Convergence and gauge dependence properties of the resummed one-loop quark-quark scattering amplitude in perturbative QCD

Abstract

The one-loop QCD effective charge α 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 ξ = −3, α eff is found to increase with increasing physical scale, Q, as lnQ or ln2 Q. For ξ = −3, α eff decreases with increasing Q and satisfies a renormalization group equation. Also, except for the case ξ = 19/9, convergence radii of geometric series are found to impose upper limits on Q.