What question did this study set out to answer?

This analysis investigates the ratio ε'/ε to evaluate direct CP violation in K→ππ decays using the 1/N_c expansion.

March 5, 2026Open Access

ε'/ε in the 1/Nc Expansion

Puntos clave

This analysis investigates the ratio ε'/ε to evaluate direct CP violation in K→ππ decays using the 1/N_c expansion.
Applied the 1/N_c expansion in the effective chiral lagrangian framework.
Conducted calculations of the matrix element for operator Q_6.
Developed general counting arguments for 1/N_c corrections.
Discovered that 1/N_c corrections to the matrix element of Q_6 are large and positive.
Showed that a Delta I = 1/2 enhancement operates for Q_6.
Indicated that this enhancement can align the standard model prediction of ε'/ε with measured values.

Resumen

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. From general counting arguments we show that the matrix element of the operator Q₆ is not protected from possible large 1/Nc corrections beyond its large-Nc or VSA value. Calculating the 1/Nc corrections, we explicitly find that they are large and positive. Our result indicates that a Delta I = 1/2 enhancement is operative for Q₆ similar to the one of Q₁ and Q₂ which dominate the CP conserving amplitude. This enhances ε'/ε and can bring the standard model prediction close to the measured value for central values of the parameters.

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