Search for the Rare Decay K_{L}\toπ^{0}π^{0}γ

The KTeV E799 experiment has conducted a search for the rare decay $K_{L}\to\pi^{0}\pi^{0}\gamma$ via the topology $K_{L}\to\pi^{0}\pi^{0}_D\gamma$ (where $\pi^0_D\to\gamma e^+e^-$). Due to 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 a 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.