epsilon'/epsilon in the Chiral Limit

TL;DR

This paper analyzes the direct CP violation parameter epsilon'/epsilon in the chiral limit within the Standard Model, connecting short-distance effects to low-energy matrix elements, and finds a larger epsilon'/epsilon value than previous studies.

Contribution

It introduces a scheme-independent method to connect short-distance running with low-energy matrix elements and calculates epsilon'/epsilon with next-to-leading order in 1/N_c, reproducing the Delta I=1/2 rule.

Findings

Reproduces the Delta I=1/2 rule within expected errors

Obtains a larger epsilon'/epsilon value than most previous analyses

Suggests the X-boson method as an option for lattice QCD calculations

Abstract

The $K\to\pi\pi$ system is analyzed in the chiral limit within the Standard Model. We discuss how to connect the short-distance running in the $|\Delta S|=1$ 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 $\epsilon_K^\prime$. The $\Delta I=1/2$ rule is reproduced within expected errors and we obtain a substantially larger value for $\epsilon_K^\prime/\epsilon_K$ 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.