Pion-pair contribution to the decayKL→π0γγ

A simple prediction for the decay $K_L\to {\pi }^0\gamma \gamma$, obtained from the rescattering to two photons of the ${\pi }^{+}{\pi }^{-}$ intermediate state in the process $K_L\to {\pi }^{+}{\pi }^{-}{\pi }^0$, is compared with a recent calculation based on chiral perturbation theory. The ${\pi }^{+}{\pi }^{-}$ rescattering model predicts a two-photon effective mass spectrum peaked at slightly higher $m_{\gamma \gamma }$ than in chiral perturbation theory, and a branching ratio $B(K_L\to {\pi }^0\gamma \gamma )\approx 7.5\times {10}^{-7\mathrm{}}$. Implications are discussed for the corresponding decay of the charged kaon.