Estimates of the higher-order QCD corrections to R(s), R_τ and deep-inelasstic scattering sum rules

Abstract

We present the attempt to study the problem of the estimates of higher-order perturbative corrections to physical quantities in the Euclidean region. Our considerations are based on the application of the scheme-invariant methods, namely the principle of minimal sensitivity and the effective charges approach. We emphasize, that in order to obtain the concrete results for the physical quantities in the Minkowskian region the results of application of this formalism should be supplemented by the explicite calculations of the effects of the analytical continuation. We present the estimates of the order $O({\alpha }_s^4)$ QCD corrections to the Euclidean quantities: the $e^{+}{e}^{-}$-annihilation $D$-function and the deep inelastic scattering sum rules, namely the non-polarized and polarized Bjorken sum rules and to the Gross--Llewellyn Smith sum rule. The results for the $D$-function are further applied to estimate the $O({\alpha }_s^4)$ QCD corrections to the Minkowskian quantities $R(s)={\sigma }_{tot}(e^{+}{e}^{-}\to \mathrm{hadrons})/\sigma (e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-})$ and $R_{\tau }=\Gamma (\tau \to {\nu }_{\tau }+\mathrm{hadrons})/\Gamma (\tau \to {\nu }_{\tau }{\overline{\nu }}_{e}e)$. The problem of the fixation of the uncertainties due to the $O({\alpha }_s^5)$ corrections to the considered quantities is also discussed.

LATEX, 17 pages; to be published in Mod.Phys.Lett.A10,N3 (1995) 235

Cited by in corpus (161)

