Various versions of analytic QCD and skeleton-motivated evaluation of observables

Abstract

We present skeleton-motivated evaluation of QCD observables. The approach can be applied in analytic versions of QCD in certain classes of renormalization schemes. We present two versions of analytic QCD which can be regarded as low-energy modifications of the ``minimal'' analytic QCD and which reproduce the measured value of the semihadronic tau decay ratio r{tau}. Further, we describe an approach of calculating the higher order analytic couplings Ak (k=2,3,...) on the basis of logarithmic derivatives of the analytic coupling A1(Q^2). This approach can be easily applied in any version of analytic QCD. We adjust the free parameters of the afore-mentioned two analytic models in such a way that the skeleton-motivated evaluation reproduces the correct known values of r{tau} and of the Bjorken polarized sum rule (BjPSR) db(Q^2) at a given point (e.g., at Q^2=2 GeV^2). We then evaluate the low-energy behavior of the Adler function dv(Q^2) and the BjPSR db(Q^2) in the afore-mentioned evaluation approach, in the three analytic versions of QCD. We compare with the results obtained in the ``minimal'' analytic QCD and with the evaluation approach of Milton et al. and Shirkov.

30 pages, 14 eps-figures; v3: parameters of the analytic QCD models M1 and M2 were refined, the numerical results modified accordingly, new paragraph at the end of Sec.II and at the end of Sec.III, discussion of Figs.4 extended, references added; version to appear in PRD

References in corpus (48)

• The Cosmological Parameters 2006
• Big-Bang nucleosynthesis (Particle Data Group mini-review)
• Analytic Model for the QCD Running Coupling with Universal ${\bar{\alpha }}_s(0)$ Value
• Dispersive Approach to Power-Behaved Contributions in QCD Hard Processes
• Hadronic contributions to $(g-2)$ of the leptons and to the effective fine structure constant $\alpha (M_Z^2)$
• Branching ratios and spectral functions of tau decays: final ALEPH measurements and physics implications
• Three-Loop Polarization Function and $\mathcal{O}({\alpha }_s^2)$ Corrections to the Production of Heavy Quarks
• Estimates of the higher-order QCD corrections to R(s), R_τ and deep-inelasstic scattering sum rules
• Matching QCD and HQET heavy--light currents at two loops and beyond
• Matching Long and Short Distances in Large-Nc QCD
• Scale Setting in QCD and the Momentum Flow in Feynman Diagrams
• Connections between Deep-Inelastic and Annihilation Processes at Next-to-Next-to-Leading Order and Beyond
• Can the QCD running coupling have a causal analyticity structure?
• Analytic perturbation theory in QCD and Schwinger's connection between the beta-function and the spectral density
• Analytic Perturbation Theory in analyzing some QCD observables
• Calculation of Feynman Diagrams from their Small Momentum Expansion
• Analytic Invariant Charge in QCD
• Testing non-perturbative strong interaction effects via the Adler function
• Experimental determination of the evolution of the Bjorken integral at low Q^2
• Analytic Perturbation Theory and Inclusive Tau Decay
• Quark-antiquark potential in the analytic approach to QCD
• QCD Analytic Perturbation Theory. From integer powers to any power of the running coupling
• The Adler Function for Light Quarks in Analytic Perturbation Theory
• The massive analytic invariant charge in QCD
• Mass Corrections to the Vector Current Correlator
• $O({\alpha }_s^2)$ corrections to polarized heavy flavour production at $Q^2\gg m^2$
• New analytic running coupling in spacelike and timelike regions
• Disentangling running coupling and conformal effects in QCD
• An approach for evaluation of observables in analytic versions of QCD
• Radiation of Heavy Quarks
• Renormalons and multiloop estimates in scalar correlators, Higgs decay and quark-mass sum rules
• Renormalization Scheme and Higher Loop Stability in Hadronic $\tau$ Decay within Analytic Perturbation Theory
• Heavy flavour contributions to the deep inelastic sum rules
• Bilocal expansion of the Borel amplitude and the hadronic tau decay width
• A novel integral representation for the Adler function
• Power corrections and resummation of radiative corrections in the single dressed gluon approximation - the average thrust as a case study
• Renormalons at the boundaries between perturbative and non-perturbative QCD
• Towards Order alpha_s^4 Accuracy in tau-decays
• Massive Quark Production in Electron Positron Annihilation to Order ${\alpha }_s^2$
• An analytic method of describing $R$-related quantities in QCD
• Analyticity properties of three-point functions in QCD beyond leading order
• Resummation of the hadronic tau decay width with the modified Borel transform method
• Infrared renormalons and the relations between the Gross-Llewellyn Smith and the Bjorken polarized and unpolarized sum rules
• 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
• Infrared Freezing of Euclidean QCD observables
• Bjorken unpolarized and polarized sum rules: comparative analysis of large-N_F expansions
• Nonperturbative Contributions in an Analytic Running Coupling of QCD

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• The QCD Adler function and the muon $g-2$ anomaly from renormalons
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• Dispersive approach to QCD and hadronic contributions to electroweak observables
• On applications of Mathematica Package "FAPT" in QCD
• pQCD running couplings finite and monotonic in the infrared: when do they reflect the holomorphic properties of spacelike observables?
• The decomposed photon anomalous dimension in QCD and the $\{\beta \}$-expanded representations for the Adler function
• Method for comparing finite temperature field theory results with lattice data
• Towards unifying perturbative and Holographic Light-Front QCD via holomorphic coupling
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