S = 1 weak decays are produced by the exchange of W -bosons. The resulting effective action, resumming αS log(MX/ν) to two-loops, is now standard. An introduction and references can be found in the lectures by Buras. The resulting effective action, Γ∆S=1 ∼ ∑10 i=1 Ci(ν) ∫ dxQi(x) + h.c. with Qi(x) four-quark operators, is dependent on the various schemes chosen in its definition. This dependence should disappear in the matrix-elements of this effective action which are usually calculated in a different way. Because currents and densities can be matched more easily across theories, we first replace the effective four-quark operator action by an equivalent one. For instance, the effective action reproducing Q1(x) = [sγ(1− γ5)d] [uγμ(1− γ5)u] (x) by the exchange of the heavy fictitious X1 is