New contribution to anomalous radiative $K^0$-decays

Abstract

We present a new contribution to the $K_L\rightarrow \gamma \gamma$ amplitude, which is ${\cal{O}}(p^4)$ within the counting rules of chiral perturbation theory. This direct (non-pole) amplitude, obtained from short-distance $s \rightarrow d \gamma$ quark diagrams of order $e G_F \alpha_s/\pi$, and similar $s \rightarrow d \gamma \gamma$ diagrams, can account for about half of the experimental amplitude. Closely following the description of the $\pi ^0\rightarrow \gamma \gamma$ and $K_L\rightarrow \gamma \gamma$ processes in the variants of the same low-energy QCD, we find that both of these processes are anomalous in the same sense. Then, by the anomaly-matching principle, we arrive from the chiral-quark to the bosonic counterparts for both of these processes. In this way we add the $K_L\rightarrow \gamma \gamma$ decay to the existing list of anomalous radiative prosesses.