A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule

TL;DR

This paper proposes a method to investigate how the charm quark influences the Delta I=1/2 rule in kaon decays by using lattice simulations with an artificially light charm quark to isolate different contributing effects.

Contribution

It introduces a novel strategy employing SU(4) symmetry and lattice QCD to disentangle charm quark effects from soft-gluon exchange in kaon decay amplitudes.

Findings

Initial lattice results in SU(4) symmetric limit obtained.

Method to track charm quark mass effects on decay amplitudes.

Framework for separating QCD scale effects from charm quark contributions.

Abstract

We present a strategy designed to separate several possible origins of the well-known enhancement of the Delta{I}=1/2 amplitude in non-leptonic kaon decays. In particular, we seek to disentangle the contribution of physics at the typical QCD scale (soft-gluon exchange) from the effects at the scale of the charm quark mass. This is achieved by considering QCD with an unphysically light charm quark, so that the theory possesses an approximate SU(4)_L x SU(4)_R chiral symmetry. By computing the relevant operator matrix elements and monitoring their values as the charm quark mass departs from the SU(4)-symmetric situation, the role of the charm quark can be assessed. We study the influence of the charm quark mass in Chiral Perturbation Theory. First results from lattice simulations in the SU(4)-symmetric limit are also discussed.