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 $K_L\to {\pi }^{+}{\pi }^{-}\gamma$ and $K^{+}\to {\pi }^{+}{\pi }^0\gamma$ is studied in detail. Including the dominant contributions of $O(p^6)$, the experimentally observed dependence of the direct emission amplitude for $K_L\to {\pi }^{+}{\pi }^{-}\gamma$ on the photon energy can be understood. A survey is made of the rare ``anomalous'' decays $K\to \pi \pi \gamma \gamma$ and $K\to 3\pi \gamma (\gamma )$, including some numerical estimates.

Comments: LaTeX, 31 pages (3 figures, not included), CERN-TH.6920/93