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Title: The QCD running coupling

Abstract

Here, we review present knowledge on $$\alpha_{s}$$, the Quantum Chromodynamics (QCD) running coupling. The dependence of $$\alpha_s(Q^2)$$ on momentum transfer $Q$ encodes the underlying dynamics of hadron physics --from color confinement in the infrared domain to asymptotic freedom at short distances. We will survey our present theoretical and empirical knowledge of $$\alpha_s(Q^2)$$, including constraints at high $Q^2$ predicted by perturbative QCD, and constraints at small $Q^2$ based on models of nonperturbative dynamics. In the first, introductory, part of this review, we explain the phenomenological meaning of the coupling, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain. In the second, more technical, part of the review, we discuss $$\alpha_s(Q^2)$$ in the high momentum transfer domain of QCD. We review how $$\alpha_s$$ is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as well as `` Commensurate Scale Relations" which connect the various definitions of the QCD coupling without renormalization scale ambiguity. We also report recent important experimental measurements and advanced theoretical analyses which have led to precise QCD predictions at high energy. As an example of an important optimization procedure, we discuss the ``Principle of Maximum Conformality" which enhances QCD's predictive power by removing the dependence of the predictions for physical observables on the choice of the gauge and renormalization scheme. In last part of the review, we discuss $$\alpha_s(Q^2)$$ in the low momentum transfer domain, where there has been no consensus on how to define $$\alpha_s(Q^2)$$ or its analytic behavior. We will discuss the various approaches used for low energy calculations. Among them, we will discuss the light-front holographic approach to QCD in the strongly coupled regime and its prediction for the analytic form of $$\alpha_s(Q^2)$$. The AdS/QCD light-front holographic analysis predicts the color confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale $$\Lambda$$ and hadron masses. One can also identify a specific scale $$Q_0$$ which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including Lattice QCD, Schwinger-Dyson equations and the Gribov-Zwanziger analysis. After describing these approaches and enumerating conflicting results, we provide a partial discussion on the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances on this difficult subject, but also to suggest what could be the best definition of $$\alpha_s(Q^2)$$ in order to bring better unity to the subject.

Authors:
 [1];  [2];  [3]
  1. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  3. Univ. of Costa Rica, San Jose (Costa Rica)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP)
OSTI Identifier:
1314949
Alternate Identifier(s):
OSTI ID: 1359800
Report Number(s):
JLAB-PHY-16-2199; DOE/OR/-23177-3645
Journal ID: ISSN 0146-6410; PII: S0146641016300035
Grant/Contract Number:  
AC05–06OR23177; AC02–76SF00515. SLAC-PUB-16448; DE–AC05–06OR23177; DE–AC02–76SF00515. SLAC-PUB-16448
Resource Type:
Accepted Manuscript
Journal Name:
Progress in Particle and Nuclear Physics
Additional Journal Information:
Journal Volume: 90; Journal Issue: C; Journal ID: ISSN 0146-6410
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; QCD; coupling constant; non-perturbative; renormalization; infrared properties; hadron physics

