$K^0 $ Decays into Three Photons

The decays $K_{L,S} \to 3 \gamma $ are not forbidden by any selection rules or symmetry principles. However, gauge invariance and Bose statistics dictate that every photon pair in these transitions has at least two units of angular momentum. This gives rise to an extraordinary suppression. Using a simple model, we obtain the branching ratios $B(K_L \to 3 \gamma) \sim 3 \cdot 10^{-19}$, $B(K_S \to 3 \gamma) \sim 5 \cdot 10^{-22} $.