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 arbitrary covariant gauge. Except for the particular choice of gauge parameter xi = -3, alpha(s) (eff) is found to increase with increasing physical scale, Q, as lnQ or ln(2) Q. For xi = -3, alpha (s) (eff) decreases with increasing Q and satisfies a renormalization group equation. Also, except for the case xi = 19/9, convergence radii of geometric series are found to impose upper limits on Q.