Citation Formats

Deur, Alexandre, Brodsky, Stanley J., and de Téramond, Guy F.. The QCD running coupling. United States: N. p., 2016. Web. https://doi.org/10.1016/j.ppnp.2016.04.003.
Deur, Alexandre, Brodsky, Stanley J., & de Téramond, Guy F.. The QCD running coupling. United States. https://doi.org/10.1016/j.ppnp.2016.04.003
Deur, Alexandre, Brodsky, Stanley J., and de Téramond, Guy F.. Mon . "The QCD running coupling". United States. https://doi.org/10.1016/j.ppnp.2016.04.003. https://www.osti.gov/servlets/purl/1314949.
@article{osti_1314949,
title = {The QCD running coupling},
author = {Deur, Alexandre and Brodsky, Stanley J. and de Téramond, Guy F.},
abstractNote = {Here, we review present knowledge on $\alpha_{s}$, the Quantum Chromodynamics (QCD) running coupling. The dependence of $\alpha_s(Q^2)$ on momentum transfer $Q$ encodes the underlying dynamics of hadron physics --from color confinement in the infrared domain to asymptotic freedom at short distances. We will survey our present theoretical and empirical knowledge of $\alpha_s(Q^2)$, including constraints at high $Q^2$ predicted by perturbative QCD, and constraints at small $Q^2$ based on models of nonperturbative dynamics. In the first, introductory, part of this review, we explain the phenomenological meaning of the coupling, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain. In the second, more technical, part of the review, we discuss $\alpha_s(Q^2)$ in the high momentum transfer domain of QCD. We review how $\alpha_s$ is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as well as `` Commensurate Scale Relations" which connect the various definitions of the QCD coupling without renormalization scale ambiguity. We also report recent important experimental measurements and advanced theoretical analyses which have led to precise QCD predictions at high energy. As an example of an important optimization procedure, we discuss the ``Principle of Maximum Conformality" which enhances QCD's predictive power by removing the dependence of the predictions for physical observables on the choice of the gauge and renormalization scheme. In last part of the review, we discuss $\alpha_s(Q^2)$ in the low momentum transfer domain, where there has been no consensus on how to define $\alpha_s(Q^2)$ or its analytic behavior. We will discuss the various approaches used for low energy calculations. Among them, we will discuss the light-front holographic approach to QCD in the strongly coupled regime and its prediction for the analytic form of $\alpha_s(Q^2)$. The AdS/QCD light-front holographic analysis predicts the color confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale $\Lambda$ and hadron masses. One can also identify a specific scale $Q_0$ which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including Lattice QCD, Schwinger-Dyson equations and the Gribov-Zwanziger analysis. After describing these approaches and enumerating conflicting results, we provide a partial discussion on the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances on this difficult subject, but also to suggest what could be the best definition of $\alpha_s(Q^2)$ in order to bring better unity to the subject.},
doi = {10.1016/j.ppnp.2016.04.003},
journal = {Progress in Particle and Nuclear Physics},
number = C,
volume = 90,
place = {United States},
year = {2016},
month = {5}
}

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Gluon propagator and confinement scenario in Coulomb gauge
journal, May 2003


Coulomb energy, vortices, and confinement
journal, May 2003


Nonperturbative Determination of α ( q 2 ) and Its Experimental Implications
journal, June 1979


On the phase structure of vector-like gauge theories with massless fermions
journal, March 1982


Infrared non-perturbative QCD running coupling from Bogolubov approach
journal, November 2007


The strong coupling constant at small momentum as an instanton detector
journal, April 2003

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  • Journal of High Energy Physics, Vol. 2003, Issue 04
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Modified instanton profile effects from lattice Green functions
journal, December 2004


Bound-State Approach to the QCD Coupling Constant at Low-Energy Scales
journal, December 2007


QCD coupling below 1 GeV from the quarkonium spectrum
journal, February 2008


Dispersive approach to power-behaved contributions in QCD hard processes
journal, June 1996


Calculation of power corrections to hadronic event shapes
journal, June 1995


Exact Sum Rule for Nucleon Magnetic Moments
journal, May 1966


Determination of the neutron spin structure function
journal, August 1993


Deep inelastic scattering of polarized electrons by polarized He 3 and the study of the neutron spin structure
journal, December 1996


Measurement of the spin-dependent structure function g1(x) of the proton
journal, June 1994


Spin asymmetry in muon-proton deep inelastic scattering on a transversely-polarized target
journal, September 1994


A new measurement of the spin-dependent structure function g1(x) of the deuteron
journal, August 1995


The spin-dependent structure function g1(x) of the deuteron from polarized deep-inelastic muon scattering
journal, March 1997


Spin structure of the proton from polarized inclusive deep-inelastic muon-proton scattering
journal, November 1997


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


Measurements of the Q2-dependence of the proton and deuteron spin structure functions g1p and g1d
journal, December 1995


Precision Determination of the Neutron Spin Structure Function g 1 n
journal, July 1997


Measurement of the neutron spin structure function gn2 and asymmetry An2
journal, July 1997


Next-to-leading order QCD analysis of polarized deep inelastic scattering data
journal, July 1997


Measurement of the neutron spin structure function gn1 with a polarized 3He internal target
journal, July 1997


Determination of the deep inelastic contribution to the generalised Gerasimov-Drell-Hearn integral for the proton and neutron
journal, December 1998


Measurement of the proton spin structure function g1p with a pure hydrogen target
journal, December 1998


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<Q2<40 (GeV/c)2
journal, September 1999


Measurements of the Q2-dependence of the proton and neutron spin structure functions g1p and g1n
journal, November 2000


