Analytic Approach to Perturbative QCD

Abstract

The two-loop invariant (running) coupling of QCD is written in terms of the Lambert W function. The analyticity structure of the coupling in the complex Q^2-plane is established. The corresponding analytic coupling is reconstructed via a dispersion relation. We also consider some other approximations to the QCD beta-function, when the corresponding couplings are solved in terms of the Lambert function. The Landau gauge gluon propagator has been considered in the renormalization group invariant analytic approach (IAA). It is shown that there is a nonperturbative ambiguity in determination of the anomalous dimension function of the gluon field. Several analytic solutions for the propagator at the one-loop order are constructed. Properties of the obtained analytical solutions are discussed.

Latex-file, 19 pages, 2 tables, 51 references, to be published in Int. J. Mod. Phys.A

References in corpus (21)

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• A Solution to Coupled Dyson-Schwinger Equations for Gluons and Ghosts in Landau Gauge
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• Analytic Perturbation Theory and Inclusive Tau Decay
• Analytic Approach in Quantum Chromodynamics
• Renormalization-Scheme Dependence of Pade Summation in QCD
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• Large-order perturbation theory for the electromagnetic current-current correlation function
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• The Two-Loop Scale Dependence of the Static QCD Potential including Quark Masses
• Borel summation and momentum-plane analyticity in perturbative QCD
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Cited by in corpus (20)

• The Renormalization Scale-Setting Problem in QCD
• New views of the solar wind with the Lambert W function
• QCD Analytic Perturbation Theory. From integer powers to any power of the running coupling
• The Adler Function for Light Quarks in Analytic Perturbation Theory
• Fractional Analytic Perturbation Theory in Minkowski space and application to Higgs boson decay into a b\bar{b} pair
• Higher-order QCD perturbation theory in different schemes: From FOPT to CIPT to FAPT
• Generalization of the BLM procedure and its scales in any order of pQCD
• FAPT: a Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory
• All-orders infrared freezing of observables in perturbative QCD
• Normal form for renormalization groups
• Analyticity properties of three-point functions in QCD beyond leading order
• Testing the Concept of Quark-Hadron Duality with the ALEPH $\tau$ Decay Data
• Scale- and scheme-independent extension of Pade approximants; Bjorken polarized sum rule as an example
• Direct extraction of QCD LambdaMSbar from moments of structure functions in neutrino-nucleon scattering, using the CORGI approach
• The absence of QCD $\beta$-function factorization property of the generalized Crewther relation in the 't Hooft $\overline{MS}$-based scheme
• Optimized determination of the polarized Bjorken sum rule in pQCD
• Direct Extraction of QCD Lambda MS-bar from e+e- Jet Observables
• Calculation of the pion-photon transition form factor using dispersion relations and renormalization-group summation
• Comparing optimized renormalization schemes for QCD observables
• Improved analysis of moments of F3 in neutrino-nucleon scattering using the Bernstein polynomial method