New Analysis of the Delta I = 1/2 Rule in Kaon Decays and the B_K Parameter

TL;DR

This paper analyzes the Delta I = 1/2 rule in kaon decays and the B_K parameter using the 1/N_c expansion within an effective chiral Lagrangian, providing new insights into hadronic matrix elements and their dependence on cutoff scales.

Contribution

It introduces a detailed 1/N_c expansion analysis of kaon decay amplitudes and the B_K parameter, highlighting the impact of higher order corrections and cutoff dependence.

Findings

Reproduces the dominant Delta I = 1/2 amplitude

Finds B_K smaller than previous estimates

Shows significant cutoff dependence for amplitudes

Abstract

We present a new analysis of the Delta I = 1/2 rule in K --> pi pi decays and the B_K parameter. We use the 1/N_c expansion within the effective chiral lagrangian for pseudoscalar mesons and compute the hadronic matrix elements at leading and next-to-leading order in the chiral and the 1/N_c expansions. Numerically, our calculation reproduces the dominant Delta I = 1/2 K --> pi pi amplitude. Our result depends only moderately on the choice of the cutoff scale in the chiral loops. The Delta I = 3/2 amplitude emerges sufficiently suppressed but shows a significant dependence on the cutoff. The B_K parameter turns out to be smaller than the value previously obtained in the 1/N_c approach. It also shows a significant dependence on the choice of the cutoff scale. Our results indicate that corrections from higher order terms and/or higher resonances are large for the Delta I = 3/2 K --> pi pi amplitude and the (|Delta S| = 2) K^0 -- anti K^0 transition amplitude.