Renormalization scheme dependence and the problem of theoretical uncertainties in next-next-to-leading order QCD predictions

Abstract

Renormalization scheme uncertainties in the next-next-to-leading order QCD predictions are discussed. To obtain an estimate of these uncertainties it is proposed to compare predictions in all schemes that do not have unnaturally large expansion coefficients. A concrete prescription for eliminating the unnatural schemes is given, based on the requirement that large cancellations in the expression for the characteristic renormalization scheme invariant should be avoided. As an example the QCD corrections to the Bjorken sum rule are considered. The importance of the next-next-to-leading order corrections for a proper evaluation of perturbative QCD predictions is emphasized.

Renormalization scheme and higher loop stability in hadronic $\tau$ decay within analytic perturbation theory

“…Nevertheless, a natural way of studying the RS dependence is to supplement results in a certain scheme with an estimate of the variability of the predictions over a range of a priori acceptable schemes specified by some criterion. In [28] it was proposed to consider the class of 'natural' RSs, which obey the condition…”

The Bjorken sum rule in the analytic approach to perturbative QCD

“…In the framework of the conventional approach, there is no resolution of this problem of the RS dependence apart from calculating indefinitely many further terms in the PT expansion, and there is no fundamental principle upon which one can choose one or another preferable RS. However, it is possible to define a class of 'natural' RS's by using the so-called cancellation index criterion [9]. According to this criterion a class of 'well-behaved' RS's are defined a such a way that the degree of cancellation between the different terms in the second RS-invariant [5] ρ…”

Renormalization scheme dependence in analytic approach to perturbative QCD

“…To compare the results obtained in various RS's, one uses the 'cancellation index criterion' proposed by P. Raczka [5]. According to it, a set of "natural" RS's can be introduced which includes schemes for which the degree of cancellation between different terms in the second RS-invariant [6] ρ…”