Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-11-19
Physics of Particles and Nuclei (2009) Vol. 40, No. 3, 353-367
Physics
High Energy Physics
High Energy Physics - Phenomenology
28 pages, 5 tables, 5 figures. v3 The one-loop amplitudes in Section 2 are recalculated using dimensional regularisation, and
Scientific paper
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 arbitary covariant gauge. Except for the particular choice of gauge parameter $\xi = -3$, $\alpha_s^{eff}$ is found to {\it increase} with increasing physical scale, $Q$, as $\ln Q$ or $\ln^2 Q$. For $\xi = -3$, $\alpha_s^{eff}$ decreases with increasing $Q$ and satisfies a renormalisation group equation. Also, except for the case $\xi = 19/9$, convergence radii of geometric series are found to impose upper limits on $Q$.
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