Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

QCD running couplings and effective charges

Journal Article · · Progress in Particle and Nuclear Physics
 [1];  [2];  [3]
  1. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  2. SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
  3. Nanjing Univ. (China)
+ Show Author Affiliations
Here 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.
Research Organization:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Organization:
National Natural Science Foundation of China (NSFC); USDOE Office of Nuclear Energy (NE); USDOE Office of Science (SC), Nuclear Physics (NP)
Grant/Contract Number:
AC02-76SF00515; AC05-06OR23177
OSTI ID:
2281722
Alternate ID(s):
OSTI ID: 2224135
Report Number(s):
DOE/OR/23177-6092; JLAB-PHY--23-3791; 12135007
Journal Information:
Progress in Particle and Nuclear Physics, Journal Name: Progress in Particle and Nuclear Physics Vol. 134; ISSN 0146-6410
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (549)

A Solution to Coupled Dyson–Schwinger Equations for Gluons and Ghosts in Landau Gauge journal July 1998
Introduction to the Functional RG and Applications to Gauge Theories book January 2012
Quantum superconformal model in (1, 2) space journal September 1983
Ward identities in gauge theories journal February 1972
A study of energy-energy correlations ine + e ? annihilations at $$\sqrt s = 34.6$$ GeV journal September 1985
Analysis of the energy weighted angular correlations in hadronice + e ? annihilations at 22 and 34 GeV journal June 1982
Measurements of energy correlations ine + e ??hadrons journal September 1984
A determination of? s( $$M_{Z^0 } $$ ) at LEP using resummed QCD calculations journal March 1993
A study of energy-energy correlations between 12 and 46.8 GeV c.m. energies journal September 1987
Small distance behaviour in field theory and power counting journal September 1970
Small-distance-behaviour analysis and Wilson expansions journal March 1971
Determination of 55-155-155-1in second order QCD from hadronicZ decays journal March 1992
Dual-symmetric theory of hadrons.—I journal October 1970
Dual-symmetric theory of hadrons: II.—Baryons journal October 1970
Introduction to complex orbital momenta journal December 1959
On a class of Lagrangian models for massive and massless Yang-mills fields journal March 1976
Über Eigenschaften von Ausbreitungsfunktionen und Renormierungskonstanten quantisierter Felder journal April 1954
Conformal invariance in quantum mechanics journal August 1976
Charge renormalization group in quantum field theory journal May 1956
On the generalized ward identity journal August 1957
$ {\Lambda_{{\overline {\text{MS}} }}} $ from the static potential for QCD with n f  = 2 dynamical quark flavors journal January 2012
Perturbative expansion of τ hadronic spectral function moments and α s extractions journal January 2013
The five-loop beta function of Yang-Mills theory with fermions journal February 2017
Probing the singularities of the Landau-Gauge gluon and ghost propagators with rational approximants journal February 2023
Complete renormalization of QCD at five loops journal March 2017
Measurement and QCD analysis of double-differential inclusive jet cross sections in pp collisions at s = 8 $$ \sqrt{s}=8 $$ TeV and cross section ratios to 2.76 and 7 TeV journal March 2017
Precise determination of αs from relativistic quarkonium sum rules journal March 2020
Determination of αs from static QCD potential: OPE with renormalon subtraction and lattice QCD journal April 2019
High precision determination of the gluon fusion Higgs boson cross-section at the LHC journal May 2016
The $$ \overline{\mathrm{MS}} $$-scheme $$ {\alpha}_s^5 $$ QCD contributions to the Adler function and Bjorken polarized sum rule in the Crewther-type two-fold {β}-expanded representation journal May 2022
Extraction of the strong coupling αs(mZ) from a combined NNLO analysis of inclusive electroweak boson cross sections at hadron colliders journal June 2020
Determination of the strong coupling constant αS(mZ) from measurements of inclusive W± and Z boson production cross sections in proton-proton collisions at $$ \sqrt{\mathrm{s}} $$ = 7 and 8 TeV journal June 2020
Scale-dependent mass anomalous dimension from Dirac eigenmodes journal July 2013
Exact N3LO results for qq′ → H + X journal July 2015
Towards the five-loop Beta function for a general gauge group journal July 2016
Strong coupling from non-equilibrium Monte Carlo simulations journal July 2020
Reconciling the contour-improved and fixed-order approaches for τ hadronic spectral moments. Part I. Renormalon-free gluon condensate scheme journal July 2022
Violations of quark-hadron duality in low-energy determinations of αs journal July 2022
High precision determination of αs from a global fit of jet rates journal August 2019
Nonperturbative study of the four gluon vertex journal September 2014
Λ MS ¯ n f = 2 $$ {\varLambda}_{\overline{\mathrm{MS}}}^{\left({n}_f=2\right)} $$ from a momentum space analysis of the quark-antiquark static potential journal September 2014
Determination of α(Mz) from an hyperasymptotic approximation to the energy of a static quark-antiquark pair journal September 2020
New analyses of event shape observables in electron-positron annihilation and the determination of αs running behavior in perturbative domain journal September 2022
Reconciling the contour-improved and fixed-order approaches for τ hadronic spectral moments. Part II. Renormalon norm and application in αs determinations journal September 2022
Scalar correlator, Higgs decay into quarks, and scheme variations of the QCD coupling journal October 2016
The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge journal October 2017
Five-loop renormalisation of QCD in covariant gauges journal October 2017
The decay constants fD and f D s $$ {f}_{D_s} $$ in the continuum limit of Nf = 2 + 1 domain wall lattice QCD journal December 2017
Non-perturbative determination of the Λ-parameter in the pure SU(3) gauge theory from the twisted gradient flow coupling journal December 2017
The Infrared Behaviour of the Pure Yang–Mills Green Functions journal January 2012
Feasibility Studies for Single Transverse-Spin Asymmetry Measurements at a Fixed-Target Experiment Using the LHC Proton and Lead Beams (AFTER@LHC) journal May 2017
Process-Independent Effective Coupling: From QCD Green’s Functions to Phenomenology journal July 2018
