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 -].

We report recent results on rare B decays searches -- specifically, the decay modes B° →??−, B° →?+?−K{sup 0*}, and B{sup {plus_minus}} →?+?−K{sup {plus_minus}} -- from the CDF collaboration using data from the 1992--1993 run of the Tevatron collider. In addition, we present the first CDF measurement of time dependent B° - {bar B}° mixing.

A summary of recent results on B rare decays from the CDF and D0 experiments operating in Run II of the Fermilab Tevatron is given; analyzed decay modes are B{sub d, s} → hh, B{sub d, s} →??−, and B →?+?− h. Data samples are relative to 1 fb−1 or more integrated luminosity of p{bar p} collisions at √s = 1.96 TeV. All reported results are in agreement with Standard Model predictions and consistent with B-Factories analyzes.

The confidence level limits of the CDF search for the B{sub s}{sup 0} and B{sub d}{sup 0} {yields} {mu}{sup +}{mu}{sup -} rare decays and the branching ratio measurement of B{sub s}{sup 0} {yields} D{sub s}{sup +} D{sub s}{sup -} are presented.

This 2nd edition is an extensive update of "B Decays?. The revisions are necessary because of the extensive amount of new data and new theoretical ideas. This book reviews what is known about b-quark decays and also looks at what can be learned in the future.The importance of this research area is increasing, as evidenced by the approval of the luminosity upgrade for CESR and the asymmetric B factories at SLAC and KEK, and the possibility of experiments at hadron colliders.The key experimental observations made thus far, measurement of the lifetimes of the different B species, B0-B0 mixing, the discovery of ?Penguin? mediated decays, and the extraction of the CKM matrix elements Vub and Vcb from semileptonic decays, as well as more mundane results, are described in great detail by the experimentalists who have been closely involved with making the measurements. Theoretical progress in understanding b-quark decays using HQET and lattice gauge techniques are described by theorists who have developed and used these techniques.Synthesizing the experimental and theoretical information, several articles discuss the implications for the ?Standard Model? and how further tests can be done using measurements of CP violation in the B system.

The authors report on a search for flavor-changing neutral current decays of B mesons B →??−K{sup {+-}} and B →?+?−K*° using data obtained in the Collider Detector at Fermilab (CDF) 1992--1993 data taking run. To reduce the amount of background in the data the authors use precise tracking information from the CDF silicon vertex detector to pinpoint the location of the decay vertex of the B candidate, and accept only events which have a large decay time. They compare this data to a B meson signal obtained in a similar fashion, but where the muon pairs originate from? decays, and calculate the relative branching ratios. In absence of any indication of flavor-changing neutral current decays they set an upper limits of BR(B →?+?−K{sup {+-}})

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.