Analysis of ε ′ / ε in the 1 / N c Expansion

We present a new analysis of the ratio ε′/ε which measures the direct CP violation in K → ππ decays. We use the 1/Nc expansion within the framework of the effective chiral lagrangian for pseudoscalar mesons. The 1/Nc 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/Nc corrections to the operator Q6 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/Nc corrections a ∆I = 1/2 enhancement is operative for Q6 similar to the one of Q1 and Q2 which dominate the CP conserving amplitude. PACS numbers: 11.30.Er, 12.39.Fe, 13.20.Eb E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]