Selected Science Opportunities for the EicC journal October 2020
Emergent Hadron Mass in Strong Dynamics journal April 2022
The theory of quark confinement journal August 1999
The common elements of atomic and hadronic physics journal March 2015
Electron-ion collider in China journal June 2021
Lattice Gluon Propagator and One-Gluon-Exchange Potential journal April 2019
Renormalization of gauge theories journal June 1976
On analytic properties of vertex parts in quantum field theory journal October 1959
Dyson-Schwinger equations and their application to hadronic physics journal January 1994
The renormalization group and the ε expansion journal August 1974
Quantum chromodynamics journal February 1978
Feynman diagrams for the Yang-Mills field journal July 1967
Deep inelastic electron scattering in perturbation theory journal November 1971
Reconstruction of the deep inelastic structure functions from their moments journal March 1978
Exclusive processes in quantum chromodynamics: Evolution equations for hadronic wavefunctions and the form factors of mesons journal November 1979
The heavy quark potential and the ϒ, J/ψ systems journal March 1979
The gell-mann-low function of QCD in the three-loop approximation journal June 1980
Renormalization group improved perturbative QCD journal September 1980
Which gauges are ghost-free? journal February 1980
Factorization and asymptotic behaviour of pion form factor in QCD journal July 1980
A no-go theorem for regularizing chiral fermions journal October 1981
The gluon is massive: A lattice calculation of the gluon propagator in the Landau gauge journal February 1987
QCD formulation of the tau decay and determination of ΛMS¯ journal August 1988
Measurements of αs in e+e− annihilation at √s=53.3 GeV and 59.5 GeV journal August 1989
Power corrections 1/Q2to parton sum rules for deep inelastic scattering from polarized nucleons journal June 1990
New clustering algorithm for multijet cross sections in e+e− annihilation journal October 1991
Order α2S contributions to the deep inelastic Wilson coefficient journal November 1991
Determination of αs from hadronic event shapes measured on the Z0 resonance journal June 1992
Gauge fixing on the lattice without ambiguity journal September 1992
Testing QCD with τ decays journal September 1992
The running coupling from lattice gauge theory journal June 1992
The running coupling from SU (3) lattice gauge theory journal November 1992
An improved measuremebts of αS (MZ0) using energy correlations with the OPAL detector at LEP journal February 1992
Measurement of the spin-dependent structure function g1(x) of the deuteron journal April 1993
The three-loop QCD β-function and anomalous dimensions journal April 1993
QCD sum rule calculation of twist-3 contributions to polarized nucleon structure functions journal January 1995
A precise determination of αS from lattice QCD journal February 1995
QCD sum rule calculation of twist-4 corrections to Bjorken and Ellis-Jaffe sum rules journal June 1995
Measurements of the Q2-dependence of the proton and deuteron spin structure functions g1p and g1d journal December 1995
On the renormalizability and unitarity of the Curci-Ferrari model for massive vector bosons journal January 1996
Goldstone theorem and diquark confinement beyond rainbow-ladder approximation journal July 1996
An analogue model for KSV theory journal July 1970
Ward identities and charge renormalization of the Yang-Mills field journal November 1971
Two-loop diagrams in Yang-Mills theory journal June 1974
Effective quark masses in the chiral limit journal December 1976
Quark-antiquark potential in QCD journal October 1977
Asymptotic freedom in parton language journal August 1977
Quantization of non-Abelian gauge theories journal June 1978
Quark confinement and vortices in massive gauge-invariant QCD journal October 1979
Slavnov-Taylor identities in Weinberg's renormalization scheme journal November 1980
Covariant quantization of gauge fields without Gribov ambiguity journal November 1981
Absence of neutrinos on a lattice journal July 1981
The background field method beyond one loop journal July 1981
Absence of neutrinos on a lattice journal December 1981
On the phase structure of vector-like gauge theories with massless fermions journal March 1982
Non-perturbative modification of the Faddeev-Popov formula and banishment of the naive vacuum journal December 1982
Exact Gell-Mann-Low function of supersymmetric Yang-Mills theories from instanton calculus journal December 1983
Superconformal quantum mechanics journal January 1984
Local and renormalizable action from the gribov horizon journal September 1989
A numerical method to compute the running coupling in asymptotically free theories journal July 1991
Vanishing of zero-momentum lattice gluon propagator and color confinement journal October 1991
Order-αs2 QCD corrections to the deep inelastic proton structure functions F2 and FL journal September 1992
QCD analysis of the tau hadronic width journal April 1992
The Schrödinger functional — a renormalizable probe for non-abelian gauge theories journal October 1992
Computation of the running coupling in the SU(2) Yang-Mills theory journal January 1993
Renormalizability of the critical limit of lattice gauge theory by BRS invariance journal July 1993
The large quark mass expansion of Λ(Z0 → hadrons) and Λ(τ− → vτ + hadrons)in the order αs3 journal March 1995
The next-next-to-leading QCD approximation for non-singlet moments of deep inelastic structure functions journal September 1994
A precise determination of the running coupling in the SU(3) Yang-Mills theory journal January 1994
The running coupling from the QCD Schrödinger functional: a one-loop analysis journal April 1996
Dispersive approach to power-behaved contributions in QCD hard processes journal June 1996
On the difficulty of computing higher-twist corrections journal November 1996
RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses journal December 2000
The relativistic bound state problem in QCD: transverse lattice methods journal January 2002
QCD forces and heavy quark bound states journal March 2001
The infrared behaviour of QCD Green's functions Confinement, dynamical symmetry breaking, and hadrons as relativistic bound states journal November 2001
Quantum chromodynamics and other field theories on the light cone journal August 1998