Precision measurement of the proton and deuteron spin structure functions g2 and asymmetries A2
journal, January 2003


Experimental Determination of the Evolution of the Bjorken Integral at Low Q 2
journal, November 2004


Experimental study of isovector spin sum rules
journal, August 2008


The deuteron spin-dependent structure function <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msubsup><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mi>d</mml:mi></mml:msubsup></mml:math> and its first moment
journal, March 2007


The spin-dependent structure function of the proton <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msubsup><mml:mi>g</mml:mi><mml:mn>1</mml:mn><mml:mi>p</mml:mi></mml:msubsup></mml:math> and a test of the Bjorken sum rule
journal, July 2010


The spin structure function g 1 p of the proton and a test of the Bjorken sum rule
journal, February 2016


Note on the Radiation Field of the Electron
journal, July 1937


Mass Singularities of Feynman Amplitudes
journal, July 1962

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  • Journal of Mathematical Physics, Vol. 3, Issue 4
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Degenerate Systems and Mass Singularities
journal, March 1964


Gerasimov-Drell-Hearn sum rule and related integrals
journal, April 2001


Experimental determination of the effective strong coupling constant
journal, July 2007


Determination of the effective strong coupling constant <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mi>α</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>Q</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math> from CLAS spin structure function data
journal, July 2008


On power corrections in the dispersive approach
journal, November 1998


Power corrections in the single dressed gluon approximation - the average thrust as a case study
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A dispersive approach to Sudakov resummation
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Hard elastic scattering in QCD: Leading behavior
journal, October 1989


The perturbative pion form factor with Sudakov suppression
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Conformal invariance in quantum mechanics
journal, August 1976

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Threefold complementary approach to holographic QCD
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Quantum superconformal model in (1, 2) space
journal, September 1983

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Superconformal quantum mechanics
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Baryon spectrum from superconformal quantum mechanics and its light-front holographic embedding
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Superconformal baryon-meson symmetry and light-front holographic QCD
journal, April 2015

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Universal effective hadron dynamics from superconformal algebra
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Baryon Number Changing Currents
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Algebraic treatment of effective supersymmetry
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Effective confining potentials for QCD
journal, October 2014

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Explanation and prediction of observables using continuum strong QCD
journal, July 2014


Spectrum of Charmed Quark-Antiquark Bound States
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Charmonium: The model
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B -Meson Gateways to Missing Charmonium Levels
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Quark-antiquark interaction at all momentum transfers
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Effective potential for heavy-quark-antiquark bound systems
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Characteristics of expected quark-antiquark resonances based on the quantum-chromodynamic potential
journal, February 1980


Regge Slope and the Λ Parameter in Quantum Chromodynamics: An Empirical Approach via Quarkonia
journal, July 1980


Quarkonia and quantum chromodynamics
journal, July 1981


Nonperturbative potential model for light and heavy quark-antiquark systems
journal, June 1980


Do Quarks Interact Pairwise and Satisfy the Color Hypothesis?
journal, July 1980


Heavy-Quark Systems
journal, December 1987


Comparing the Schrödinger and spinless Salpeter equations for heavy-quark bound states
journal, June 1986


Strings, monopoles, and gauge fields
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Harmonic-Oscillator Analogy for the Veneziano Model
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Dual-symmetric theory of hadrons.—I
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Dual-symmetric theory of hadrons: II.—Baryons
journal, October 1970

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An analogue model for KSV theory
journal, July 1970


QCD forces and heavy quark bound states
journal, March 2001


Running coupling and the Λ parameter from SU(3) lattice simulations
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Observing long color flux tubes in SU(2) lattice gauge theory
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Are there short distance non-perturbative contributions to the QCD static potential?
journal, August 1999


The Nf=0 heavy quark potential from short to intermediate distances
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Detailed analysis of the three-quark potential in SU(3) lattice QCD
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Covariant quantization of gauge fields without Gribov ambiguity
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Non-perturbative modification of the Faddeev-Popov formula and banishment of the naive vacuum
journal, December 1982


Local and renormalizable action from the gribov horizon
journal, September 1989


Vanishing of zero-momentum lattice gluon propagator and color confinement
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Renormalizability of the critical limit of lattice gauge theory by BRS invariance
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The one loop $$ \overline {\text{MS}} $$ static potential in the Gribov-Zwanziger lagrangian
journal, February 2010


