The $\Delta I = 1/2$ Selection Rule. A Review

Abstract

I review a recent attempt to reproduce the isospin $I= 0$ and 2 amplitudes for the decay of a kaon into two pions by estimating the relevant hadronic matrix elements in the chiral quark model. The results are parametrized in terms of the quark and gluon condensates and of the constituent quark mass $M$. The latter is a parameter characteristic of the model. For values of these parameters within the current determinations, the $\Delta I= 1/2$ selection rule is well reproduced by means of the cumulative effects of short-distance NLO Wilson coefficients, penguin diagrams, non-factorizable soft-gluon corrections and meson-loop renormalization.