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

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Abstract

The one-loop QCD effective charge α eff s 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 s is found to increase with increasing physical scale, Q, as lnQ or ln2 Q. For ξ = −3, α eff s 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.

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  1. Département de Physique Nucléaire et Corpusculaire Université de Genève 24, quai Ernest-Ansermet, CH-1211, Genève 4, France

    J. H. Field

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Field, J.H. Convergence and gauge dependence properties of the resummed one-loop quark-quark scattering amplitude in perturbative QCD. Phys. Part. Nuclei 40, 353–367 (2009). https://doi.org/10.1134/S1063779609030046

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