Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1992-11-16
Phys.Rev.D48:3310-3318,1993
Physics
High Energy Physics
High Energy Physics - Phenomenology
Plain TEX, 4 figures (available upon request), 22 pages, DOE/ER/40322-178
Scientific paper
10.1103/PhysRevD.48.3310
We discuss the St\"uckelberg-Peterman extended renormalization group equations in perturbative QCD, which express the invariance of physical observables under renormalization-scale and scheme-parameter transformations. We introduce a universal coupling function that covers all possible choices of scale and scheme. Any perturbative series in QCD is shown to be equivalent to a particular point in this function. This function can be computed from a set of first-order differential equations involving the extended beta functions. We propose the use of these evolution equations instead of perturbative series for numerical evaluation of physical observables. This formalism is free of scale-scheme ambiguity and allows a reliable error analysis of higher-order corrections. It also provides a precise definition for $\Lambda_{\overline{\rm MS}}$ as the pole in the associated 't Hooft scheme. A concrete application to $R(e^+e^- \to {\rm hadrons})$ is presented.
Brodsky Stanley J.
Lu Hung Jung
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