Non-Leptonic Kaon Decays and the Chiral Anomaly

Abstract

An investigation is performed of all non-leptonic kaon decays sensitive to the chiral anomaly. Within the framework of chiral perturbation theory, there are two classes of anomalous amplitudes at $O(p^4)$: reducible and direct contributions. Only radiative transitions are affected by the anomaly. The phenomenology of the decays $K_L \to π^+ π^- γ$ and $K^+ \to π^+ π^0 γ$ is studied in detail. Including the dominant contributions of $O(p^6)$, the experimentally observed dependence of the direct emission amplitude for $K_L \to π^+ π^- γ$ on the photon energy can be understood. A survey is made of the rare ``anomalous'' decays $K \to ππγγ$ and $K \to 3 πγ(γ)$, including some numerical estimates.