Variance reduction techniques for a quantitative understanding of the \Delta I = 1/2 rule

TL;DR

This paper investigates the  I = 1/2 rule in kaon decays by applying variance reduction techniques to improve the statistical accuracy of lattice QCD calculations involving charm quarks.

Contribution

It introduces a combined approach of low-mode averaging and stochastic volume sources to control quark loop contributions in lattice QCD simulations of kaon decays.

Findings

Significant improvement in statistical signals using variance reduction methods.

Progress in computing diagrams with closed quark loops.

Evidence that low-energy QCD effects largely drive the  I = 1/2 rule enhancement.

Abstract

The role of the charm quark in the dynamics underlying the \Delta I = 1/2 rule for kaon decays can be understood by studying the dependence of kaon decay amplitudes on the charm quark mass using an effective \Delta S = 1 weak Hamiltonian in which the charm is kept as an active degree of freedom. Overlap fermions are employed in order to avoid renormalization problems, as well as to allow access to the deep chiral regime. Quenched results in the GIM limit have shown that a significant part of the enhancement is purely due to low-energy QCD effects; variance reduction techniques based on low-mode averaging were instrumental in determining the relevant weak effective lowenergy couplings in this case. Moving away from the GIM limit requires the computation of diagrams containing closed quark loops. We report on our progress to employ a combination of low-mode averaging and stochastic volume sources in order to control these contributions. Results showing a significant improvement in the statistical signal are presented.