The three-loop relation between the and the pole quark masses journal June 2000
Measurements of the Q2-dependence of the proton and neutron spin structure functions g1p and g1n journal November 2000
Consistent OPE description of gluon two- and three-point Green functions? journal November 2000
Two-loop QCD vertices and three-loop MOM β functions journal December 2000
First results on the running coupling in QCD with two massless flavours journal August 2001
Determination of ΛMS from quenched and Nf=2 dynamical QCD journal November 2001
Testing perturbation theory on the Nf=0 static quark potential journal December 2001
Infrared exponents and running coupling of SU(N) Yang–Mills theories journal May 2002
Precision measurement of the proton and deuteron spin structure functions g2 and asymmetries A2 journal January 2003
The four-loop β-function in quantum chromodynamics journal May 1997
Measurement of the neutron spin structure function gn1 with a polarized 3He internal target journal July 1997
Measurement of the neutron spin structure function gn2 and asymmetry An2 journal July 1997
Quadratic mass corrections of order to the decay rate of Z- and W-bosons journal July 1997
Next-to-leading order QCD analysis of polarized deep inelastic scattering data journal July 1997
Aspects of SU(Nc) gauge theories in the limit of small number of colors journal January 1998
On the definition of gauge field operators in lattice gauge-fixed theories journal July 1998
Measurement of the proton spin structure function g1p with a pure hydrogen target journal December 1998
Determination of the deep inelastic contribution to the generalised Gerasimov-Drell-Hearn integral for the proton and neutron journal December 1998
The static potential in QCD to two loops journal February 1999
Measurement of the proton and deuteron spin structure functions g2 and asymmetry A2 journal July 1999
Measurement of the deuteron spin structure function g1d(x) for 1 (GeV/c)2 journal September 1999
Analytical approximations for real values of the Lambert W-function journal August 2000
Improved calculation of F2 in electroproduction and xF3 in neutrino scattering to NNLO and determination of αs journal September 2001
The Nf=0 heavy quark potential from short to intermediate distances journal February 2002
Generalized pinch technique and the background field method in general gauges journal March 1997
The static potential in QCD — a full two-loop calculation journal September 1997
αs from the non-perturbatively renormalised lattice three-gluon vertex journal September 1997
The 3-loop QCD calculation of the moments of deep inelastic structure functions journal May 1997
Non-perturbative quark mass renormalization in quenched lattice QCD journal April 1999
Calculation of electroproduction to NNLO and precision determination of αs journal December 1999
Aspects of the functional renormalisation group journal December 2007
The quark–gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement journal January 2009
Version 3 of RunDec and CRunDec journal March 2018
REvolver: Automated running and matching of couplings and masses in QCD journal January 2022
Science Requirements and Detector Concepts for the Electron-Ion Collider journal October 2022
Computation of the strong coupling in QCD with two dynamical flavors journal May 2005
The running coupling of QCD with four flavors journal November 2010
The strange quark mass and Lambda parameter of two flavor QCD journal December 2012
Analytical study of Yang–Mills theory in the infrared from first principles journal June 2016
The role of different schemes in the QCD analysis and determination of the strong coupling journal August 2017
The deuteron spin-dependent structure function g1d and its first moment journal March 2007
Experimental determination of the effective strong coupling constant journal July 2007
Matching NLLA+NNLO for event shape distributions journal June 2008
Determination of the effective strong coupling constant αs,g1(Q2) from CLAS spin structure function data journal July 2008
Maximum wavelength of confined quarks and gluons and properties of quantum chromodynamics journal August 2008
Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared journal June 2009
The strong coupling and its running to four loops in a minimal MOM scheme journal November 2009
The spin-dependent structure function of the proton g1p and a test of the Bjorken sum rule journal July 2010
Lifting the Gribov ambiguity in Yang–Mills theories journal May 2012
Threefold complementary approach to holographic QCD journal February 2014
Deconfinement transition in SU( N ) theories from perturbation theory journal March 2015
Bridging a gap between continuum-QCD and ab initio predictions of hadron observables journal March 2015
Connecting the hadron mass scale to the fundamental mass scale of quantum chromodynamics journal November 2015
The spin structure function g 1 p of the proton and a test of the Bjorken sum rule journal February 2016
Leading-twist parton distribution amplitudes of S -wave heavy-quarkonia journal February 2016
On the interface between perturbative and nonperturbative QCD journal June 2016
Universal effective hadron dynamics from superconformal algebra journal August 2016
Gluon Green functions free of quantum fluctuations journal September 2016
On the zero crossing of the three-gluon vertex journal October 2016
α s and | V cs | determination, and CKM unitarity test, from W decays at NNLO journal December 2016
The generalized scheme-independent Crewther relation in QCD journal July 2017
Implications of the principle of maximum conformality for the QCD strong coupling journal October 2017
Determination of α from static QCD potential with renormalon subtraction journal February 2019
Spectral functions of confined particles journal February 2020
Precise α determination from charmonium sum rules journal July 2020
Infrared facets of the three-gluon vertex journal July 2021
Semileptonic transitions: B() → π(K); D → K; D → π,K; and K → π journal January 2022
Experimental study of the behavior of the Bjorken sum at very low Q2 journal February 2022
Parton distributions of light quarks and antiquarks in the proton journal June 2022
Proton and pion distribution functions in counterpoint journal July 2022
Lattice three-gluon vertex in extended kinematics: Planar degeneracy journal March 2023
Schwinger mechanism for gluons from lattice QCD journal June 2023
