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

Abstract

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 $Q$.

28 pages, 5 tables, 5 figures. v3 The one-loop amplitudes in Section 2 are recalculated using dimensional regularisation, and several errors in the on-shell calculation of Reference[1] are pointed out. v4 one figure removed one added. Three tables and new text in Section 5 added. Published version

References in corpus (5)

• Historical roots of gauge invariance
• Ten years of the Analytic Perturbation Theory in QCD
• Renormalon approach to higher-twist distribution amplitudes and the convergence of the conformal expansion
• Perturbative Part of the Non-Singlet Structure Function F_2 in the Large-N_F Limit
• Renormalon chains contributions to the non-singlet evolutional kernels in QCD