Generalized Crewther relation and a novel demonstration of the scheme independence of commensurate scale relations up to all orders

Abstract

In the paper, we make a detailed study on the generalized Crewther Relation (GCR) between the Adler function ($D$) and the Gross-Llewellyn Smith sum rules coefficient ($C^{\mathrm{GLS}}$) by using the newly suggested single-scale approach of the principle of maximum conformality (PMC). The resultant GCR is scheme-independent, whose residual scale dependence due to unknown higher-order terms are highly suppressed. Thus a precise test of QCD theory without renormalization scheme and scale ambiguities can be achieved by comparing with the data. Moreover, a demonstration of the scheme independence of commensurate scale relation up to all orders has been presented. And as the first time, the Pade approximation approach has been adopted for estimating the unknown $5_{\mathrm{th}}$-loop contributions from the known four-loop perturbative series.

arXiv comment8 pages, 2 figures

References in corpus (45)

• Renormalons
• Hadronic Z- and tau-Decays in Order alpha_s^4
• The Uses of Conformal Symmetry in QCD
• 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
• QCD Corrections to the $e^{+}{e}^{-}$ Cross Section and the $Z$ Boson Decay Rate
• 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
• Optimization of R(e+e-) and "Freezing" of the QCD Couplant at Low Energies
• Scale Setting in QCD and the Momentum Flow in Feynman Diagrams
• ERRATUM TO: Power corrections $1/Q^2$ to parton sum rules for deep inelastic scattering from polarized targets
• Connections between Deep-Inelastic and Annihilation Processes at Next-to-Next-to-Leading Order and Beyond
• 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
• Corrections of order ${\alpha }_s^3$ to $R_{had}$ in pQCD with light gluinos
• Vector Correlator in Massless QCD at Order O(alpha_s^4) and the QED beta-function at five loop
• The Generalized Crewther Relation in QCD and its Experimental Consequences
• Q^2-Dependence of the Proton's G_1 Structure Function Sum Rule
• Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
• Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
• QCD Sum Rule Calculation of Twist-3 Contributions to Polarized Nucleon Structure Functions
• QCD Sum Rule Calculation of Twist-4 Corrections to Bjorken and Ellis-Jaffe Sum Rules
• The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality
• Scheme variations of the QCD coupling and hadronic $\tau$ decays
• Relating inclusive e+e- annihilation to electroproduction sum rules in Quantum Chromodynamics
• The Jacobi Polinomials QCD Analysis of the CCFR Data for xF_3 and the Q^2-Dependence of the Gross-Llewllyn Smith Sum Rule
• Novel All-Orders Single-Scale Approach to QCD Renormalization Scale-Setting
• Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy
• Improved QCD sum rule estimates of the higher twist contributions to polarised and unpolarised nucleon structure functions
• Degeneracy Relations in QCD and the Equivalence of Two Systematic All-Orders Methods for Setting the Renormalization Scale
• A novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the $C$-scheme coupling
• Extending the Predictive Power of Perturbative QCD
• Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the $\beta$-factorization property?
• Adler Function, DIS sum rules and Crewther Relations
• The Importance of Proper Renormalization Scale-Setting for Testing QCD at Colliders
• Adler function and Bjorken polarized sum rule: Perturbation expansions in powers of $SU(N_c)$ conformal anomaly and studies of the conformal symmetry limit
• The Generalized Scheme-Independent Crewther Relation in QCD
• 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
• Scale-Fixed Predictions for $\gamma +{\eta }_c$ production in electron-positron collisions at NNLO in perturbative QCD
• Properties of the decay $H\to \gamma \gamma$ using the approximate ${\alpha }_s^4$-corrections and the principle of maximum conformality

Cited by in corpus (6)

• Precise perturbative predictions from fixed-order calculations
• Detailed Comparison of Renormalization Scale-Setting Procedures based on the Principle of Maximum Conformality
• Reanalysis of the top-quark pair production via the $e^{+}{e}^{-}$ annihilation near the threshold region up to N${}^3$LO QCD corrections
• New determination of $|V_{\mathrm{cb}}|$ using the three-loop QCD corrections for the $B\to D^{\ast }$ semi-leptonic decays
• 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