Comparison of the Pade Approximation Method to Perturbative QCD Calculations

Abstract

We present a method of estimating perturbative coefficients in Quantum Field Theory using Pade Approximants. We test this method on various known QCD results, and find that the method works very well.

14 pages (phyzzx macropackage) + 1 postscript figure encoded through uufiles, appended at the end of the tex file. Additional relevant references added

References in corpus (2)

• Estimates of the higher-order QCD corrections to R(s), R_τ and deep-inelasstic scattering sum rules
• Renormalon Singularities of the QCD Vacuum Polarization Function to Leading Order in $1/N_f$

Cited by in corpus (94)

• The four-loop beta-function in Quantum Chromodynamics
• Decoupling Relations to O(alpha_s^3) and their Connection to Low-Energy Theorems
• The third-order QCD corrections to deep-inelastic scattering by photon exchange
• Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme
• From Useful Algorithms for Slowly Convergent Series to Physical Predictions Based on Divergent Perturbative Expansions
• Strong-Coupling Constant with Flavor Thresholds at Five Loops in the MS-bar Scheme
• Higher twists and ${\alpha }_s(M_Z)$ extractions from the NNLO QCD analysis of the CCFR data for $x{F}_3$ structure function
• Results and Techniques of Multi-Loop Calculations
• Pade Approximants, Borel Transforms and Renormalons: the Bjorken Sum Rule as a Case Study
• Rhad: A program for the evaluation of the hadronic R-ratio in the perturbative regime of QCD
• Renormalization-Scheme Dependence of Pade Summation in QCD
• Asymptotic Pade Approximant Predictions: up to Five Loops in QCD and SQCD
• Numerical Evidence that the Perturbation Expansion for a Non-Hermitian $\mathcal{P}\mathcal{T}$-Symmetric Hamiltonian is Stieltjes
• Restricted conformal invariance in QCD and its predictive power for virtual two-photon processes
• The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality
• Relations between Observables and the Infrared Fixed-Point in QCD
• Pade Approximants, Optimal Renormalization Scales, and Momentum Flow in Feynman Diagrams
• Renormalons and multiloop estimates in scalar correlators, Higgs decay and quark-mass sum rules
• On the role of power expansions in quantum field theory
• Heavy flavour contributions to the deep inelastic sum rules
• Why Padé Approximants reduce the Renormalization-Scale dependence in QFT?
• Pade-Improvement of QCD Running Coupling Constants, Running Masses, Higgs Decay Rates, and Scalar Channel Sum Rules
• Non-singlet structure functions beyond the next-to-next-to leading order
• The Cross Section of e^+ e^- Annihilation into Hadrons of Order alpha_s^4 n_f^2 in Perturbative QCD
• Higher-order QCD corrections to hadronic $\tau$ decays from Padé approximants
• A Prediction for the 4-Loop βFunction
• RG/Pade Estimate of the Three-Loop Contribution to the QCD Static Potential Function
• Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by Č\'ıžek, Zamastil, and Skála. I. Algebraic Theory
• Prediction Properties of Aitken's Iterated Delta^2 Process, of Wynn's Epsilon Algorithm, and of Brezinski's Iterated Theta Algorithm
• Nonsinglet parton distribution functions from the precise next-to-next-to-next-to leading order QCD fit
• Resummation of QED Perturbation Series by Sequence Transformations and the Prediction of Perturbative Coefficients
• Unveiling the scattering behavior of small spheres
• Asymptotic Pade-Approximant Methods and QCD Current Correlation Functions
• Extending the Predictive Power of Perturbative QCD
• Chiral Symmetry Breaking in QCD: A Variational Approach
• Quark mass anomalous dimension at O(1/N_f^2) in QCD
• Is Radiative Electroweak Symmetry Breaking Consistent with a 125 GeV Higgs Mass?
• Perturbative Finite-Temperature Results and Pad'e Approximants
• Improvement of the method of diagonal Pade approximants for perturbative series in gauge theories
• Asymptotic Improvement of Resummation and Perturbative Predictions in Quantum Field Theory
• Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants
