Ten years of the Analytic Perturbation Theory in QCD

Abstract

The renormalization group method enables one to improve the properties of the QCD perturbative power series in the ultraviolet region. However, it ultimately leads to the unphysical singularities of observables in the infrared domain. The Analytic Perturbation Theory constitutes the next step of the improvement of perturbative expansions. Specifically, it involves additional analyticity requirement which is based on the causality principle and implemented in the Källen--Lehmann and Jost--Lehmann representations. Eventually, this approach eliminates spurious singularities of the perturbative power series and enhances the stability of the latter with respect to both higher loop corrections and the choice of the renormalization scheme. The paper contains an overview of the basic stages of the development of the Analytic Perturbation Theory in QCD, including its recent applications to the description of hadronic processes.

26 pages, 9 figures, to be published in Theor. Math. Phys. (2007)

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Cited by in corpus (72)

• The QCD Running Coupling
• Bound state approach to the QCD coupling at low energy scales
• 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
• The running fine structure constant alpha(E) via the Adler function
• Non-Perturbative Contribution to the Thrust Distribution in $e^{+}{e}^{-}$ Annihilation
• On Gribov's supercriticality picture of quark confinement
• QCD coupling below 1 GeV from quarkonium spectrum
• Global Fractional Analytic Perturbation Theory in QCD with Selected Applications
• Bjorken Sum Rule and pQCD frontier on the move
• Nucleon spin structure and pQCD frontier on the move
• Four-loop QCD analysis of the Bjorken sum rule vs data
• Analogs of noninteger powers in general analytic QCD
• The running coupling from the four-gluon vertex in Landau gauge Yang-Mills theory
• Extended analytic QCD model with perturbative QCD behavior at high momenta
• FAPT: a Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory
• Bjorken polarized sum rule and infrared-safe QCD couplings
• Nearly perturbative lattice-motivated QCD coupling with zero IR limit
• Reconciling the analytic QCD with the ITEP operator product expansion philosophy
• Nucleon spin structure at low momentum transfers
• QCDMAPT: program package for Analytic approach to QCD
• QCD sum rules with nonlocal condensates and the spacelike pion form factor
• anQCD: a Mathematica package for calculations in general analytic QCD models
• Feasibility studies of the time-like proton electromagnetic form factor measurements with PANDA at FAIR
• Modified Contour-Improved Perturbation Theory
• Testing axial and electromagnetic nucleon form factors in time-like regions in the processes $\bar{p}+n\to {\pi }^{-}+{\ell }^{-}+{\ell }^{+}$ and $\bar{p}+p\to {\pi }^0+{\ell }^{-}+{\ell }^{+}$, $\ell =e$, $\mu$
• Simple analytic QCD model with perturbative QCD behavior at high momenta
• Dispersive approach to QCD and inclusive tau lepton hadronic decay
• Operator Product Expansion with analytic QCD in tau decay physics
• Hadronic vacuum polarization function within dispersive approach to QCD
• Calculation of binding energies and masses of quarkonia in analytic QCD models
• Renormalon-motivated evaluation of QCD observables
• Graviton propagator, renormalization scale and black-hole like states
• 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
• The QCD analysis of the combined set for the F_3 structure function data based on the analytic approach
• On the low-energy behavior of the Adler function
• Explicit solutions for effective four- and five-loop QCD running coupling
• How to perform QCD analysis of DIS in Analytic Perturbation Theory
• Applying generalized Padé approximants in analytic QCD models
• Lattice-motivated holomorphic nearly perturbative QCD
• Extending the application of the LCSR method to low momenta using QCD renormalization-group summation. Theory and phenomenology
• Exploring dynamical gluon mass generation in three dimensions
• Explicit form of the R-ratio of electron-positron annihilation into hadrons
• Lattice-motivated QCD coupling and hadronic contribution to muon $g-2$
• Inclusive tau lepton hadronic decay in vector and axial-vector channels within dispersive approach to QCD
• Perturbative QCD in acceptable schemes with holomorphic coupling
• Dispersive approach to QCD: tau lepton hadronic decay in vector and axial-vector channels
• Calculation of the pion-photon transition form factor using dispersion relations and renormalization-group summation
• A nonperturbative model for the strong running coupling within potential approach
• Evaluation of neutrinoless double beta decay: QCD running to sub-GeV scales
• Comment on "Infrared freezing of Euclidean QCD observables"
• Spontaneous mass generation and the small dimensions of the Standard Model gauge groups U(1), SU(2) and SU(3)
• Confined gluon from Minkowski space continuation of PT-BFM SDE solution
• QCD-Instantons and Conformal Space-Time Inversion Symmetry
• Exponentially Modified QCD Coupling
• Analytic perturbation theory versus 1/N expansion in the Gross-Neveu model
• Resummation Approach in QCD Analytic Perturbation Theory
• pQCD running couplings finite and monotonic in the infrared: when do they reflect the holomorphic properties of spacelike observables?
• On applications of Mathematica Package "FAPT" in QCD
• Towards unifying perturbative and Holographic Light-Front QCD via holomorphic coupling
• Wavelet regularization of gauge theories
• Can effective four-dimensional scalar theory be asymptotically free in a spacetime with extra dimensions?
• Novel Sets of Coupling Expansion Parameters for low-energy pQCD
• Renormalon-based resummation for spacelike and timelike QCD quantities whose perturbation expansion has general form
• A Few Lessons from pQCD Analysis at Low Energies
• Convergence and Gauge Dependence Properties of the Resummed One-loop Quark-Quark Scattering Amplitude in Perturbative QCD
• R-ratio of electron-positron annihilation into hadrons: higher-order pi2-terms
• On the analytically-improved running coupling in QCD
• Analytical Inverse QCD Coupling Constant approach and its result for ${\alpha }_s$
• Perturbative QCD fitting of KEDR and BESIII $e^{+}{e}^{-}$ data for R(s) and ${\alpha }_s$ determination