Pinch technique: Theory and applications journal August 2009
Fundamentals of the exact renormalization group journal February 2012
The Gribov problem and QCD dynamics journal November 2012
Physics opportunities of a fixed-target experiment using LHC beams journal January 2013
Light-front holographic QCD and emerging confinement journal July 2015
Nonperturbative properties of Yang–Mills theories journal October 2020
The nonperturbative functional renormalization group and its applications journal May 2021
A fixed-target programme at the LHC: Physics case and projected performances for heavy-ion, hadron, spin and astroparticle studies journal May 2021
Lattice determinations of the strong coupling journal July 2021
Collider physics at the precision frontier journal August 2021
On the running coupling constant in QCD journal April 2007
Explanation and prediction of observables using continuum strong QCD journal July 2014
The QCD running coupling journal September 2016
Baryons as relativistic three-quark bound states journal November 2016
Parton distributions and lattice QCD calculations: A community white paper journal May 2018
QCD at finite temperature and chemical potential from Dyson–Schwinger equations journal March 2019
The QCD renormalization group equation and the elimination of fixed-order scheme-and-scale ambiguities using the principle of maximum conformality journal September 2019
Strong coupling constant and quark masses from lattice QCD journal July 2020
Precision physics with inclusive QCD processes journal March 2021
Insights into the emergence of mass from studies of pion and kaon structure journal September 2021
Artificial dynamical effects in quantum field theory journal May 2022
SU(3) Yang Mills theory at small distances and fine lattices journal January 2018
Dynamical fermions, centre vortices, and emergent phenomena journal January 2022
Origin of the Proton Mass journal January 2023
Spin Sum Rules and the Strong Coupling Constant at large distance conference January 2009
On the Green's functions of quantized fields. I journal July 1951
On the Green's functions of quantized fields. II journal July 1951
Impressions of the Continuum Bound State Problem in QCD journal December 2020
Valence Quark Ratio in the Proton journal April 2022
Novel and Self-Consistency Analysis of the QCD Running Coupling α s(Q) in Both the Perturbative and Nonperturbative Domains journal June 2022
Generalized sum rules for spin-dependent structure functions of the nucleon journal December 2000
Event shapes in e + e   annihilation and deep inelastic scattering journal February 2004
Infrared properties of QCD from Dyson–Schwinger equations journal June 2006
Fermion interactions and universal behavior in strongly interacting theories journal January 2012
Better jet clustering algorithms journal August 1997
Can the QCD running coupling have a causal analyticity structure? journal July 1998
Lattice calculation of α s in momentum scheme journal October 1998
Three-loop beta function and non-perturbative α s in asymmetric momentum scheme journal December 1998
Lattice calculation of 1/ p 2 corrections to α s and of Λ (QCD) in the MOM -tilde scheme journal March 2000
Preliminary Calculation of α S from Green Functions with Dynamical Quarks journal January 2002
The strong coupling constant at small momentum as an instanton detector journal April 2003
Non-perturbative power corrections to ghost and gluon propagators journal January 2006
Is the QCD ghost dressing function finite at zero momentum ? journal June 2006
IR finiteness of the ghost dressing function from numerical resolution of the ghost SD equation journal June 2008
On the IR behaviour of the Landau-gauge ghost propagator journal June 2008
α s and the τ hadronic width: fixed-order, contour- improved and higher-order perturbation theory journal September 2008
Indirect determination of the Kugo-Ojima function from lattice data journal November 2009
Lattice-motivated holomorphic nearly perturbative QCD journal May 2017
Determination of ${{\rm{\Lambda }}}_{\overline{{\rm{MS}}}}$ at five loops from holographic QCD journal September 2017
Centre vortex removal restores chiral symmetry journal November 2017
Infrared-suppressed QCD coupling and the hadronic contribution to muon g-2 journal August 2020
Lattice-motivated QCD coupling and hadronic contribution to muon g − 2 journal April 2021
The Large Hadron–Electron Collider at the HL-LHC journal November 2021
Revealing the structure of light pseudoscalar mesons at the electron–ion collider journal May 2021
The PDF4LHC21 combination of global PDF fits for the LHC Run III* journal July 2022
Fractional analytic QCD beyond leading order journal November 2022
The spin structure of the nucleon journal June 2019
A window on infrared QCD with small expansion parameters journal December 2021
Drawing insights from pion parton distributions journal March 2020
Effective charge from lattice QCD * journal August 2020
Pion parton distribution function in light-front holographic QCD journal October 2020
Revealing pion and kaon structure via generalised parton distributions * journal January 2022
Emergence of mass in the gauge sector of QCD* journal November 2022
pQCD running couplings finite and monotonic in the infrared: when do they reflect the holomorphic properties of spacelike observables? journal January 2021
Review of Particle Physics journal August 2022
Elimination of Ghosts in Propagators journal November 1958
Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I journal April 1961
Gauge Invariance and Mass journal January 1962
Gauge Invariance and Mass. II journal December 1962
Applications of the Chiral U ( 6 ) ⊗ U ( 6 ) Algebra of Current Densities journal August 1966
Inelastic Electron-Proton and γ -Proton Scattering and the Structure of the Nucleon journal September 1969
The S Matrix in Quantum Electrodynamics journal June 1949
An Identity in Quantum Electrodynamics journal April 1950
Divergence of Perturbation Theory in Quantum Electrodynamics journal February 1952
Quantum Electrodynamics at Small Distances journal September 1954
Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture journal November 1971
Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior journal November 1971
Confinement contains condensates journal June 2012
Inelastic Scattering of Polarized Leptons from Polarized Nucleons journal March 1970
Confinement of quarks journal October 1974
