QCD coupling below 1 GeV from quarkonium spectrum

Abstract

In this paper we extend the work synthetically presented in Ref.[1] and give theoretical details and complete tables of numerical results. We exploit calculations within a Bethe-Salpeter (BS) formalism adjusted for QCD, in order to extract an ``experimental'' strong coupling α_s^{exp}(Q^2) below 1 GeV by comparison with the meson spectrum. The BS potential follows from a proper ansatz on the Wilson loop to encode confinement and is the sum of a one-gluon-exchange and a confinement terms. Besides, the common perturbative strong coupling is replaced by the ghost-free expression α_E(Q^2) according to the prescription of Analytic Perturbation Theory (APT). The agreement of α_s^{exp}(Q^2) with the APT coupling α_E(Q^2) turns out to be reasonable from 1 GeV down to the 200 MeV scale, thus confirming quantitatively the validity of the APT prescription. Below this scale, the experimental points could give a hint on the vanishing of α_s(Q^2) as Q approaches zero. This infrared behaviour would be consistent with some lattice results and a ``massive'' generalization of the APT approach. As a main result, we claim that the combined BS-APT theoretical scheme provides us with a rather satisfactory correlated understanding of very high and rather low energy phenomena from few hundreds MeV to few hundreds GeV.

Preliminary revision. Typos corrected, comments and references added

References in corpus (52)

• The Cosmological Parameters 2006
• Big-Bang nucleosynthesis (Particle Data Group mini-review)
• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• Analytic Model for the QCD Running Coupling with Universal ${\bar{\alpha }}_s(0)$ Value
• Dispersive Approach to Power-Behaved Contributions in QCD Hard Processes
• Optimization of R(e+e-) and "Freezing" of the QCD Couplant at Low Energies
• On the running coupling constant in QCD
• Valence-quark distributions in the pion
• Experimental Tests of Asymptotic Freedom
• Analytic perturbation theory in QCD and Schwinger's connection between the beta-function and the spectral density
• Ten years of the Analytic Perturbation Theory in QCD
• Analytic Invariant Charge in QCD
• Quark-antiquark potential in the analytic approach to QCD
• Analytic Approach in Quantum Chromodynamics
• QCD Analytic Perturbation Theory. From integer powers to any power of the running coupling
• Bound state approach to the QCD coupling at low energy scales
• Freezing of QCD coupling affects the short distance static potential
• Form Factors and QCD in Spacelike and Timelike Region
• Various versions of analytic QCD and skeleton-motivated evaluation of observables
• Analytic Approach to Perturbative QCD and Renormalization Scheme Dependence
• Fractional Analytic Perturbation Theory in Minkowski space and application to Higgs boson decay into a b\bar{b} pair
• Decay constants of the heavy-light mesons from the field correlator method
• New analytic running coupling in spacelike and timelike regions
• An approach for evaluation of observables in analytic versions of QCD
• Infrared behavior of the running coupling constant and bound states in QCD
• Confinement: Understanding the Relation Between the Wilson Loop and Dual Theories of Long Distance Yang Mills Theory
• A novel integral representation for the Adler function
• Accelerated convergence of perturbative QCD by optimal conformal mapping of the Borel plane
• The two-fermion relativistic wave equations of Constraint Theory in the Pauli-Schrödinger form
• All-orders infrared freezing of observables in perturbative QCD
• Masses and electroweak properties of light mesons in the relativistic quark model
• Renorm-group, Causality and Non-power Perturbation Expansion in QFT
• Can the QCD Effective Charge Be Symmetrical in the Euclidean and the Minkowskian Regions?
• Masses of light mesons in the relativistic quark model
• Convergence of the expansion of the Laplace-Borel integral in perturbative QCD improved by conformal mapping
• Analyticity and Minimality of Nonperturbative Contributions in Perturbative region for ${\bar{\alpha }}_s$
• Synthetic Running Coupling of QCD
• B_{c} meson and the light-heavy quarkonium spectrum
• Running coupling constant and masses in QCD, the meson spectrum
• Bound state equation in the Wilson loop approach with minimal surfaces
• Bethe--Salpeter equation in QCD
• A novel series solution to the renormalization group equation in QCD
• Unquenched calculation of alpha_s from Green functions: progress report
• Quark-gluon vertex in a momentum subtraction scheme
• An Invariant Charge Model for All q^2>0 in QCD and Gluon Condensate
• How to obtain a covariant Breit type equation from relativistic Constraint Theory
• Regge trajectories and quarkonium spectrum from a first principle Salpeter equation
• Infrared Freezing of Euclidean QCD observables
• Analytic Perturbation Theory for Practitioners and Upsilon Decay
• Extracting infrared QCD coupling from meson spectrum
• On the infrared freezing of perturbative QCD in the Minkowskian region
• Analytic structure in the coupling constant plane in perturbative QCD

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• The QCD Running Coupling
• The running coupling from the four-gluon vertex in Landau gauge Yang-Mills theory
• Bjorken polarized sum rule and infrared-safe QCD couplings
• Nearly perturbative lattice-motivated QCD coupling with zero IR limit
• QCDMAPT: program package for Analytic approach to QCD
• Reconciling the analytic QCD with the ITEP operator product expansion philosophy
• anQCD: a Mathematica package for calculations in general analytic QCD models
• 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
• Condition for confinement in non-Abelian gauge theories
• Renormalon-motivated evaluation of QCD observables
• Concavity of the meson Regge trajectories
• Electron-positron annihilation into hadrons at the higher-loop levels
• Bjorken sum rule in QCD frameworks with analytic (holomorphic) coupling
• On the low-energy behavior of the Adler function
• Gluon Propagator in Fractional Analytic Perturbation Theory
• Spectrum of Yang-Mills theory in 3 and 4 dimensions
• Techniques of evaluation of QCD low-energy physical quantities with running coupling with infrared fixed point
• QCD Effective Coupling in the Infrared Region
• Lattice-motivated holomorphic nearly perturbative QCD
• Structure of the meson Regge trajectories
• Infrared QCD
• Confinement in a three-dimensional Yang-Mills theory
• Open string QED meson description of the X17 particle and dark matter
• Hadronic effects in low-energy QCD: inclusive tau lepton decay
• Revisiting the pion Regge trajectories
• Yang-Mills Propagators and QCD
• Explicit form of the R-ratio of electron-positron annihilation into hadrons
• Lattice-motivated QCD coupling and hadronic contribution to muon $g-2$
• Bjorken sum rule in QCD with analytic coupling
• 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
• Infrared-suppressed QCD coupling and the hadronic contribution to muon g-2
• Adler function in the analytic approach to QCD
• Evaluation of neutrinoless double beta decay: QCD running to sub-GeV scales
• On the question of quark confinement in the Abelian U(1) QED gauge interaction
• Hadronic contributions to electroweak observables within DPT
• pQCD running couplings finite and monotonic in the infrared: when do they reflect the holomorphic properties of spacelike observables?
• Regge trajectories for the triply heavy triquarks
• Finite temperature corrections to a NLO Nambu-Jona-Lasinio model
• Inevitability and Importance of Non-Perturbative Elements in Quantum Field Theory
• QED meson description of the anomalous particles at ~17 and ~38 MeV
• R-ratio of electron-positron annihilation into hadrons: higher-order pi2-terms
• The four-gluon vertex and the running coupling in Landau gauge Yang-Mills theory