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 $Q$.
Categories: hep-ph