Extending the Predictive Power of Perturbative QCD

Abstract

The predictive power of perturbative QCD (pQCD) depends on two important issues: (1) how to eliminate the renormalization scheme-and-scale ambiguities at fixed order, and (2) how to reliably estimate the contributions of unknown higher-order terms using information from the known pQCD series. The Principle of Maximum Conformality (PMC) satisfies all of the principles of the renormalization group and eliminates the scheme-and-scale ambiguities by the recursive use of the renormalization group equation to determine the scale of the QCD running coupling ${\alpha }_s$ at each order. Moreover, the resulting PMC predictions are independent of the choice of the renormalization scheme, satisfying the key principle of renormalization group invariance. In this letter, we show that by using the conformal series derived using the PMC single-scale procedure, in combination with the Padé Approximation Approach (PAA), one can achieve quantitatively useful estimates for the unknown higher-order terms from the known perturbative series. We illustrate this procedure for three hadronic observables $R_{e^{+}{e}^{-}}$, $R_{\tau }$, and $\Gamma (H\to b\bar{b})$ which are each known to 4 loops in pQCD. We show that if the PMC prediction for the conformal series for an observable (of leading order ${\alpha }_s^p$) has been determined at order ${\alpha }_s^n$, then the $[N/M]=[0/n-p]$ Padé series provides quantitatively useful predictions for the higher-order terms. We also show that the PMC + PAA predictions agree at all orders with the fundamental, scheme-independent Generalized Crewther relations which connect observables, such as deep inelastic neutrino-nucleon scattering, to hadronic $e^{+}{e}^{-}$ annihilation. Thus, by using the combination of the PMC series and the Padé method, the predictive power of pQCD theory can be greatly improved.

arXiv comment7 pages, 1 figure. Discussions improved and references updated

References in corpus (38)

• Renormalons
• Hadronic Z- and tau-Decays in Order alpha_s^4
• Conformal Regge theory
• Quantum spectral curve for AdS_5/CFT_4
• Naive nonabelianization and resummation of fermion bubble chains
• 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
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• 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
• 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
• Vector Correlator in Massless QCD at Order O(alpha_s^4) and the QED beta-function at five loop
• Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4
• Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
• NNLO BFKL Pomeron eigenvalue in N=4 SYM
• Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
• Asymptotic Pade Approximant Predictions: up to Five Loops in QCD and SQCD
• Connecting the Hadron Mass Scale to the Fundamental Mass Scale of Quantum Chromodynamics
• Aspects of SU(N_c) Gauge Theories in the Limit of Small Number of Colors
• Pade Approximants, Optimal Renormalization Scales, and Momentum Flow in Feynman Diagrams
• On the Interface between Perturbative and Nonperturbative QCD
• Why Padé Approximants reduce the Renormalization-Scale dependence in QFT?
• Novel All-Orders Single-Scale Approach to QCD Renormalization Scale-Setting
• Higher-order QCD corrections to hadronic $\tau$ decays from Padé approximants
• A Prediction for the 4-Loop βFunction
• Degeneracy Relations in QCD and the Equivalence of Two Systematic All-Orders Methods for Setting the Renormalization Scale
• Implications of the Principle of Maximum Conformality for the QCD Strong Coupling
• The Higgs boson inclusive decay channels $H\to b\bar{b}$ and $H\to gg$ up to four-loop level
• Asymptotic Padé Approximants and the SQCD $\beta$-function
• The Importance of Proper Renormalization Scale-Setting for Testing QCD at Colliders
• The Generalized Scheme-Independent Crewther Relation in QCD
• A solution to the $\gamma {\gamma }^{\ast }\to {\eta }_c$ puzzle using the Principle of Maximum Conformality
• Application of Pade Approximants to Determination of alpha_s(M_Z^2) from Hadronic Event Shape Observables in e+e- Annihilation

Cited by in corpus (26)

• The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality
• Novel and self-consistency analysis of the QCD running coupling ${\alpha }_s(Q)$ in both the perturbative and nonperturbative domains
• Precise perturbative predictions from fixed-order calculations
• The heavy quarkonium inclusive decays using 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
• A novel determination of non-perturbative contributions to Bjorken sum rule
• QCD improved top-quark decay at next-to-next-to-leading order
• Scale-Fixed Predictions for $\gamma +{\eta }_c$ production in electron-positron collisions at NNLO in perturbative QCD
• QCD effective charges and the structure function $F_2$ at small-$x$: Higher twist effects
• Detailed Comparison of Renormalization Scale-Setting Procedures based on the Principle of Maximum Conformality
• Higher-order QCD corrections to $H\to b\bar{b}$ from rational approximants
• Generalized Crewther relation and a novel demonstration of the scheme independence of commensurate scale relations up to all orders
• $Z$-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
• The Gross-Llewellyn Smith sum rule up to $\mathcal{O}({\alpha }_s^4)$-order QCD corrections
• Self-consistent analysis for the ${\eta }_c\to \gamma \gamma$ process
• Precise determination of the top-quark on-shell mass $M_t$ via its scale-invariant perturbative relation to the top-quark $\overline{\mathrm{MS}}$ mass ${\overline{m}}_t({\overline{m}}_t)$
• Elimination of QCD Renormalization Scale and Scheme Ambiguities
• A new analysis of the pQCD contributions to the electroweak parameter $\rho$ using the single-scale approach of principle of maximum conformality
• Approximate N${}^5$LO Higgs boson decay width $\Gamma (H\to \gamma \gamma )$
• New determination of $|V_{\mathrm{cb}}|$ using the three-loop QCD corrections for the $B\to D^{\ast }$ semi-leptonic decays
• Precise determination of the bottom-quark on-shell mass using its four-loop relation to the $\overline{\mathrm{MS}}$-scheme running mass
• 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
• Analysis of the Pion Electromagnetic Form Factor with Next-to-Next-to-Leading Order QCD Corrections
• QCD corrections of $e^{+}{e}^{-}\to J/\psi +c+\bar{c}$ using the principle of maximum conformality