This thesis presents a search for the rare B meson decay B -> pi ll− (l=e or mu) using 428 fb−1 of data collected at the Upsilon(4S) resonance by the BaBar detector at the PEP-II asymmetric energy ee− storage rings located located at SLAC National Accelerator Laboratory in Menlo Park, California. Four exclusive modes are studied: B+ -> pi+ e+e−, B+ -> pi+ mu+mu−, B0 -> pi0 e+e−, and B0 -> pi0 mu+mu−. Branching fraction upper limits at the 90% confidence level are presented for the exclusive modes B+ -> pi+ mu+mu− and B0 -> pi0 mu+mu−, and the combined mode B -> pi mu+mu−.

The hadronic transition UPSILON(2S) .-->. .pi.°.pi.°UPSILON(1S) is utilized to search for the reactions: UPSILON(1S) .-->. non-interacting particles and UPSILON(1S) .-->. .gamma. + non-interacting particles. 44 pb−1 of UPSILON(2S) data were taken by the Crystal Ball detector at the DORIS II storage ring in order to perform this study. An upper limit of BR(UPSILON .-->. Unseen) 12% (90% C.L.), is obtained via this approach. The second process investigated involved the radiative decay of the Upsilon into non-interacting particles. 57 pb−1 of UPSILON(2S) data was available for this study. An upper limit on the branching ratio BR(UPSILON .--. .gamma. + Unseen) is measured for photon energies in the range 500 MeV E.gamma.

The hadronic transitions UPSILON(2S) .-->. .pi.°.pi. UPSILON(1S) .-->. .gamma gamma gamma gamma.ll− (l = .mu. or e) are investigated using the Crystal Ball detector. The analysis is based on 193,000 UPSILON(2S) events produced at the DORIS II ee− storage ring from November 1982 to February 1984. We observe 44 events with a muon pair and 46 events with an electron pair in the final state. The signals in both channels are relatively background free. Assuming lepton universality, we average the results for the two channels and obtain the product branching ratio B(UPSILON(2S) .-->. .pi.°.pi.°UPSILON(1S)) x B/sub ll/(UPSILON(1S)) = (2.3 +- 0.3 +- 0.3) x 10−3 where the first error is statistical and the second is systematic. Using the present world average value of B/sub ll/(UPSILON(1S)) = (2.9 +- 0.3)% we derive a branching ratio B(UPSILON(2S) .-->. .pi.°.pi.°UPSILON(1S)) = (8.0 +- 1.5)% where the statistical and systematic errors have been added in quadrature. This result is compared with previous results for the charged pion transitions UPSILON(2S) .-->. .pi.+.pi.−UPSILON(1S) and with the expectation from theory. We have also investigated the mass spectrum M/sub .pi.°.pi.°/ resulting from these decays and find a peaking toward high masses not accounted for the phase space alone. Fits to the .pi.°.pi.° mass spectrum are in quantitative agreement with previous results for the .pi.+.pi.− transitions. Angular distribution for the .pi.°.pi.° system and its decay products are presented in reference frames appropriate for analyzing the spin of the .pi.°.pi.° system, even if the initial UPSILON(1S) and the di-pion system are emitted in a relative S-wave. We find the decay distributions to be consistent with those expected for a spin zero di-pion system emitted in a relative S-wave with the UPSILON(1S).