Kaon Weak Decays in Chiral Theories

The ten nonleptonic weak decays $K\to 2\pi$, $K\to 3\pi$, $K_L \to 2\gamma$,$K_S \to 2\gamma$,$K_L \to \pi^\circ 2\gamma$, are predicted for a chiral pole model based on the linear sigma model theory which automatically satisfies the partial conservation of axial current (PCAC) hypothesis. These predictions, agreeing with data to the 5% level and containing no or at most one free parameter, are compared with the results of chiral perturbation theory (ChPT). The latter ChPT approach to one-loop level is known to contain at least four free parameters and then predicts a $K_L\to {\pi }^{\circ }\gamma \gamma$ rate which is 60% shy of the experimental value. This suggests that ChPT is an unsatisfactory approach towards predicting kaon weak decays.