Detailed Comparison of Renormalization Scale-Setting Procedures based on the Principle of Maximum Conformality

Abstract

The {\it Principle of Maximum Conformality} (PMC), which generalizes the conventional Gell-Mann-Low method for scale-setting in perturbative QED to non-Abelian QCD, provides a rigorous method for achieving unambiguous scheme-independent, fixed-order predictions for physical observables consistent with the principles of the renormalization group. In addition to the original multi-scale-setting approach (PMCm), two variations of the PMC have been proposed to deal with ambiguities associated with the uncalculated higher order terms in the pQCD series, i.e. the single-scale-setting approach (PMCs) and the procedures based on ``intrinsic conformality" (PMC${}_{\infty }$). In this paper, we will give a detailed comparison of these PMC approaches by comparing their predictions for three important quantities $R_{e^{+}{e}^{-}}$, $R_{\tau }$, and $\Gamma (H\to b\bar{b})$ up to four-loop pQCD corrections. The PMCs approach determines an overall effective running coupling ${\alpha }_s(Q)$ by the recursive use of the renormalization group equation, whose argument $Q$ represents the actual momentum flow of the process. Our numerical results show that the PMCs method, which involves a somewhat simpler analysis, can serve as a reliable substitute for the full multi-scale PMCm method, and that it leads to more precise pQCD predictions with small residual scale dependence.

arXiv comment17 pages, 6 figures, to be published in Nuclear Physics B

References in corpus (51)

• The four-loop beta-function in Quantum Chromodynamics
• Renormalons
• 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
• Branching ratios and spectral functions of tau decays: final ALEPH measurements and physics implications
• Naive nonabelianization and resummation of fermion bubble chains
• The Physics of Hadronic Tau Decays
• Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses
• 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
• Update of the ALEPH non-strange spectral functions from hadronic $\tau$ decays
• Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations
• 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
• Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops
• The Renormalization Scale-Setting Problem in QCD
• Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions
• Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality
• Comparison of the Pade Approximation Method to Perturbative QCD Calculations
• Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
• Meaningful characterisation of perturbative theoretical uncertainties
• Determination of the strong coupling constant using matched NNLO+NLLA predictions for hadronic event shapes in e+e- annihilations
• Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
• Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
• Aspects of SU(N_c) Gauge Theories in the Limit of Small Number of Colors
• The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality
• Why Padé Approximants reduce the Renormalization-Scale dependence in QFT?
• Novel All-Orders Single-Scale Approach to QCD Renormalization Scale-Setting
• Probabilistic definition of the perturbative theoretical uncertainty from missing higher orders
• Degeneracy Relations in QCD and the Equivalence of Two Systematic All-Orders Methods for Setting the Renormalization Scale
• "Massive" Perturbative QCD, regular in the IR limit
• A novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the $C$-scheme coupling
• Implications of the Principle of Maximum Conformality for the QCD Strong Coupling
• Extending the Predictive Power of Perturbative QCD
• The Higgs boson inclusive decay channels $H\to b\bar{b}$ and $H\to gg$ up to four-loop level
• PMC${}_{\infty }$: Infinite-Order Scale-Setting using the Principle of Maximum Conformality, A Remarkably Efficient Method for Eliminating Renormalization Scale Ambiguities for Perturbative QCD
• The Importance of Proper Renormalization Scale-Setting for Testing QCD at Colliders
• Novel and self-consistency analysis of the QCD running coupling ${\alpha }_s(Q)$ in both the perturbative and nonperturbative domains
• Ambiguities of the principle of maximum conformality procedure for hadron collider processes
• The heavy quarkonium inclusive decays using the principle of maximum conformality
• Hadronic decays of the spin-singlet heavy quarkomium under the principle of maximum conformality
• Determination of the top-quark $\overline{\mathrm{MS}}$ running mass via its perturbative relation to the on-shell mass with the help of principle of maximum conformality
• Properties of the decay $H\to \gamma \gamma$ using the approximate ${\alpha }_s^4$-corrections and the principle of maximum conformality
• Thrust Distribution for 3-Jet Production from $e^{+}{e}^{-}$ Annihilation within the QCD Conformal Window and in QED
• Generalized Crewther relation and a novel demonstration of the scheme independence of commensurate scale relations up to all orders
• The Gross-Llewellyn Smith sum rule up to $\mathcal{O}({\alpha }_s^4)$-order QCD corrections
• $Z$-boson hadronic decay width up to $\mathcal{O}({\alpha }_s^4)$-order QCD corrections using the single-scale approach of the principle of maximum conformality
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations

Cited by in corpus (3)

• Precise perturbative predictions from fixed-order calculations
• QCD corrections of $e^{+}{e}^{-}\to J/\psi +c+\bar{c}$ using the principle of maximum conformality
• Renormalisation