The $\Delta I=1/2$ Rule for Kaons

Abstract

We report on recent advances at understanding the $\Delta I= 1/2$ rule for kaons. We get reasonable matching between short-- and long--distances for scales between between 0.6 and 1.0 GeV and reproduce the $\Delta I=1/2$ rule huge enhancement in the chiral limit. A detailed analysis of the different contributions to the relevant octet and 27-plet couplings is done. For the $B_6^{(1/2)}(\mu) \equiv < (\pi\pi)_0 | Q_6 | K > / [< (\pi\pi)_0 | Q_6 | K > {\Large|}_{N_c}]$ parameter, we get in the chiral limit $B_6^{(1/2)}(\mu) = 2.2 \pm 0.5$ for scales $\mu \in [0.6, 1.0]$ GeV.