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

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 dy-namics underlying the ∆I = 1/2 rule can be studied by monitoring the dependence of kaon decay amplitudes on the charm quark mass using an effective ∆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 ∆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 or-der 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. Xth Quark Confinement and the Hadron Spectru