ε′_K/ε_K in the chiral limit

The K → ππ system is analyzed in the chiral limit within the Standard Model. We discuss how to connect the short-distance running in the |ΔS| = 1 case to the matrix-elements calculated in a low-energy approximation in a scheme-independent fashion. We calculate this correction and the resulting Wilson Coefficients. The matrix elements are calculated to next-to-leading order in the 1/N_c expansion and combined with the Wilson coefficients to calculate the two isospin amplitudes and ε′_K. The ΔI = 1/2 rule is reproduced within expected errors and we obtain a substantially larger value for ε′_K/ε_K than most other analysises. We discuss the reasons for this difference. We also suggest that the X-boson method is an option for lattice QCD calculations.