Extending the Predictive Power of Perturbative QCD Using the Principle of Maximum Conformality and Bayesian Analysis

Abstract

In addition to the evaluation of high-order loop contributions, the precision and predictive power of perturbative QCD (pQCD) predictions depends on two important issues: (1) how to achieve a reliable, convergent fixed-order series, and (2) how to reliably estimate the contributions of unknown higher-order terms. The recursive use of renormalization group equation, together with the Principle of Maximum Conformality (PMC), eliminates the renormalization scheme-and-scale ambiguities of the conventional pQCD series. The result is a conformal, scale-invariant series of finite order which also satisfies all of the principles of the renormalization group. In this paper we propose a novel Bayesian-based approach to estimate the size of the unknown higher order contributions based on an optimized analysis of probability distributions. We show that by using the PMC conformal series, in combination with the Bayesian analysis, one can consistently achieve high degree of reliability estimates for the unknown high order terms. Thus the predictive power of pQCD can be greatly improved. We illustrate this procedure for two pQCD observables: $R_{e^{+}{e}^{-}}$ and $R_{\tau }$, which are each known up to four loops in pQCD. Numerical analyses confirm that by using the scale-independent and more convergent PMC conformal series, one can achieve reliable Bayesian probability estimates for the unknown higher-order contributions.

arXiv comment14 pages, 4 figures, published version

References in corpus (30)

• The four-loop beta-function in Quantum Chromodynamics
• Renormalons
• RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses
• The three-loop QCD $\beta$-function and anomalous dimensions
• Five-Loop Running of the QCD coupling constant
• The Four-Loop QCD Beta-Function and Anomalous Dimensions
• Hadronic Z- and tau-Decays in Order alpha_s^4
• Version 3 of {\tt RunDec} and {\tt CRunDec}
• Naive nonabelianization and resummation of fermion bubble chains
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• A Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in PQCD
• Commensurate Scale Relations in Quantum Chromodynamics
• Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations
• alpha_s and the tau hadronic width: fixed-order, contour-improved and higher-order perturbation theory
• Scale Setting in QCD and the Momentum Flow in Feynman Diagrams
• Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
• The Renormalization Scale-Setting Problem in QCD
• Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions
• Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
• Vector Correlator in Massless QCD at Order O(alpha_s^4) and the QED beta-function at five loop
• Meaningful characterisation of perturbative theoretical uncertainties
• Aspects of SU(N_c) Gauge Theories in the Limit of Small Number of Colors
• Scheme variations of the QCD coupling and hadronic $\tau$ decays
• An extensive survey of the estimation of uncertainties from missing higher orders in perturbative calculations
• Higher-order QCD corrections to hadronic $\tau$ decays from Padé approximants
• Probabilistic definition of the perturbative theoretical uncertainty from missing higher orders
• Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy
• Degeneracy Relations in QCD and the Equivalence of Two Systematic All-Orders Methods for Setting the Renormalization Scale
• PMC${}_{\infty }$: Infinite-Order Scale-Setting using the Principle of Maximum Conformality, A Remarkably Efficient Method for Eliminating Renormalization Scale Ambiguities for Perturbative QCD
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations

Cited by in corpus (7)

• Precise perturbative predictions from fixed-order calculations
• 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
• Revisiting the top-quark pair production at future $e^{+}{e}^{-}$ colliders
• Approximate N${}^5$LO Higgs boson decay width $\Gamma (H\to \gamma \gamma )$
• The Principle of Maximum Conformality Correctly Resolves the Renormalization-Scheme-Dependence Problem
• Scale-invariant total decay width $\Gamma (H\to b\bar{b})$ using the novel method of characteristic operator