Precise perturbative predictions from fixed-order calculations

Abstract

The intrinsic conformality 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 intrinsic conformality, 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 as the PMC${}_{\infty }$-s approach, in which an overall effective ${\alpha }_s$, and hence an overall effective scale is achieved by identifying the $\{{\beta }_0\}$-terms at each order. Its resultant conformal series is scale-invariant and satisfies all renormalization group requirements. The PMC${}_{\infty }$-s approach is applicable to any perturbatively calculable observables, and its resultant perturbative series provides an accurate basis for estimating the contribution from the unknown higher-order (UHO) terms. Using the Higgs decays into two gluons up to five-loop QCD corrections as an example, we show how the PMC${}_{\infty }$-s works, and we obtain ${\Gamma }_{\mathrm{H}}{|}_{{\text{PMC}}_{\infty }\text{-s}}^{\mathrm{PAA}}=334.45_{-7.03}^{+7.07}\mathrm{KeV}$ and ${\Gamma }_{\mathrm{H}}{|}_{{\text{PMC}}_{\infty }\text{-s}}^{B.A.}=334.45_{-6.29}^{+6.34}\mathrm{KeV}$. Here the errors are squared averages of those mentioned in the body of the text. The Pad$\acute{e}$ approximation approach (PAA) and the Bayesian approach (B.A.) have been adopted to estimate the contributions from the UHO-terms. We also demonstrate that the PMC${}_{\infty }$-s approach is equivalent to our previously suggested single-scale setting approach (PMCs), which also follows from the PMC but treats the $\{{\beta }_i\}$-terms from different point of view. Thus a proper using of the renormalization group equation can provide a solid way to solve the scale-setting problem.

arXiv comment13 pages, 8 figures, to be published in J.Phys.G

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