A precise determination of the running coupling in the SU(3) Yang-Mills theory

Lüscher, Martin; Sommer, Rainer; Weisz, Peter; Wolff, Ulli

doi:10.1016/0550-3213(94)90629-7

Cited by 371 publications

(655 citation statements)

References 27 publications

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“…3 In particular, by comparing data at different lattice sizes and same β value, we find (for each β) a range of momenta for which the data are free from finitevolume corrections. We then perform the matching using data for these momenta and V = 26 4 .…”

Section: Determination Of Renormalization Constantsmentioning

confidence: 99%

“…For example, the corrections to the Coulomb law of the staticquark potential may be used to define the running coupling [1,2]. Alternatively, the finite-size scaling has its imprint on the running coupling and may be used for a highprecision measurement of the coupling [3,4]. The approach adopted in [5]- [7] is based on extracting the running coupling directly from a vertex function.…”

Section: Introductionmentioning

confidence: 99%

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Propagators and running coupling from SU(2) lattice gauge theory

et al. 2004

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We perform numerical studies of the running coupling constant α R (p 2 ) and of the gluon and ghost propagators for pure SU (2) lattice gauge theory in the minimal Landau gauge. Different definitions of the gauge fields and different gauge-fixing procedures are used respectively for gaining better control over the approach to the continuum limit and for a better understanding of Gribov-copy effects. We find that the ghost-ghost-gluon-vertex renormalization constant is finite in the continuum limit, confirming earlier results by all-order perturbation theory. In the low momentum regime, the gluon form factor is suppressed while the ghost form factor is divergent. Correspondingly, the ghost propagator diverges faster than 1/p 2 and the gluon propagator appears to be finite. Precision data for the running coupling α R (p 2 ) are obtained. These data are consistent with an IR fixed point given by lim p→0 α R (p 2 ) = 5(1).

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Section: Determination Of Renormalization Constantsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Propagators and running coupling from SU(2) lattice gauge theory

et al. 2004

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“…Moreover, perturbation theory remains tractable in this framework, as the absolute minimum of the action is unique up to gauge equivalence. For the observable we choose the traditional SF coupling [25,26] and a 1-parameter family of close relatives [27]. The most important reason for this choice is the existence of a 2-loop calculation in this case [14,15], which, in combination with [16,17] allows to infer the 3-loop β-function for these schemes.…”

Section: Sf Couplingsmentioning

confidence: 99%

A non-perturbative exploration of the high energy regime in $$N_{\mathrm{f}}=3$$ N f = 3 QCD

et al. 2018

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Using continuum extrapolated lattice data we trace a family of running couplings in three-flavour QCD over a large range of scales from about 4 to 128 GeV. The scale is set by the finite space time volume so that recursive finite size techniques can be applied, and Schrödinger functional (SF) boundary conditions enable direct simulations in the chiral limit. Compared to earlier studies we have improved on both statistical and systematic errors. Using the SF coupling to implicitly define a reference scale 1 MS , a reliable estimate of the truncation error requires non-perturbative data for a sufficiently large range of values of α s =ḡ 2 /(4π). In the present work we reach this precision by studying scales that vary by a factor 2 5 = 32, reaching down to α s ