Analysis of \epsilon'/\epsilon in the 1/N_c Expansion

TL;DR

This paper analyzes the direct CP violation ratio '/ in Kf0 decays using the 1/N_c expansion and chiral Lagrangian, finding potential enhancements that align with experimental measurements.

Contribution

It introduces a new calculation of '/ using the 1/N_c expansion, including leading and next-to-leading order corrections, and explores '/ predictions within this framework.

Findings

'/ ranges from 1.5e-4 to 31.6e-4.

Large positive 1/N_c corrections to Q_6 enhance '/.

Results suggest '/ can match experimental values with corrections.

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. The 1/N_c corrections to the hadronic matrix elements of all operators are calculated at leading order in the chiral expansion. Numerically, doing a simple scanning of the input parameters we find 1.5 \cdot 10^{-4}\leq \epsilon'/\epsilon \leq 31.6\cdot 10^{-4}. We also investigate, in the chiral limit, the 1/N_c corrections to the operator Q_6 at next-to-leading order in the chiral expansion. We find large positive corrections which can further enhance \epsilon'/\epsilon and bring the standard model prediction close to the measured value for central values of the parameters. Our result indicates that a \Delta I=1/2 enhancement may be operative for Q_6 similar to the one of Q_1 and Q_2 which dominate the CP conserving amplitude.