• Renormalons
• Hadronic Z- and tau-Decays in Order alpha_s^4
• Measurements of the Proton and Deuteron Spin Structure Functions g1 and g2
• Decoupling Relations to O(alpha_s^3) and their Connection to Low-Energy Theorems
• Precise determination of the spin structure function ${\mathbf{g}}_1$ of the proton, deuteron and neutron
• Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme
• Branching ratios and spectral functions of tau decays: final ALEPH measurements and physics implications
• Precision Tau Physics
• Spin Structure of the Proton from Polarized Inclusive Deep-Inelastic Muon-Proton Scattering
• The Physics of Hadronic Tau Decays
• Masses, decays and mixings of gluonia in QCD
• 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
• QCD Corrections to the $e^{+}{e}^{-}$ Cross Section and the $Z$ Boson Decay Rate
• Determination of the QCD Coupling ${\alpha }_s$
• Flavor Decomposition of the Polarized Quark Distributions in the Nucleon from Inclusive and Semi-inclusive Deep-inelastic Scattering
• The Determination of alpha_s from Tau Decays Revisited
• On the running coupling constant in QCD
• The Renormalization Scale-Setting Problem in QCD
• Comparison of the Pade Approximation Method to Perturbative QCD Calculations
• Strong-Coupling Constant with Flavor Thresholds at Five Loops in the MS-bar Scheme
• Power corrections to alpha_s(M_τ),|V_{us}| and m_s
• Higher twists and ${\alpha }_s(M_Z)$ extractions from the NNLO QCD analysis of the CCFR data for $x{F}_3$ structure function
• Next-to-next-to-leading order QCD analysis of the revised CCFR data for xF_3 structure function and the higher twist contributions
• Results and Techniques of Multi-Loop Calculations
• A measurement of $alph{a}_s(Q^2)$ from the Gross-Llewellyn Smith Sum Rule
• Effective QCD Interactions of CP-odd Higgs Bosons at Three Loops
• Pade Approximants, Borel Transforms and Renormalons: the Bjorken Sum Rule as a Case Study
• Next-to-next-to-leading order prediction for the photon-to-pion transition form factor
• Duality between QCD Perturbative Series and Power Corrections
• Rhad: A program for the evaluation of the hadronic R-ratio in the perturbative regime of QCD
• On The Difficulty of Computing Higher-Twist Corrections
• Renormalization-Scheme Dependence of Pade Summation in QCD
• ${\alpha }_s$ from $\tau$ decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion
• The check of QCD based on the tau-decay data analysis in the complex q^2-plane
• Analytic Approach to Perturbative QCD and Renormalization Scheme Dependence
• Various versions of analytic QCD and skeleton-motivated evaluation of observables
• Higher-order QCD perturbation theory in different schemes: From FOPT to CIPT to FAPT
• On the QCD Sum Rule Determination of the Strange Quark Mass
• Restricted conformal invariance in QCD and its predictive power for virtual two-photon processes
• QCD Analysis of Hadronic $\tau$ Decays Revisited
• The Complete $O({\alpha }_s^2)$ Non-Singlet Heavy Flavor Corrections to the Structure Functions $g_{1,2}^{ep}(x,Q^2)$, $F_{1,2,L}^{ep}(x,Q^2)$, $F_{1,2,3}^{\nu (\bar{\nu })}(x,Q^2)$ and the Associated Sum Rules
• Relations between Observables and the Infrared Fixed-Point in QCD
• Pade Approximants, Optimal Renormalization Scales, and Momentum Flow in Feynman Diagrams
• Condensates in Quantum Chromodynamics
• Renormalons and multiloop estimates in scalar correlators, Higgs decay and quark-mass sum rules
• Generalization of the Brodsky-Lepage-Mackenzie optimization within the $\{\beta \}$-expansion and the Principle of Maximal Conformality
• Heavy flavour contributions to the deep inelastic sum rules
• Why Padé Approximants reduce the Renormalization-Scale dependence in QFT?
• Bilocal expansion of the Borel amplitude and the hadronic tau decay width
• Estimations of Order alpha_s^3 and alpha_s^4 Corrections to Mass-Dependent Observables
• Non-singlet structure functions beyond the next-to-next-to leading order
• QCD vacuum condensates from tau-lepton decay data
• 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 novel integral representation for the Adler function
• A Prediction for the 4-Loop βFunction
• Exact Adler Function in Supersymmetric QCD
• Thermodynamics of Large-N Super Yang-Mills Theory and AdS/CFT Correspondence
• Contour-improved versus fixed-order perturbation theory in hadronic tau decays
• Reconciling the analytic QCD with the ITEP operator product expansion philosophy
• Renormalons at the boundaries between perturbative and non-perturbative QCD
• A new determination of the QED coupling alpha(M_Z^2) lets the Higgs off the hook
• Towards Order alpha_s^4 Accuracy in tau-decays
• The Gross--Llewellyn Smith Sum Rule in the Analytic Approach to Perturbative QCD
• Derivation of the exact expression for the D function in N=1 SQCD
• Fourth-order QCD renormalization group quantities in the {\rm{V}}-scheme and the relation of the $\beta$-function to the Gell-Mann--Low function in QED
• Simple analytic QCD model with perturbative QCD behavior at high momenta
• Asymptotic Pade-Approximant Methods and QCD Current Correlation Functions
• Dispersive approach to QCD and inclusive tau lepton hadronic decay
• Test of the Running of ${\alpha }_s$ in $\tau$ Decays
• Reconsidered estimates of the 10th order QED contributions to the muon anomaly
• Strong coupling constant from $\tau$ decay within renormalization scheme invariant treatment
• Calculation of binding energies and masses of quarkonia in analytic QCD models
• Is there evidence for dimension-two corrections in QCD two-point functions?
• An analytic method of describing $R$-related quantities in QCD
• x-Dependent Polarized Parton Distributions
• Renormalon-motivated evaluation of QCD observables
• Precision physics with inclusive QCD processes
• Pade Improvement of the Free Energy in High Temperature QCD
• Higher-order perturbative coefficients in QCD from series acceleration by conformal mappings
• Perturbative Finite-Temperature Results and Pad'e Approximants
• Improvement of the method of diagonal Pade approximants for perturbative series in gauge theories
• Determination of QCD condensates from tau-decay data
• Electron-positron annihilation into hadrons at the higher-loop levels
• Analytic QCD coupling with no power terms in UV regime
