Analysis of ε′/ ε in the 1/ Nc expansion

Abstract

We present a new analysis of the ratio ε′/ ε which measures the direct CP violation in K→ ππ 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. Performing a simple scanning of the input parameters we obtain 1.5×10 −4⩽ ε′/ ε⩽31.6×10 −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 further enhance ε′/ ε and can bring the standard model prediction close to the measured value for central values of the parameters. Our result indicates that at the level of the 1/ N c corrections a ΔI=1/2 enhancement is operative for Q 6 similar to the one of Q 1 and Q 2 which dominate the CP-conserving amplitude.