The high cross-section for the production of b quarks at the Tevatron hadron collider make it an ideal place to search for rare B meson species and very low branching fraction decay modes of the more common B mesons. This paper reports the recent discovery of the Bc meson by the CDF collaboration. It also discusses the observation of rare B meson final states involving?(2S) mesons and searches for ultra-rare decays such as B 2!??−

We report on the search for B°{sub s}→??−, B°{sub d}→?+?− decays and b→ s?+?− transitions in exclusive decays of B mesons using the CDF II detector at the Fermilab Tevatron Collider. Using 2 fb−1 of Run II data we find upper limits on the branching fractions?(B°{sub s}→?+?−)

We present results and prospects for searches for rare B and D meson decays with final state dimuons, including B{sub s}{sup 0} {yields} {mu}{sup +}{mu}{sup -}, B{sub d}{sup 0} {yields} {mu}{sup +}{mu}{sup -}, and D{sup 0} {yields} {mu}{sup +}{mu}{sup -}. B0 Upper limits on the branching fractions are compared to previous CDF measurements, recent results from the B factories and theoretical expectations. We also report on new measurements of production and decay properties of the X(3872) particle, discovered in 2003 by the Belle Collaboration. New results on the measurement of the relative branching fraction for the Cabibbo suppressed decay B{sup +} {yields} J/{psi}{pi}{sup +} {Beta}(B{sup +} {yields} J/{psi}{pi}{sup +})/{Beta}(B{sup +} {yields} J/{psi}K{sup +}) are presented too. The presented results are based on the analyses of 70 to 220 pb{sup -1} of data collected by the CDF II detector in p{bar p} collisions at {radical}s = 1.96 GeV at Fermilab Tevatron.

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This thesis describes a search for the rare radiative decay of a B meson to two photons. where the charged congugate mode is implied throughout. These decays are highly suppressed in the Standard Model where the branching fraction is expected to be of order 10^-8. In some new physics scenarios this could be enhanced by up to an order of magnitude to 10^-7. Therefore an observation of a significant signal above the Standard Model prediction could be a sign of new physics. The search for this rare decay was performed using the data collected with the BaBar detector at the SLAC National Accelerator Laboratory PEP-II storage ring operating at the Upsilon(4S) resonance. The analysis uses a dataset with an integrated luminosity of 425.7 fb-1 corresponding to 467 million BB pairs. A signal yield of 21.3 +12.8 -11.8 events with a significance of 1.88 sigma was measured using an unbinned extended maximum likelihood fit. An upper limit on the branching fraction is set at the 90% confidence level of less than 3.2 times 10^-7. This is about two times more stringent than the best upper limit of less than 6.2 times 10^-7 published by the Belle collaboration.