Convergence and Gauge Dependence Properties of the Resummed One-loop   Quark-Quark Scattering Amplitude in Perturbative QCD
  The one-loop QCD effective charge $\alpha_s^{eff}$ for quark-quark scattering is derived by diagrammatic resummation of the one-loop amplitude using an arbitary covariant gauge. Except for the particular choice of gauge parameter $\xi = -3$, $\alpha_s^{eff}$ is found to {\it increase} with increasing physical scale, $Q$, as $\ln Q$ or $\ln^2 Q$. For $\xi = -3$, $\alpha_s^{eff}$ decreases with increasing $Q$ and satisfies a renormalisation group equation. Also, except for the case $\xi = 19/9$, convergence radii of geometric series are found to impose upper limits on $Q$. 
J.H. Field (D\'epartement de Physique Nucl\'eaire et Corpusculaire   Universit\'e de Gen\`eve, Gen\`eve, CH)