• Resummation of the hadronic tau decay width with the modified Borel transform method
• Renormalization-scale-invariant continuation of truncated QCD (QED) series -- an analysis beyond large-beta_0 approximation
• Variational Quark Mass Expansion and the Order Parameters of Chiral Symmetry Breaking
• HHH Whitepaper
• Towards a physical expansion in perturbative gauge theories by using improved Baker-Gammel approximants
• Pade-Improved Extraction of ${\alpha }_s(M_{\tau })$ from $R_{\tau }$
• Scale- and scheme-independent extension of Pade approximants; Bjorken polarized sum rule as an example
• Asymptotic Pade-Approximant Predictions for Renormalization-Group Functions of Massive ${\varphi }^4$ Scalar Field Theory
• Bjorken unpolarized and polarized sum rules: comparative analysis of large-N_F expansions
• Estimate of the Three-Loop Perturbative Contribution to Inclusive Semileptonic b to u Decays
• Perturbative QCD Calculations of Total Cross Sections and Decay Widths in Hard Inclusive Processes
• Scheme dependence of NLO corrections to exclusive processes
• The QCD Static Energy using Optimal Renormalization and Asymptotic Padé-approximant Methods
• A Convergent Reformulation of QCD Perturbation Theory
• Precise perturbative predictions from fixed-order calculations
• The heavy quarkonium inclusive decays using the principle of maximum conformality
• A novel determination of non-perturbative contributions to Bjorken sum rule
• 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
• Estimating higher order perturbative coefficients using Borel transform
• QCD improved top-quark decay at next-to-next-to-leading order
• $P$-wave quarkonium wavefunctions at the origin in the $\overline{\mathrm{MS}}$ scheme
• 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
• The QCD analysis of the revised CCFR data for xF_3 structure function: the next-to-next-to-leading order and Padé approximants
• Renormalization-Scale Invariance, Minimal Sensitivity, and the Inclusive Hadronic Decays of a 115 GeV Higgs Particle
• 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
• Application of Padé interpolation to stationary state problems
• Application of Pade Approximants to Determination of alpha_s(M_Z^2) from Hadronic Event Shape Observables in e+e- Annihilation
• QCD effects to Bjorken unpolarized sum rule for $\nu N$ deep-inelastic scattering
• S-duality invariant perturbation theory improved by holography
• Pade Interpolation: Methodology and Application to Quarkonium
• Self-consistent analysis for the ${\eta }_c\to \gamma \gamma$ process
• Estimate of the Three-Loop MS bar Contribution to sigma(W_L^+ W_L^- --> Z_L Z_L)
• 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
• New determination of $|V_{\mathrm{cb}}|$ using the three-loop QCD corrections for the $B\to D^{\ast }$ semi-leptonic decays
• A new analysis of the pQCD contributions to the electroweak parameter $\rho$ using the single-scale approach of principle of maximum conformality
• Precise determination of the bottom-quark on-shell mass using its four-loop relation to the $\overline{\mathrm{MS}}$-scheme running mass
• Using an Effective Charges Method to extract Lambda-MS-bar from event shape moments in e+e- annihilation
• Approximate N${}^5$LO Higgs boson decay width $\Gamma (H\to \gamma \gamma )$
• Renormalization-group improved Higgs to two gluons decay rate
• Parton densities and structure functions at next-to-next-to-leading order and beyond
• Modeling power corrections to the Bjorken sum rule for the neutrino structure function F_1
• Can Large $u,d$ Quark Masses be Inferred from the $D_s\to n\pi$ decay rate?
• Analysis of the Pion Electromagnetic Form Factor with Next-to-Next-to-Leading Order QCD Corrections
• Summary of Working Group 3 of the Neutrino Factory '02 Workshop
• QCD corrections of $e^{+}{e}^{-}\to J/\psi +c+\bar{c}$ using the principle of maximum conformality
• Updated Determination of Ellis-Jaffe Sum Rules up to ${\mathrm{N}}^3\mathrm{LO}$ QCD corrections
• Renormalisation
• Spiral Multi-component Structure in Pade - Approximant QCD