Loop calculations in the three dimensional Gribov–Zwanziger Lagrangian
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Variational solution of the Yang-Mills Schrödinger equation in Coulomb gauge
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Confining solution of the Dyson-Schwinger equations in Coulomb gauge
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The heavy quark potential from Wilson's exact renormalization group
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Asymptotic freedom and IR freezing in QCD: the role of gluon paramagnetism
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Mesons in a relativized quark model with chromodynamics
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A relativistic quark model
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Heavy-quark mesons in a relativistic quark model
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The π-ϱ mass splitting
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The Static Force in Background Perturbation Theory
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QCD coupling constant below 1 GeV in the poincare-covariant model
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Infrared behavior of the running coupling constant and bound states in QCD
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The heavy quark potential and the ϒ, J/ψ systems
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A Nonperturbative Model for the Strong Running Coupling Within Potential Approach
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Dyson–Schwinger Approach to Strongly Coupled Theories
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journal, July 2012

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Dyson-Schwinger equations: Density, temperature and continuum strong QCD
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Dyson-Schwinger equations and their application to hadronic physics
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Infrared properties of QCD from Dyson–Schwinger equations
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The Infrared Behaviour of the Pure Yang–Mills Green Functions
journal, January 2012


Gauge bosons at zero and finite temperature
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Dynamical mass generation in continuum quantum chromodynamics
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Nonperturbative comparison of QCD effective charges
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Positivity issues for the pinch-technique gluon propagator and their resolution
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A non-perturbative calculation of the infrared limit of the axial gauge gluon propagator (I)
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Propagators and running coupling from SU(2) lattice gauge theory
journal, May 2004


Numerical Study of the Ghost-Gluon Vertex in Landau gauge
journal, December 2004


Power law running of the effective gluon mass
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Gluon mass generation in the PT-BFM scheme
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On the infrared scaling solution of SU(N) Yang–Mills theories in the maximally Abelian gauge
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Infrared analysis of propagators and vertices of Yang-Mills theory in Landau and Coulomb gauge
journal, June 2006


Yang-Mills two-point functions in linear covariant gauges
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Nonperturbative Landau gauge and infrared critical exponents in QCD
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Infrared Behavior of Gluon and Ghost Propagators in Landau Gauge QCD
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A Solution to Coupled Dyson–Schwinger Equations for Gluons and Ghosts in Landau Gauge
journal, July 1998

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Running coupling in nonperturbative QCD: Bare vertices and y -max approximation
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Qcd in the Infrared with Exact Angular Integrations
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Multiplicative renormalizability of gluon and ghost propagators in QCD
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Infrared exponent for gluon and ghost propagation in Landau gauge QCD
journal, June 2002


Infrared exponents and running coupling of SU(N) Yang–Mills theories
journal, May 2002


Analytic properties of the Landau gauge gluon and quark propagators
journal, July 2004


Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory
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Infrared behavior of three-point functions in Landau gauge Yang–Mills theory
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Infrared singularities in Landau gauge Yang-Mills theory
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Hamiltonian flow in Coulomb gauge Yang-Mills theory
journal, January 2011


Renormalization flow of Yang-Mills propagators
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Infrared Behavior and Fixed Points in Landau-Gauge QCD
journal, October 2004


What the Gribov copy tells about confinement and the theory of dynamical chiral symmetry breaking
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Infrared Features of Unquenched Lattice Landau Gauge QCD
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Propagator of the Lattice Domain Wall Fermion and the Staggered Fermion
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Infrared behavior of gluons and ghosts in ghost-antighost symmetric gauges
journal, August 2003


BRST symmetry versus horizon condition in Yang-Mills theories
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Subcritical solution of the Yang-Mills Schrödinger equation in the Coulomb gauge
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Finite volume effects in a quenched lattice-QCD quark propagator
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The infrared behavior of Landau gauge Yang–Mills theory in <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math>, 3 and 4 dimensions
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Two- and three-point functions in two-dimensional Landau-gauge Yang-Mills theory: continuum results
journal, November 2012

