Precise perturbative predictions from fixed-order calculations

Abstract

The intrinsic conformality (iCF) is a general property of the renormalizable gauge theory, which ensures the scale invariance of a fixed-order series at each perturbative order. Following the idea of iCF, we suggest a novel single-scale setting approach under the principle of maximum conformality (PMC) with the purpose of removing the conventional renormalization scheme and scale ambiguities. We call this newly suggested single-scale procedure the PMC∞-s approach, in which an overall effective α s , and hence an overall effective scale is achieved by identifying the {β 0} terms at each order. Its resultant conformal series is scale-invariant and satisfies all renormalization group requirements. The PMC∞-s approach is applicable to any perturbatively calculable observable, and its resultant perturbative series provides an accurate basis for estimating the contribution from the unknown higher-order (UHO) terms. Using the Higgs decay into two gluons up to five-loop quantum chromondynamics (QCD) corrections as an example, we show how the PMC∞-s works, and we obtain and . Here the errors are squared averages of those mentioned in the body of the text. The approximation approach (PAA) and the Bayesian approach (BA) have been adopted to estimate the contributions from the UHO terms. We also demonstrate that the PMC∞-s approach is equivalent to our previously suggested single-scale setting approach (PMCs), which also follows from the PMC but treats the {β i } terms from a different point of view. Thus, proper use of the renormalization group equation can provide a solid way to solve the scale-setting problem.