Search for the rare decay kaon(long) going to neutral pion-neutral pion-muon-antimuon

This thesis describes the search for KL → pi0 pi0mu+mu-, which was conducted using data collected by the KTeV Experiment at Fermi National Accelerator Laboratory in Batavia, Illinois. Although this decay mode is possible within the Standard Model, it is limited to a very narrow band of phase space. The HyperCP Experiment has recently observed three Sigma+ → pmu+mu- events within a narrow dimuon mass range of 213.8 MeV/c2 to 214.8 MeV/c2. This suggests that the process could occur via a neutral intermediary particle, Sigma+ → pX0 → pmu+mu -, with an X0 mass of 214.3 MeV/ c2+/-0.5 MeV/c2. Since the X0 has a light mass and a low interaction probability, then it is most likely a new neutral boson that exists beyond the Standard Model. Recent theoretical predictions suggest that the decay mode KL → pi0pi 0mu+mu- can also occur via the aforementioned neutral boson: KL → pi0pi 0X0 → pi0pi0mu +mu-. Therefore, in addition to a Standard Model measurement, the search for KL → pi 0pi0mu+mu- is also carried out in an effort to address the viability of X 0 in explaining the HyperCP phenomena.;Measurement of the upper limits presented in this thesis were performed using blind analysis techniques. The upper limit of the decay K L → pi0pi0mu +mu- has been measured in this thesis to be BR(KL → pi 0pi0mu+mu-) < 8.63 x 10-11 at 90% confidence level. In addition, this thesis has measured the upper limit of the decay KL → pi 0pi0X0 → pi 0pi0mu+mu- to be BR(KL → pi0 pi0X0 → pi 0pi0mu+mu-) < 9.44 x 10-11 at the 90% confidence level.