Perturbative Calculations And The Top Quark (ambiguity, Quantum Chromodynamics)

I calculate the $O(\alpha\sb{s})$ QCD and the $O(\alpha \sb{W}m\sbsp{t }{2}/M\sbsp{W}{2})$ Yukawa corrections to the production of a single top quark via the weak process $q\bar q\to t\bar b$ at the Fermilab Tevatron and the CERN Large Hadron Collider. An accurate calculation of the cross section is necessary in order to extract $\vert V\sb{tb }\vert$ from experiment. Additionally, I show that the pole mass of a heavy quark is ambiguous by an amount proportional to $\rm\Lambda\sb{QCD}$, and that this ambiguity is independent of the width of the heavy quark. The ambiguity is a consequence of the definition of the pole mass, and is unavoidable, even for a quark such as the top quark that decays more quickly than $\Lambda\sbsp{\rm QCD }{-1}$, and so might be expected to escape the effects of nonperturbative QCD. Lastly, I show that the nonrelativistic perturbation series for heavy quarkonia energies diverges at large orders. This results in a perturbative ambiguity in the energy that scales as $e\sp{-2/na\Lambda \sb{\rm QCD}}$, where n is the principal quantum number and a is the Bohr radius. This ambiguity is associated with a nonperturbative contribution to the energies arising from distances of order $\rm \Lambda\sbsp{QCD}{-1}$ and greater.