• Testing the Concept of Quark-Hadron Duality with the ALEPH $\tau$ Decay Data
• Extracting alpha_s from Electron-Positron Annihilation around 10 GeV
• The renormalization group inspired approaches and estimates of the tenth-order corrections to the muon anomaly in QED
• Perturbative relations between $e^{+}{e}^{-}$ annihilation and $\tau$ decay observables including resummation effects
• Antiquark Polarization inside the Proton is Small
• A novel series solution to the renormalization group equation in QCD
• Measurement of the Lifetime of the Tau Lepton
• Renormalization-scale-invariant continuation of truncated QCD (QED) series -- an analysis beyond large-beta_0 approximation
• Peculiar features of the relations between pole and running heavy quark masses and estimates of the O(α_s^4) contributions
• Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the $\beta$-factorization property?
• Parton model sum rules
• Towards a physical expansion in perturbative gauge theories by using improved Baker-Gammel approximants
• Applying generalized Padé approximants in analytic QCD models
• Pade-Improved Extraction of ${\alpha }_s(M_{\tau })$ from $R_{\tau }$
• Fit to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules in a renormalon based approach
• Scale- and scheme-independent extension of Pade approximants; Bjorken polarized sum rule as an example
• Determination of perturbative QCD coupling from ALEPH $\tau$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules
• Constraints on the I=1 hadronic tau decay and e^+e^- --> hadrons data sets and implications for (g-2)_mu
• The QCD Coupling Constant
• Nuclear effects in F_3 structure function of nucleon
• Bjorken unpolarized and polarized sum rules: comparative analysis of large-N_F expansions
• Resummation analysis of the $\tau$ decay width using the four-loop $\beta$-function
• Borel-Laplace Sum Rules with $\tau$ decay data, using OPE with improved anomalous dimensions
• Bjorken sum rule with hyperasymptotic precision
• Measurement of the Tau Branching Fractions into Leptons
• New high order relations between physical observables in perturbative QCD
• ALEPH Tau Spectral Functions and QCD
• The absence of QCD $\beta$-function factorization property of the generalized Crewther relation in the 't Hooft $\overline{MS}$-based scheme
• Scheme dependence of NLO corrections to exclusive processes
• Improved Evaluation of the Next-Next-To-Leading Order QCD Corrections to the e+e- Annihilation Into Hadrons
• Resummations of free energy at high temperature
• Ratio of strange to non-strange quark condensates in QCD
• The uncertainty in ${\alpha }_s(M_Z^2)$ determined from hadronic tau decay measurements
• Resurgence of the QCD Adler function
• Achieving renormalization-scale- and scheme-independence in Pade-related resummation in QCD
• Dependence of five and six-loop estimated QCD corrections to the relation between pole and running masses of heavy quarks on the number of light flavours
• Explicit form of the R-ratio of electron-positron annihilation into hadrons
• Renormalization group summation and analytic continuation from spacelike to timeline regions
• Evaluation of Bjorken polarised sum rule with a renormalon-motivated approach
• NNLO QCD Analysis of CCFR data on $x{F}_3$ Structure Function and Gross-Llewellyn Smith Sum Rule with Higher Twist and Nuclear Corrections
• The $\overline{\mathrm{MS}}$-scheme ${\alpha }_s^5$ QCD contributions to the Adler function and Bjorken polarized sum rule in the Crewther-type two-fold $\{\beta \}$-expanded representation
• 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
• Five-loop vacuum polarization in pQCD: O(m_q^2α_s^4 n_f^2) contribution
• Extraction of alpha_s from the Gross--Llewellyn Smith sum rule using Borel resummation
• Nonperturbative Effects from the Resummation of Perturbation Theory
• Perturbative QCD in acceptable schemes with holomorphic coupling
• Global approximants with renormalization scale invariance in pQCD
• Estimating higher order perturbative coefficients using Borel transform
• 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
• The QCD observables expansion over the scheme-independent two-loop coupling constant powers, the scheme dependence reduction
• Comment on polarized quark distributions extracted from SIDIS experiments
• Using improved Operator Product Expansion in Borel-Laplace Sum Rules with ALEPH $\tau$ decay data, and determination of pQCD coupling
• Improvement of perturbation theory in QCD for e^+e^- -> hadrons and the problem of α_s freezing
• Dispersive approach to QCD and hadronic contributions to electroweak observables
• QCD effects to Bjorken unpolarized sum rule for $\nu N$ deep-inelastic scattering
• The QCD Adler function and the muon $g-2$ anomaly from renormalons
• The Proton Spin and Flavor Structure in the Chiral Quark Model
• Three-Jet Event Orientation in e+e- Annihilation: New Tests of the Standard Model
• Multiloop Calculations: towards R at Order alpha_s^4
• Disentangling perturbative and power corrections in precision tau decay analysis
• Resummation Approach in QCD Analytic Perturbation Theory
• The R ratio in e+ e-, the determination of alpha(Mz^2) and a possible non-perturbative gluonic contribution
• Analytical continuation and resummed perturbation theory
• Modeling power corrections to the Bjorken sum rule for the neutrino structure function F_1
• Transmutation of Scale Dependence into Truncation Uncertainty via RG-Improvement of the $R(s)$ Series
• QCD parameters and SM-high precision from $e^{+}{e}^{-}$ to Hadrons: Updated
• On the relation between pole and running heavy quark masses beyond the four-loop approximation
• R-ratio of electron-positron annihilation into hadrons: higher-order pi2-terms
• Deviation pattern approach for optimizing perturbative terms of QCD renormalization group invariant observables
• Summary of Working Group 3 of the Neutrino Factory '02 Workshop
• Determination of ${\alpha }_s$ from Gross-Llewellyn Smith sum rule by accounting for infrared renormalon
• A new determination of higher-order QCD corrections to hadronic $\tau$ decays
• Renormalization-group improvement in hadronic $\tau$ decays in 2018
• Perturbative QCD fitting of KEDR and BESIII $e^{+}{e}^{-}$ data for R(s) and ${\alpha }_s$ determination