Asymptotic freedom and Goldstone realization of chiral symmetry journal October 1974
Strings, monopoles, and gauge fields journal December 1974
Two-loop calculation of Yang-Mills propagators in the Curci-Ferrari model journal August 2019
Light-meson leptonic decay rates in lattice QCD + QED journal August 2019
Strong coupling constant and heavy quark masses in ( 2 + 1 )-flavor QCD journal August 2019
Calculation of the nonperturbative strong coupling from first principles journal October 2019
Determination of the QCD coupling from the static energy and the free energy journal December 2019
Symmetry, symmetry breaking, and pion parton distributions journal March 2020
QCD phase structure at finite temperature and density journal March 2020
Renormalons in integrated spectral function moments and α s extractions journal April 2020
Landau gauge Yang-Mills propagators in the complex momentum plane journal November 2020
Ghost-antighost-gluon vertex from the Curci-Ferrari model: Two-loop corrections journal December 2020
Analytic structure of the lattice Landau gauge gluon and ghost propagators journal December 2020
New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC journal January 2021
Strong coupling from an improved τ vector isovector spectral function journal February 2021
Ghost dynamics in the soft gluon limit journal September 2021
Screened massive expansion of the quark propagator in the Landau gauge journal October 2021
Two-loop corrections to the QCD propagators within the Curci-Ferrari model journal November 2021
Towards a single scale-dependent Pomeron in holographic light-front QCD journal February 2022
One-loop unquenched three-gluon and ghost-gluon vertices in the Curci-Ferrari model journal May 2022
Probing an intrinsically flavorful ALP via tau-lepton flavor physics journal May 2022
Borel representation of τ hadronic spectral function moments in contour-improved perturbation theory journal May 2022
Smoothing algorithms for projected center-vortex gauge fields journal July 2022
Impact of dynamical fermions on the center vortex gluon propagator journal July 2022
Static quark potential from center vortices in the presence of dynamical fermions journal September 2022
Two-loop three-gluon vertex from the Curci-Ferrari model and its leading infrared behavior to all loop orders journal December 2022
Determining wave equations in holographic QCD from Wilsonian renormalization group journal December 2022
Static energy in ( 2+1+1 )-flavor lattice QCD: Scale setting and charm effects journal April 2023
Hamiltonian formulation of Wilson's lattice gauge theories journal January 1975
Infrared behavior of non-Abelian gauge theories journal June 1976
Infrared behavior of non-Abelian gauge theories. II journal May 1977
Charmonium: The model journal June 1978
Broken Scale Invariance in Scalar Field Theory journal October 1970
Renormalization-prescription dependence of the quantum-chromodynamic coupling constant journal September 1979
Exclusive processes in perturbative quantum chromodynamics journal November 1980
Dynamical mass generation in continuum quantum chromodynamics journal September 1982
On the elimination of scale ambiguities in perturbative quantum chromodynamics journal July 1983
Renormalization-scheme-invariant QCD and QED: The method of effective charges journal May 1984
Measurement of energy-energy correlations in e + e − →hadrons at √s =29 GeV journal June 1985
Mesons in a relativized quark model with chromodynamics journal July 1985
Determination ofαsfrom energy-energy correlations ine+e−annihilation at 29 GeV journal June 1988
Perturbative QCD corrections to the ratio R for τ decay journal March 1989
Gauge-invariant three-gluon vertex in QCD journal November 1989
On some ambiguities in the method of effective charges journal July 1989
Light-cone-quantized QCD in 1+1 dimensions journal June 1990
Running coupling and the Λ parameter from SU(3) lattice simulations journal January 1993
Ellis-Jaffe sum rule: The estimates of the next-to-next-to-leading-order QCD corrections journal November 1994
Commensurate scale relations in quantum chromodynamics journal April 1995
Observing long color flux tubes in SU(2) lattice gauge theory journal May 1995
Measurement of α s ( M Z 2 ) from hadronic event observables at the Z 0 resonance journal February 1995
From spectroscopy to the strong coupling constant with heavy Wilson quarks journal July 1995
Dynamical chiral symmetry breaking, Goldstone’s theorem, and the consistency of the Schwinger-Dyson and Bethe-Salpeter equations journal October 1995
Specific features of heavy quark production: Local parton-hadron duality approach to heavy particle spectra journal January 1996
Deep inelastic scattering of polarized electrons by polarized He 3 and the study of the neutron spin structure journal December 1996
Massive Yang-Mills model and diffractive scattering journal February 1999
α S from Υ spectroscopy with dynamical Wilson fermions journal September 1999
Properties of Regge trajectories journal June 2000
Static QCD potential in coordinate space with quark masses through two loops journal September 2000
Hadronic Regge trajectories: Problems and approaches journal February 2001
Generalized Gerasimov-Drell-Hearn sum rule for the proton-neutron difference in chiral perturbation theory journal April 2001
Testing the Landau gauge operator product expansion on the lattice with a 〈 A 2 〉 condensate journal April 2001
Gerasimov-Drell-Hearn sum rule and related integrals journal April 2001
Spin-dependent twist-4 matrix elements from the instanton vacuum: Flavor-singlet and nonsinglet journal January 2002
Renormalization flow of bound states journal February 2002
Detailed analysis of the three-quark potential in SU(3) lattice QCD journal June 2002
Infrared exponent for gluon and ghost propagation in Landau gauge QCD journal June 2002
Running coupling in Yang-Mills theory: A flow equation study journal July 2002
Time-independent stochastic quantization, Dyson-Schwinger equations, and infrared critical exponents in QCD journal May 2003
Vortex structures in pureSU(3)lattice gauge theory journal January 2004
Physical renormalization schemes and grand unification journal May 2004
Observation of string breaking in QCD journal June 2005
Large momentum behavior of the ghost propagator in SU(3) lattice gauge theory journal December 2005
