Optimization of QCD Perturbation Theory: Results for R(e+e-) at fourth order
Abstract
Physical quantities in QCD are independent of renormalization scheme (RS), but that exact invariance is spoiled by truncations of the perturbation series. "Optimization" corresponds to making the perturbative approximant, at any given order, locally invariant under small RS changes. A solution of the resulting optimization equations is presented. It allows an efficient algorithm for finding the optimized result. Example results for R(e+e-)=3(Sum q_i^2)(1+R) to fourth order (NNNLO) are given that show nice convergence, even down to arbitrarily low energies. The Q=0 "freezing" behaviour, R=0.3+/-0.3, found at third order is confirmed and made more precise; R=0.2+/-0.1. Low-energy results in the MS-bar scheme, by contrast, show the typical pathologies of a non-convergent asymptotic series.
Cite
@article{arxiv.1210.7001,
title = {Optimization of QCD Perturbation Theory: Results for R(e+e-) at fourth order},
author = {P. M. Stevenson},
journal= {arXiv preprint arXiv:1210.7001},
year = {2016}
}
Comments
36 pages, 7 eps figures. LaTeX. Mathematica notebook file available. Referencess added