Single top quarks at the Fermilab Tevatron

We present a calculation of the single top quark cross section for proton-antiproton interactions with $\sqrt{s}=1.8\mathrm{}\mathrm{}\mathrm{TeV}$ at the Fermilab Tevatron collider. We examine the effects of the top quark mass, parton distribution functions, QCD scale, and collision energy, on each of the component production mechanisms, and study the kinematic distributions for standard model electroweak production. At the upgraded Tevatron with $\sqrt{s}=2.0\mathrm{}\mathrm{}\mathrm{TeV}$ and high luminosity, it will be possible to test the nature of the $\mathrm{Wtb}$ coupling using single top quark production. We estimate the sensitivity to measure the single top quark cross section, and thus to directly measure $V_{\mathrm{tb}}$ and the top quark partial width. We show what happens to the $V_{\mathrm{tb}}$ measurement when an anomalous $\mathrm{}(V+A)\mathrm{}$ component is added to the $\mathrm{Wtb}$ coupling, and how the top quark polarization affects the kinematic distributions.