The Collider Detector at Fermilab (CDF) is a multi-purpose detector designed to study proton-antiproton collisions at center-of-mass energies of 1.96 TeV/c2. One of the most importatn components of CDF is the silicon tracking detector. A detailed description of the testing and construction of the CDF silicon tracker is presented. Measurements of the tracking efficiency of the completed detector are also provided. Using 36 pb−1 of the J/[psi] data sample collected by CDF between February and October 2002, the inclusive B → J/[psi] X cross-section is measured in p{bar p} interactions at √s = 1.96 TeV/c2. The fraction of J/[psi] events arising from the decay of b hadrons is extracted using an unbinned maximum likelihood fit to the decay length of the J/[psi] candidates. The p{sub T} dependent differential cross section for inclusive B → J/[psi] X events with rapidity.

This dissertation describes the measurement of the average B hadron lifetime using a high statistics sample of B--> J/psi X decays produced in proton antiproton collisions at a center of mass energy of 1.8 TeV at the Fermilab Tevatron. The integrated luminosity of the sample is 10.1 pb-1 recorded with the Collider Detector at Fermilab (CDF). In this analysis the decay vertex of the decay J/psi -->mu^+ mu^-$ as reconstructed by a silicon vertex detector is used to extract the lifetime from the data. We find the following value for the average b hadron lifetime: [ tau_{B} = 1.46 pm 0.06; (stat.); pm 0.06; (syst.); ps] This is the first measurement of the b-hadron lifetime at a hadron collider. It demonstrates that it is possible to access the large b-quark production cross section in $poverline{p}$ collisions and to achieve high statistics even in modes which have small product branching ratios as in this case: $BR(Brightarrow J/psi X) cdot BR(J/psi rightarrow mu^+ mu^-) = 7.7 times 10^{-4}$.

Inclusive J/[psi] and [psi](2S) production has been studied in [bar p]p collisions at [radical]s = 1.8 TeV using the Collider Detector at Fermilab. The products of production cross section times branching fraction have been measured as functions of P[sub T] for J/[psi]([psi](2S)) [yields] [mu][sup +][mu][sup [minus]] in the kinematic range P[sub T][sup J/[psi]([psi](2S))]> 6 GeV/c and [vert bar][eta][sup J/[psi]([psi](2S))[vert bar]] [le] 0.5. The products of the integrated cross section times branching fraction are calculated and used to obtain an inclusive b-quark production cross section.