Calculation of $K\to\pi\pi$ decay amplitudes from $K\to\pi$ matrix elements in quenched domain-wall QCD

TL;DR

This study computes $K o\pi\pi$ decay amplitudes from $K o\pi$ matrix elements using quenched domain-wall QCD, revealing partial agreement with experimental data and insights into the $\Delta I=1/2$ rule.

Contribution

It introduces a method to estimate $K o\pi\pi$ decay amplitudes from $K o\pi$ matrix elements within quenched domain-wall QCD, highlighting the limitations of leading order chiral relations.

Findings

I=2 amplitude aligns reasonably with experiment.

I=0 amplitude is significantly smaller than experimental value.

The $\Delta I=1/2$ enhancement is only half of the observed value.

Abstract

We present a calculation of the $K\to\pi\pi$ decay amplitudes from the $K\to\pi$ matrix elements using leading order relations derived in chiral perturbation theory. Numerical simulations are carried out in quenched QCD with the domain-wall fermion action and the renormalization group improved gluon action. Our results show that the I=2 amplitude is reasonably consistent with experiment whereas the I=0 amplitude is sizably smaller. Consequently the $\Delta I=1/2$ enhancement is only half of the experimental value, and $\epsilon'/\epsilon$ is negative.