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arXiv · hep-ph/0305187

Optimal RG-Improvement of Perturbative Calculations in QCD

V. Elias
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Abstract

Using renormalization-group methods, differential equations can be obtained for the all-orders summation of leading and subsequent non-leading logarithmic corrections to QCD perturbative series for a number of processes and correlation functions. For a QCD perturbative series known to four orders, such as the e+ e- annihilation cross-section, explicit solutions to these equations are obtained for the summation to all orders in alpha_s of the leading set and the subsequent two non-leading sets of logarithms. Such summations are shown for a number of processes to lead to a substantial reduction in sensitivity to the renormalization scale parameter. Surprisingly, such summations are also shown to lower the infrared singularity within the perturbative expression for the e+ e- annihilation cross-section to coincide with the Landau pole of the naive one-loop running QCD couplant.

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V. Elias. 2003-05-16. Optimal RG-Improvement of Perturbative Calculations in QCD. https://arxiv.org/abs/hep-ph/0305187

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