Optimal Renormalization-Group Improvement of R(s) via the Method of Characteristics
V. Elias (University of Western Ontario), D.G.C. McKeon (University of, Western Ontario), T.G. Steele (University of Saskatchewan)
TL;DR
This paper applies the method of characteristics to the renormalization-group equation in QCD, enabling a closed-form summation of key logarithms in the perturbative series for electron-positron annihilation cross-section.
Contribution
It introduces a novel application of the method of characteristics to improve the renormalization-group summation in QCD perturbation series.
Findings
Achieves a closed-form summation of the first four towers of RG-accessible logarithms.
Demonstrates equivalence to a specific RG improvement of the perturbative series.
Provides a new technique for summing logarithms in QCD calculations.
Abstract
We discuss the application of the method of characteristics to the renormalization-group equation for the perturbative QCD series within the electron-positron annihilation cross-section. We demonstrate how one such renormalization-group improvement of this series is equivalent to a closed-form summation of the first four towers of renormalization-group accessible logarithms to all orders of perturbation theory.
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