Optimization of QCD Perturbation Theory: Results for R(e+e-) at fourth order

TL;DR

This paper develops an optimization method for QCD perturbation series that improves convergence and precision of R(e+e-) calculations at low energies, confirming the freezing behavior of the observable.

Contribution

It introduces an efficient algorithm for optimizing perturbative QCD series, enhancing convergence and accuracy at low energies compared to standard schemes.

Findings

Optimized results show good convergence down to low energies.

Confirmed the R=0.3±0.3 freezing at third order.

Low-energy MS-bar scheme results exhibit typical asymptotic series pathologies.

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.