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 $B_6^{(1/2)}(\mu )\equiv <(\pi \pi {)}_0|Q_6|K>/[<(\pi \pi {)}_0|Q_6|K>{|}_{N_c}]$ 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.

Comments: 9 LaTeX pages, 2 ps figures included. Invited talk at QCD '99 High Energy Euro Conference on Quantum Chromodynamics, July 1999, Montpellier, France. Corrected eq. (16) and misprints