epsilon'/epsilon in the 1/N_c Expansion

TL;DR

This paper analyzes the ratio epsilon'/epsilon, a measure of direct CP violation in kaon decays, using the 1/N_c expansion within an effective chiral Lagrangian framework, revealing large positive corrections that align predictions with experimental data.

Contribution

It introduces a detailed 1/N_c correction analysis for the Q_6 operator, showing significant positive effects that enhance epsilon'/epsilon in the standard model.

Findings

Large positive 1/N_c corrections to Q_6 matrix element.

Enhanced =1/2 transition for Q_6 similar to Q_1 and Q_2.

Standard model prediction of epsilon'/psilon close to experimental value.

Abstract

We present a new analysis of the ratio epsilon'/epsilon which measures the direct CP violation in K\to\pi\pi decays. We use the 1/N_c expansion within the framework of the effective chiral lagrangian for pseudoscalar mesons. From general counting arguments we show that the matrix element of the operator Q_6 is not protected from possible large 1/N_c corrections beyond its large-N_c or VSA value. Calculating the 1/N_c corrections, we explicitly find that they are large and positive. Our result indicates that a \Delta I=1/2 enhancement is operative for Q_6 similar to the one of Q_1 and Q_2 which dominate the CP conserving amplitude. This enhances epsilon'/epsilon and can bring the standard model prediction close to the measured value for central values of the parameters.