Search for the rare decayKL→π0π0γ

The KTeV E799 experiment has conducted a search for the rare decay $K_L\to {\pi }^0{\pi }^0\gamma$ via the topology $K_L\to {\pi }^0{\pi }_D^0\gamma$ (where ${\pi }_D^0\to \gamma e^{+}{e}^{-}$). Because of Bose statistics of the ${\pi }^0$ pair and the real nature of the photon, the $K_L\to {\pi }^0{\pi }^0\gamma$ decay is restricted to proceed at lowest order by the $CP$ conserving direct emission (DE) of an E2 electric quadrupole photon. The rate of this decay is interesting theoretically since chiral perturbation theory predicts that this process vanishes at level $O(p^4)$. Therefore, this mode probes chiral perturbation theory at $O(p^6)$. In this paper we report a determination of an upper limit of $2.43\times {10}^{-7}$ (90% CL) for $K_L\to {\pi }^0{\pi }^0\gamma$. This is approximately a factor of 20 lower than previous results.