Higher twists in polarized DIS and the size of the constituent quark journal April 2006
Hadronic unquenching effects in the quark propagator journal November 2007
New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach journal April 2008
Running coupling from the four-gluon vertex in Landau gauge Yang-Mills theory journal July 2008
Experimental study of isovector spin sum rules journal August 2008
High-precision charm-quark mass and QCD coupling from current-current correlators in lattice and continuum QCD journal September 2008
Update: Accurate determinations of α s from realistic lattice QCD journal December 2008
Ghost-gluon running coupling, power corrections, and the determination of Λ MS ¯ journal January 2009
Lattice study of the vacuum polarization function and determination of the strong coupling constant journal April 2009
Nonperturbative comparison of QCD effective charges journal October 2009
Indirect lattice evidence for the refined Gribov-Zwanziger formalism and the gluon condensate ⟨ A 2 ⟩ in the Landau gauge journal April 2010
High-precision c and b masses, and QCD coupling from current-current correlators in lattice and continuum QCD journal August 2010
Strong coupling constant from vacuum polarization functions in three-flavor lattice QCD with dynamical overlap fermions journal October 2010
Alternative refined Gribov-Zwanziger Lagrangian journal October 2010
Infrared propagators of Yang-Mills theory from perturbation theory journal November 2010
Non-Gaussian wave functionals in Coulomb gauge Yang-Mills theory journal November 2010
S U ( 3 ) Landau gauge gluon and ghost propagators using the logarithmic lattice gluon field definition journal March 2011
Running coupling constant of ten-flavor QCD with the Schrödinger functional method journal April 2011
Role of center vortices in chiral symmetry breaking in SU(3) gauge theory journal August 2011
Dynamical origin of the refinement of the Gribov-Zwanziger theory journal September 2011
Ghost-gluon coupling, power corrections, and Λ MS ¯ from lattice QCD with a dynamical charm journal February 2012
Systematics of radial and angular-momentum Regge trajectories of light nonstrange q q ¯ -states journal May 2012
SU(3)center vortices underpin confinement and dynamical chiral symmetry breaking journal September 2012
Perturbative expansion of the QCD Adler function improved by renormalization-group summation and analytic continuation in the Borel plane journal January 2013
Walking signals in N f = 8 QCD on the lattice journal May 2013
QCD effective charge from the three-gluon vertex of the background-field method journal June 2013
Three-point correlation functions in Yang-Mills theory journal December 2013
Systematic scale-setting to all orders: The principle of maximum conformality and commensurate scale relations journal January 2014
High statistics determination of the strong coupling constant in Taylor scheme and its OPE Wilson coefficient from lattice QCD with a dynamical charm journal January 2014
Gluonic three-point correlations in pure Landau gauge QCD journal March 2014
Three-gluon vertex in Landau gauge journal May 2014
High precision determination of the Q 2 evolution of the Bjorken sum journal July 2014
Effective confining potentials for QCD journal October 2014
Gluon propagator in Feynman gauge by the method of stationary variance journal November 2014
Baryon spectrum from superconformal quantum mechanics and its light-front holographic embedding journal February 2015
Chiral symmetry breaking in continuum QCD journal March 2015
High-precision quark masses and QCD coupling from n f = 4 lattice QCD journal March 2015
Superconformal baryon-meson symmetry and light-front holographic QCD journal April 2015
Exact nilpotent nonperturbative BRST symmetry for the Gribov-Zwanziger action in the linear covariant gauge journal August 2015
Fourth-order QCD renormalization group quantities in the V scheme and the relation of the β function to the Gell-Mann–Low function in QED journal September 2015
Second order gluon polarization for SU(N) theory in a linear covariant gauge journal October 2015
Connection between center vortices and instantons through gauge-field smoothing journal October 2015
Influence of Gribov ambiguities in a class of nonlinear covariant gauges journal November 2015
New parton distribution functions from a global analysis of quantum chromodynamics journal February 2016
Light mesons in QCD and unquenching effects from the 3PI effective action journal February 2016
More on the nonperturbative Gribov-Zwanziger quantization of linear covariant gauges journal March 2016
Structure of the neutral pion and its electromagnetic transition form factor journal April 2016
Local gauge transformation for the quark propagator in an SU(N) gauge theory journal April 2016
Symmetry preserving truncations of the gap and Bethe-Salpeter equations journal May 2016
Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond journal May 2016
Constraints on large- x parton distributions from new weak boson production and deep-inelastic scattering data journal June 2016
Lattice gluon and ghost propagators and the strong coupling in pure SU(3) Yang-Mills theory: Finite lattice spacing and volume effects journal July 2016
From quarks and gluons to hadrons: Chiral symmetry breaking in dynamical QCD journal August 2016
Determination of the QCD coupling from ALEPH τ decay data journal August 2016
Quark masses and strong coupling constant in 2 + 1 flavor QCD journal August 2016
Unified description of seagull cancellations and infrared finiteness of gluon propagators journal August 2016
Landau gauge Yang-Mills correlation functions journal September 2016
Short-distance charmonium correlator on the lattice with Möbius domain-wall fermion and a determination of charm quark mass journal September 2016
Further evidence for zero crossing on the three gluon vertex journal October 2016
Transverse force on transversely polarized quarks in longitudinally polarized nucleons journal November 2016
Analytic structure of QCD propagators in Minkowski space journal December 2016
Equation of state for SU(3) gauge theory via the energy-momentum tensor under gradient flow journal December 2016
Analysis of nucleon electromagnetic form factors from light-front holographic QCD: The spacelike region journal January 2017
Natural constraints on the gluon-quark vertex journal February 2017
Strong coupling from hadronic τ decays: A critical appraisal journal February 2017