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IR finiteness of the ghost dressing function from numerical resolution of the ghost SD equation
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On the IR behaviour of the Landau-gauge ghost propagator
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On-Shell Asymptotics of Non-Abelian Gauge Theories
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Infrared behavior of non-Abelian gauge theories
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Infrared behavior of non-Abelian gauge theories. II
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Quark confinement and vortices in massive gauge-invariant QCD
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A dynamical gluon mass solution in a coupled system of the Schwinger-Dyson equations
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Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
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On the infrared behavior of Landau gauge Yang–Mills theory
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Gluon mass through ghost synergy
journal, January 2012

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Indirect lattice evidence for the refined Gribov-Zwanziger formalism and the gluon condensate A 2 in the Landau gauge
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Dynamical origin of the refinement of the Gribov-Zwanziger theory
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Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism
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Large volume behaviour of Yang-Mills propagators
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Renormalization of gauge theories
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Local Covariant Operator Formalism of Non-Abelian Gauge Theories and Quark Confinement Problem
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Low-momentum ghost dressing function and the gluon mass
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Natural solution in the refined Gribov-Zwanziger theory
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Infrared properties of the glue propagator in non-abelian gauge theories
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Infrared properties of the coupling constant in non-abelian gauge theories
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Infrared properties of the coupling constant in non-Abelian gauge theories
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Approximation scheme for quantum chromodynamics
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On low energy tests of QCD
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Dynamical symmetry breaking in non-Abelian gauge field theories
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Estimate of the quark-gluon coupling strength from baryon masses
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Pinch technique: Theory and applications
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Leading-order perturbative QCD calculation of nucleon Dirac form factors
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Phenomenological Tests for the Freezing of the qcd Running Coupling Constant
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Freezing of the QCD coupling constant and solutions of Schwinger-Dyson equations
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Dynamical equation of the effective gluon mass
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Unquenching the gluon propagator with Schwinger-Dyson equations
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Gluon mass generation in the presence of dynamical quarks
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All-order equation of the effective gluon mass
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Interaction model for the gap equation
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Bridging a gap between continuum-QCD and ab initio predictions of hadron observables
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Monte Carlo evaluation of the effective gluon mass
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Adjoint Wilson lines and the effective gluon mass
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Glueballs as bound states of massive gluons
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The gluon is massive: A lattice calculation of the gluon propagator in the Landau gauge
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Relating the QCD Pomeron to an effective gluon mass
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Gauge-invariant three-gluon vertex in QCD
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Coupled fermion gap and vertex equations for chiral-symmetry breakdown in QCD
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Propagation properties and condensate formation of the confined Yang-Mills field
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Gluon propagator in the infrared region
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The gluon propagator on a large volume, at β = 6.0
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Running gluon mass from a Landau gauge lattice QCD propagator
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The Gribov–Zwanziger action in the presence of the gauge invariant, nonlocal mass operator Tr∫d4xFμν(D2)-1Fμν in the Landau gauge
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Short-distance tachyonic gluon mass and 1/Q2 corrections
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Multiplicative renormalizability and quark propagator
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Overlapping-divergence-free skeleton expansion in non-Abelian gauge theories
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Infrared behavior of three- and four-gluon vertices in Yang-Mills theory
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Gauge-invariant four-gluon vertex and its Ward identity
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Three-point correlation functions in Yang-Mills theory
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Running coupling from the four-gluon vertex in Landau gauge Yang-Mills theory
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A Dyson–Schwinger study of the four-gluon vertex
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Three-gluon vertex in Landau gauge
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Gluonic three-point correlations in pure Landau gauge QCD
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A systematic extended iterative solution for quantum chromodynamics
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Extended iterative scheme for QCD: the four-gluon vertex
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Hadronic unquenching effects in the quark propagator
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Dynamically Induced Scalar Quark Confinement
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String Breaking in Non-Abelian Gauge Theories with Fundamental Matter Fields
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String breaking and lines of constant physics in the SU(2) Higgs model
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First Signs for String Breaking in Two-Flavor QCD
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Looking into the Matter of Light-Quark Hadrons
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Truncating First-Order Dyson–Schwinger Equations in Coulomb Gauge Yang–Mills Theory
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Problems on Lattice Gauge Fixing
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Exploratory study of the three-gluon vertex on the lattice
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Quark-gluon vertex from lattice QCD
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Infrared gluon and ghost propagators from lattice QCD: Results from large asymmetric lattices
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Landau gauge ghost propagator and running coupling in S U ( 2 ) lattice gauge theory
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