QCD Running Couplings and Effective Charges

Abstract

We discuss our present knowledge of ${\alpha }_s$, the fundamental running coupling or effective charge of Quantum Chromodynamics (QCD). A precise understanding of the running of ${\alpha }_s(Q^2)$ at high momentum transfer, $Q$, is necessary for any perturbative QCD calculation. Equally important, the behavior of ${\alpha }_s$ at low $Q^2$ in the nonperturbative QCD domain is critical for understanding strong interaction phenomena, including the emergence of mass and quark confinement. The behavior of ${\alpha }_s(Q^2)$ at all momentum transfers also provides a connection between perturbative and nonperturbative QCD phenomena, such as hadron spectroscopy and dynamics. We first sketch the origin of the QCD coupling, the reason why its magnitude depends on the scale at which hadronic phenomena are probed, and the resulting consequences for QCD phenomenology. We then summarize latest measurements in both the perturbative and nonperturbative domains. New theory developments include the derivation of the universal nonperturbative behavior of ${\alpha }_s(Q^2)$ from both the Dyson-Schwinger equations and light-front holography. We also describe theory advances for the calculation of gluon and quark Schwinger functions in the nonperturbative domain and the relation of these quantities to ${\alpha }_s$. We conclude by highlighting how the nonperturbative knowledge of ${\alpha }_s$ is now providing a parameter-free determination of hadron spectroscopy and structure, a central and long-sought goal of QCD studies.

arXiv commentInvited review article, Prog Part. Nucl. Phys., in press. (143 pages, 9 figures)

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• SU(3) Landau gauge gluon and ghost propagators using the logarithmic lattice gluon field definition
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• Determination of ${\alpha }_s$ from static QCD potential with renormalon subtraction
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• Bethe-Salpeter kernel and properties of strange-quark mesons
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• Centre vortex removal restores chiral symmetry
• Strong coupling constant from moments of quarkonium correlators revisited
• Lattice determinations of the strong coupling
• High precision determination of ${\alpha }_s$ from a global fit of jet rates
• The Determination of the Strong Coupling Constant
• Lattice computation of the Dirac eigenvalue density in the perturbative regime of QCD
• Lattice-motivated holomorphic nearly perturbative QCD
• Determination of perturbative QCD coupling from ALEPH $\tau$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules
• Pion Parton Distribution Function in Light-Front Holographic QCD
• Two-loop three-gluon vertex from the Curci-Ferrari model and its leading infrared behavior to all loop orders
• Nucleon axial form factor at large momentum transfers
• Calculation of the non-perturbative strong coupling from first principles
• QCD gluon vertices from the string-inspired formalism
• Artificial Dynamical Effects in Quantum Field Theory
• Reply to "Comment on 'Lattice Gluon and Ghost Propagators, and the Strong Coupling in Pure SU(3) Yang-Mills Theory: Finite Lattice Spacing and Volume Effects' "
• Violations of Quark-Hadron Duality in Low-Energy Determinations of ${\alpha }_s$
• Strong coupling constant and quark masses from lattice QCD
• QCD effective charge from the three-gluon vertex of the background-field method
• Renormalons in integrated spectral function moments and ${\alpha }_s$ extractions
• SU(3) Yang Mills theory at small distances and fine lattices
• Nonperturbative QCD, gauge-fixing, Gribov copies, and the lattice
• From Spectroscopy to the Strong Coupling Constant with Heavy Wilson Quarks
• Origin of the Proton Mass
• The Generalized Scheme-Independent Crewther Relation in QCD
• Fractional Analytic QCD beyond Leading Order
• The Massive Yang-Mills Model and Diffractive Scattering
• Gluon Green functions free of Quantum fluctuations
• Novel and self-consistency analysis of the QCD running coupling ${\alpha }_s(Q)$ in both the perturbative and nonperturbative domains
• Static Energy in ($2+1+1$)-Flavor Lattice QCD: Scale Setting and Charm Effects
• Strong coupling from non-equilibrium Monte Carlo simulations
• ${\alpha }_s$ and ${\mathrm{V}}_{\mathrm{cs}}$ determination, and CKM unitarity test, from W decays at NNLO
• Higher twists in polarized DIS and the size of the constituent quark
• The Role of Different Schemes in the QCD Analysis and Determination of the Strong Coupling
• Precise ${\alpha }_s$ determination from charmonium sum rules
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• Measurements of the Running of the Electromagnetic Coupling at LEP
• Transverse Force on Transversely Polarized Quarks in Longitudinally Polarized Nucleons
• Probing an intrinsically flavorful ALP via tau-lepton flavor physics
• Spin Sum Rules and the Strong Coupling Constant at large distance
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• Dynamical fermions, centre vortices, and emergent phenomena
• A method for getting a finite $\alpha$ in the IR region from an all-order beta function
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