Partonic structure of neutral pseudoscalars via two photon transition form factors journal April 2017
Scale-setting, flavor dependence, and chiral symmetry restoration journal June 2017
Refining the detection of the zero crossing for the three-gluon vertex in symmetric and asymmetric momentum subtraction schemes journal June 2017
How nonperturbative is the infrared regime of Landau gauge Yang-Mills correlators? journal July 2017
Parton distribution functions, α s , and heavy-quark masses for LHC Run II journal July 2017
Exposing strangeness: Projections for kaon electromagnetic form factors journal August 2017
Process-independent strong running coupling journal September 2017
Comment on “Lattice gluon and ghost propagators and the strong coupling in pure S U ( 3 ) Yang-Mills theory: Finite lattice spacing and volume effects” journal November 2017
Reply to “Comment on ‘Lattice gluon and ghost propagators and the strong coupling in pure S U ( 3 ) Yang-Mills theory: Finite lattice spacing and volume effects’ ” journal November 2017
Small parameters in infrared quantum chromodynamics journal December 2017
Locating the Gribov horizon journal February 2018
Ghost-gluon vertex in the presence of the Gribov horizon journal February 2018
Muon g − 2 and α ( M Z 2 ) : A new data-based analysis journal June 2018
Lattice computation of the Dirac eigenvalue density in the perturbative regime of QCD journal July 2018
Gluon propagator in linear covariant R ξ gauges journal August 2018
Strong coupling from e + e − → hadrons below charm journal October 2018
Gluon propagator on a center-vortex background journal November 2018
QCD β -function on the string worldsheet journal December 2018
Determination of Λ MS ¯ ( n f = 2 ) and analytic parametrization of the static quark-antiquark potential journal December 2018
Discretization effects on renormalized gauge-field Green’s functions, scale setting, and the gluon mass journal December 2018
γ * γ → η , η ′ transition form factors journal January 2019
Conjecture Concerning the Properties of Nonrenormalizable Field Theories journal August 1958
Order α s 4 QCD Corrections to Z and τ Decays journal July 2008
Light-Front Holography: A First Approximation to QCD journal February 2009
Toward TeV Conformality journal February 2010
Three-Loop Static Potential journal March 2010
Static QCD Potential at Three-Loop Order journal March 2010
Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order α s 4 in a General Gauge Theory journal March 2010
Strong Running Coupling at τ and Z 0 Mass Scales from Lattice QCD journal June 2012
Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality journal July 2012
Imaging Dynamical Chiral-Symmetry Breaking: Pion Wave Function on the Light Front journal March 2013
Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in Perturbative QCD journal May 2013
Total Top-Quark Pair-Production Cross Section at Hadron Colliders Through O ( α S 4 ) journal June 2013
Precise QCD Predictions for the Production of Dijet Final States in Deep Inelastic Scattering journal July 2016
Scheme Variations of the QCD Coupling and Hadronic τ Decays journal October 2016
Determination of the QCD Λ Parameter and the Accuracy of Perturbation Theory at High Energies journal October 2016
Five-Loop Running of the QCD Coupling Constant journal February 2017
QCD Coupling from a Nonperturbative Determination of the Three-Flavor Λ Parameter journal September 2017
Universality of Generalized Parton Distributions in Light-Front Holographic QCD journal May 2018
Strong Running Coupling from the Gauge Sector of Domain Wall Lattice QCD with Physical Quark Masses journal April 2019
Gauge Coupling β Functions to Four-Loop Order in the Standard Model journal February 2020
Unified Description of Polarized and Unpolarized Quark Distributions in the Proton journal February 2020
Running Coupling Constant from Position-Space Current-Current Correlation Functions in Three-Flavor Lattice QCD journal December 2020
Four-Loop Gauge and Three-Loop Yukawa Beta Functions in a General Renormalizable Theory journal July 2021
Exact Sum Rule for Nucleon Magnetic Moments journal May 1966
Harmonic-Oscillator Analogy for the Veneziano Model journal September 1969
Scaling, Duality, and the Behavior of Resonances in Inelastic Electron-Proton Scattering journal October 1970
Ultraviolet Behavior of Non-Abelian Gauge Theories journal June 1973
Reliable Perturbative Results for Strong Interactions? journal June 1973
Price of Asymptotic Freedom journal September 1973
Asymptotic Behavior of Non-Abelian Gauge Theories to Two-Loop Order journal July 1974
Spectrum of Charmed Quark-Antiquark Bound States journal February 1975
On-Shell Asymptotics of Non-Abelian Gauge Theories journal August 1975
Nonperturbative Determination of α ( q 2 ) and Its Experimental Implications journal June 1979
Efficient calculation of one-loop QCD amplitudes journal April 1991
Determination of the strong coupling constant from the charmonium spectrum journal August 1992
Determination of the neutron spin structure function journal August 1993
Manifestation of Sea Quark Effects in the Strong Coupling Constant in Lattice QCD journal January 1995
Precision Measurement of the Proton Spin Structure Function g 1 p journal January 1995
Precision Measurement of the Deuteron Spin Structure Function g 1 d journal July 1995
Measurements of the Proton and Deuteron Spin Structure Function g 2 and Asymmetry A 2 journal January 1996
Static Quark-Antiquark Potential in QCD to Three Loops journal January 1997
Analytic Model for the QCD Running Coupling with Universal α ¯ s ( 0 ) Value journal August 1997
Strong Coupling Constant with Flavor Thresholds at Four Loops in the Modified Minimal-Subtraction Scheme journal September 1997
Precision Determination of the Neutron Spin Structure Function g 1 n journal July 1997
Infrared Behavior of Gluon and Ghost Propagators in Landau Gauge QCD journal November 1997
Is There a Landau Pole Problem in QED? journal May 1998
Measurement of the Running of Effective QED Coupling at Large Momentum Transfer in the Spacelike Region journal September 1998
Measurement of α s ( Q 2 ) from the Gross–Llewellyn Smith Sum Rule journal October 1998
Hard Scattering and Gauge/String Duality journal January 2002
B -Meson Gateways to Missing Charmonium Levels journal September 2002
High-Precision Lattice QCD Confronts Experiment journal January 2004
