The authors study on the rare decay K{sub L} 2![pi]°[gamma][gamma], measure a{sub V}, and branching ratio by analyzing 96, 97 and 99 data. The measurements were taken by KTeV at Fermi National Accelerator Laboratory. After all cuts, they have 1982 K{sub L} 2![pi]°[gamma][gamma] candidate. The background level is estimated as 30%. K{sub L} 2![pi]°[gamma][gamma] branching ratio is measured as (1.29 ± 0.03(stat) ± 0.04(sys)) x 10−6. By using D'Ambrosio's theory to fit a{sub V}, a{sub V} = -( -0.31 ± 0.05(stat) ± 0.07(sys)).

It appears that using K/sup + -/ ..-->.. ..pi ... pi..° is a useful source of tagged ..pi..°'s to investigate the rare decays ..pi..° ..-->.. ee−, ..pi..° ..-->.. ..gamma gamma..approx., and ..pi..° ..-->.. ..nu.. anti ..nu ... Present accelerator intensities may be sufficient to study the first process, although a detailed experimental design may show that higher intensities are needed. Higher flux beams clearly are needed to achieve the best sensitivity to ..pi..° ..-->.. ..nu.. anti ..nu.. and ..pi..° ..-->.. ..gamma gamma..approx.

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.