Convergence and Gauge Dependence Properties of the Resummed One-loop Quark-Quark Scattering Amplitude in Perturbative QCD
Abstract
The one-loop QCD effective charge αseff 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 = -3, αseff is found to increase with increasing physical scale, Q, as Q or 2 Q. For = -3, αseff decreases with increasing Q and satisfies a renormalisation group equation. Also, except for the case = 19/9, convergence radii of geometric series are found to impose upper limits on Q.
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