Infrared Behavior and Fixed Points in Landau-Gauge QCD journal October 2004
Experimental Determination of the Evolution of the Bjorken Integral at Low Q 2 journal November 2004
Accurate Determinations of α s from Realistic Lattice QCD journal July 2005
Hadronic Spectra and Light-Front Wave Functions in Holographic QCD journal May 2006
Space-Time Approach to Non-Relativistic Quantum Mechanics journal April 1948
Forms of Relativistic Dynamics journal July 1949
On the Invariant Regularization in Relativistic Quantum Theory journal July 1949
Radiative Corrections to Elastic and Inelastic ep and up Scattering journal January 1969
Colloquium : Roper resonance: Toward a solution to the fifty year puzzle journal March 2019
The quark-gluon vertex in Landau gauge bound-state studies journal May 2015
Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all journal September 2016
Concerning pion parton distributions journal January 2022
Nucleon axial form factor at large momentum transfers journal October 2022
Bethe–Salpeter kernel and properties of strange-quark mesons journal March 2023
More on the renormalization of the horizon function of the Gribov–Zwanziger action and the Kugo–Ojima Green function(s) journal April 2010
A Dyson–Schwinger study of the four-gluon vertex journal March 2015
Parton distributions in the LHC era: MMHT 2014 PDFs journal May 2015
Constraints on parton distribution functions and extraction of the strong coupling constant from the inclusive jet cross section in pp collisions at $$\sqrt{s} = 7$$ s = 7 $$\,\text {TeV}$$ TeV journal June 2015
Combination of measurements of inclusive deep inelastic $${e^{\pm }p}$$ e ± p scattering cross sections and QCD analysis of HERA data: H1 and ZEUS Collaborations journal December 2015
Measurement of the triple-differential dijet cross section in proton-proton collisions at $$\sqrt{s}=8\,\text {TeV} $$ s = 8 TeV and constraints on parton distribution functions journal November 2017
Determination of the strong coupling constant $${\varvec{{\alpha _\mathrm{s} (m_\mathrm{Z})}}}$$ α s ( m Z ) in next-to-next-to-leading order QCD using H1 jet cross section measurements: H1 Collaboration journal November 2017
Energy–energy correlation in electron–positron annihilation at NNLL + NNLO accuracy journal November 2017
A method for getting a finite $$\alpha $$ α in the IR region from an all-order beta function journal November 2017
Determination of the strong coupling constant $$\alpha _\mathrm {s}$$ α s from transverse energy–energy correlations in multijet events at $$\sqrt{s} = 8~\hbox {TeV}$$ s = 8 TeV using the ATLAS detector journal December 2017
Precision determination of the strong coupling constant within a global PDF analysis: NNPDF Collaboration journal May 2018
NLO PDFs from the ABMP16 fit journal June 2018
Precise determination of $$\alpha _{S}(M_Z)$$ α S ( M Z ) from a global fit of energy–energy correlation to NNLO+NNLL predictions journal June 2018
Update of the global electroweak fit and constraints on two-Higgs-doublet models journal August 2018
Determination of the strong coupling constant using inclusive jet cross section data from multiple experiments journal January 2019
The gradient flow coupling at high-energy and the scale of SU(3) Yang–Mills theory journal August 2019
Kaon and pion parton distributions journal November 2020
An analysis of systematic effects in finite size scaling studies using the gradient flow journal January 2021
Gluon propagator and three-gluon vertex with dynamical quarks journal February 2020
Why $$\alpha _s$$ cannot be determined from hadronic processes without simultaneously determining the parton distributions journal February 2020
Measurement of $$\hbox {t}{\bar{\hbox {t}}}$$ normalised multi-differential cross sections in $${\text {p}}{\text {p}} $$ collisions at $$\sqrt{s}=13\,{\text {TeV}} $$, and simultaneous determination of the strong coupling strength, top quark pole mass, and parton distribution functions journal July 2020
Determination of $$\alpha _{S}$$ beyond NNLO using event shape averages journal April 2021
An investigation of the $$\alpha _S$$ and heavy quark mass dependence in the MSHT20 global PDF analysis journal August 2021
Determination of perturbative QCD coupling from ALEPH $$\tau $$ decay data using pinched Borel–Laplace and Finite Energy Sum Rules journal October 2021
Strong coupling constant from moments of quarkonium correlators revisited journal January 2022
FLAG Review 2021 journal October 2022
On the difference between FOPT and CIPT for hadronic tau decays journal September 2021
The Determination of the Strong Coupling Constant book August 2016
Deep Inelastic sum Rules at the Boundaries Between Perturbative and Nonperturbative qcd journal September 2005
Strong coupling constant from Adler function in lattice QCD journal October 2016
On the analytically-improved running coupling in QCD journal May 2022
Problems on Lattice Gauge Fixing journal August 2001
Meson/baryon/tetraquark supersymmetry from superconformal algebra and light-front holography journal July 2016
Dyson–Schwinger Equations: A Tool for Hadron Physics journal June 2003
QCD gluon vertices from the string-inspired formalism journal July 2016
Chiral Dynamics in Nucleons and Nuclei journal June 1995
Nonperturbative QCD, Gauge-Fixing, Gribov Copies and the Lattice journal January 2003
Experimental Tests of Perturbative QCD journal December 1989
On the Theory of Dispersion of X-Rays journal January 1926
Gluon condensates and effective gluon mass journal August 2022
Experimental Determination of the QCD Effective Charge αg1(Q) journal May 2022
Emergence of Hadron Mass and Structure journal January 2023
Gauge Sector Dynamics in QCD journal February 2023
Critical Phenomena: field theoretical approach journal January 2010
The large $N$ limit of superconformal field theories and supergravity journal January 1998

Similar Records

The QCD running coupling
Journal Article · Sun May 08 20:00:00 EDT 2016 · Progress in Particle and Nuclear Physics · OSTI ID:1314949
Determination of ${{\rm{\Lambda }}}_{\overline{{\rm{MS}}}}$ at five loops from holographic QCD
Journal Article · Thu Aug 24 20:00:00 EDT 2017 · Journal of Physics. G, Nuclear and Particle Physics · OSTI ID:1379486

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
QCD
coupling constant
effective changes
nonperturbative QCD
perturbative QCD
renormalization group