Rare B meson decays are an excellent probe for beyond the Standard Model physics. Two very sensitive processes are the B{sub s, d}° →??− and b → s?+?− decays. We report recent results at a center of mass energy of √s = 1.96 TeV from the CDF II and D0 collaborations using between 3.7 fb−1 and 6.9 fb−1 taken during Run II of the Fermilab Tevatron Collider.

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}→?+?−)

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 [psi](2S) mesons and searches for ultra-rare decays such as B [yields] [mu][sup +][mu][sup -].

Studying flavor changing neutral current transitions provides important information that helps searches for physics beyond the standard model. In this paper we report on recent measurements of these transitions using data collected by the CDF and D0 experiments at the Tevatron p{bar p} collider, including world-leading limits on the branching fraction of the decay B{sub (s)}° →??−, a forward-backward asymmetry measurement in B° → K*°?+?− and B+ → K+?+?− decays which is consistent and competitive with best B-factories results, and the first observation of the decay B{sub s}° →??+?−.

After a five year upgrade period, the Fermilab experiments CDF and D0 are taking high quality data in Run II of the Tevatron Collider. We report on the start-up of both detectors and present a selection of first B physics results from the Tevatron. We also compare different B hadron producers such as the [Upsilon](4S) with the hadron collider environment and discuss general features of B physics at a hadron collider.