Variance reduction techniques for a quantitative understanding of the ΔI = 1/2 rule

The role of the charm quark in the dynamics underlying the ΔI = 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 ΔS = 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.

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