epsilon'/epsilon in the Chiral Limit

Abstract

The $K\toππ$ 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 $ε_K^\prime$. The $ΔI=1/2$ rule is reproduced within expected errors and we obtain a substantially larger value for $ε_K^\prime/ε_K$ 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.