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Convergence and Gauge Dependence Properties of the Resummed One-loop Quark-Quark Scattering Amplitude in Perturbative QCD

J. H. Field
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Abstract

The one-loop QCD effective charge $α_s^{eff}$ 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 $ξ= -3$, $α_s^{eff}$ is found to {\it increase} with increasing physical scale, $Q$, as $\ln Q$ or $\ln^2 Q$. For $ξ= -3$, $α_s^{eff}$ decreases with increasing $Q$ and satisfies a renormalisation 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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J. H. Field. 2009-07-09. Convergence and Gauge Dependence Properties of the Resummed One-loop Quark-Quark Scattering Amplitude in Perturbative QCD. https://doi.org/10.1134/s1063779609030046

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