Lattice understanding of the Delta I=1/2 rule & some implications

Abstract

After decades of intensive efforts, lattice methods finally revealed one clear source of the large enhancement of the ratio $Re A_0/Re A_2$ \cite{RBC_UKQCD_PRL13}, which has been a puzzle in particle physics for about sixty years. Lattice studies of direct $K \to ππ$ in the $I=2$ channel show that in fact this channel clearly suffers from a severe suppression due to a significant cancellation between the two amplitudes for the original, charged current (tree) operator. % [($\bar s_αγ_mu (1 - γ_5) u_α)(\bar u_βγ_mu(1-gamma_5)d_β$)], One of these amplitudes goes as N and the other one goes as $N^2$, where $N=3$ for QCD. For physical pion masses the cancellation between the two contributions towards $Re A_2$ is about $70\%$. This appreciable cancellation suggests that expectations from large N for QCD may be amenable to receiving significant corrections. The penguin operators seem to make a small contribution to $ReA_0$ at a scale $\gsim 1.5 GeV$. Possible repercussions of the lattice observation for other decays are briefly discussed.