The Delta I=1/2 Rule in Kaon Decays: A New Look

TL;DR

This paper investigates the $ ext{Δ}I=1/2$ rule in kaon decays using a generalized factorization approach, highlighting the importance of nonfactorized contributions and radiative corrections in explaining the amplitude ratio.

Contribution

It introduces a gauge-invariant, scheme-independent framework for decay amplitudes and phenomenologically extracts large nonfactorized effects to explain the $ ext{Δ}I=1/2$ rule.

Findings

Predicted $A_0/A_2$ ratio of 15-17 for specific strange quark masses.

Nonfactorized contributions are significant in explaining the amplitude suppression and enhancement.

Radiative corrections and soft-gluon exchanges account for most of the $ ext{Δ}I=1/2$ rule.

Abstract

The $K\to\pi\pi$ decay amplitudes are studied within the framework of generalized factorization in which the effective Wilson coefficients are gauge-invariant, renormalization-scale and -scheme independent while factorization is applied to the tree-level hadronic matrix elements. Nonfactorized contributions to the hadronic matrix elements of (V-A)(V-A) four-quark operators, which are needed to account for the suppression of the $\Delta I=3/2 K\to\pi\pi$ amplitude $A_2$ and the enhancement of the $\Delta I=1/2 A_0$ amplitude, are phenomenologically extracted from the measured $K^+\to\pi^+\pi^0$ decay and found to be large. The $A_0/A_2$ ratio is predicted to lie in the range 15-17 for $m_s(1 GeV)=(127-150)$ MeV. Vertex and penguin-type radiative corrections to the matrix elements of four-quark operators and nonfactorized effects due to soft-gluon exchange account for the bulk of the $\Delta I=1/2$ rule. Comparison of the present analysis with the chiral-loop approach is given.