Optimization of QCD perturbation theory: Results for Re+e- at fourth order

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 Sigma 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 behavior, 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) over bar scheme, by contrast, show the typical pathologies of a non-convergent asymptotic series. (c) 2012 Elsevier B.V. All rights reserved.