Contribution of the charm quark to the \Delta I=1/2 rule

TL;DR

This paper investigates how the charm quark influences the /2 rule in kaon decays by studying decay amplitude dependence on charm mass, using active charm quarks and advanced variance reduction techniques in lattice QCD.

Contribution

It introduces a method to analyze the charm quark's role in kaon decay amplitudes by keeping it active and employing novel variance reduction techniques for better statistical accuracy.

Findings

Significant part of /2 enhancement is due to low-energy QCD effects.

Active charm quark approach provides new insights into decay dynamics.

Variance reduction techniques improve diagram signal quality.

Abstract

We report on the progress of our ongoing project to quantify the role of the charm quark in the non-leptonic decay of a kaon into two pions. The effect of its associated mass scale in the dynamics underlying the \Delta I = 1/2 rule can be studied by monitoring the dependence of kaon decay amplitudes on the charm quark mass using an effective \Delta S = 1 weak Hamiltonian. In contrast to commonly used approaches the charm quark is kept as an active degree of freedom. Quenched results in the GIM limit have shown that a significant part of the \Delta I = 1/2 enhancement is purely due to low-energy QCD effects. Moving away from the GIM limit involves the computation of diagrams containing closed quark loops which requires new variance reduction techniques in order to determine the relevant weak effective low-energy couplings. We employ a combination of low-mode averaging and stochastic volume sources in order to compute these diagrams and observe a significant improvement in the statistical signal.