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.

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

References in corpus (8)

• The five-loop beta function of Yang-Mills theory with fermions
• Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
• Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
• An extensive survey of the estimation of uncertainties from missing higher orders in perturbative calculations
• Degeneracy Relations in QCD and the Equivalence of Two Systematic All-Orders Methods for Setting the Renormalization Scale
• Extending the Predictive Power of Perturbative QCD Using the Principle of Maximum Conformality and Bayesian Analysis
• Gauge dependence of the perturbative QCD predictions under the momentum space subtraction scheme
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations

Cited by in corpus (7)

• Novel Method to Reliably Determine the QCD Coupling from $R_{\mathrm{uds}}$ Measurements and its effects to Muon $g-2$ and $\alpha (M_Z^2)$ within the Tau-Charm Energy Region
• Reanalysis of the top-quark pair production via the $e^{+}{e}^{-}$ annihilation near the threshold region up to N${}^3$LO QCD corrections
• Elimination of QCD Renormalization Scale and Scheme Ambiguities
• Revisiting the top-quark pair production at future $e^{+}{e}^{-}$ colliders
• Scale-invariant total decay width $\Gamma (H\to b\bar{b})$ using the novel method of characteristic operator
• The Principle of Maximum Conformality Correctly Resolves the Renormalization-Scheme-Dependence Problem
• Updated Determination of Ellis-Jaffe Sum Rules up to ${\mathrm{N}}^3\mathrm{LO}$ QCD corrections