This thesis describes a search for the rare decay K{sub L} {yields} {pi}{sup 0}{pi}{sup 0}{gamma} using data from the KTeV experiment, using the topology K{sub L} {yields} {pi}{sup 0}{pi}{sub D}{sup 0}{gamma} (where {pi}{sub D}{sup 0} {yields} {gamma}e{sup +}e{sup -}). Due to Bose statistics and the real nature of the photon, the K{sub L} {yields} {pi}{sup 0}{pi}{sup 0}{gamma} decay can proceed at lowest order only by the Cp conserving direct emission of an E2 photon. The decay vanishes to O(p{sup 4}) in chiral perturbation theory and is a probe of the theory to the sixth order. The primary background to this decay consists of K{sub L} {yields} {pi}{sup 0}{pi}{sup 0}{pi}{sub D}{sup 0} events with one lost photon. The upper limit for the decay K{sub L} {yields} {pi}{sup 0}{pi}{sup 0}{gamma} presented in this thesis is 2.32 x 10{sup -7} at the 90% confidence level. This upper limit was derived from both 1997 and 1999 data, using a blind analysis. The upper limit was derived from a Feldman-Cousins method, based on a weighted total of 0.53 data events in the signal region with an expected K{sub L} {yields} {pi}{sup 0}{pi}{sup 0}{pi}{sub D}{sup 0} background of 0.37 {+-} 0.28 events. The previous upper limit for this decay was 5.6 x 10{sup -6} at the 90% confidence level.

The KTeV E799 experiment has conducted a search for the rare decay K{sub L} 2![pi]°°[gamma] via the topology K{sub L} 2![pi]°[pi]°{sub D}[gamma] (where [pi]°{sub D} 2![gamma]ee−). Due to Bose statistics of the [pi]° pair and the real nature of the photon, the K{sub L} 2![pi]°[pi]°[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(p4). Therefore, this mode probes chiral perturbation theory at O(p6). In this paper we report a determination of an upper limit of 2.43 x 10−7 (90% CL) for K{sub L} 2![pi]°[pi]°[gamma]. This is approximately a factor of 20 lower than previous results.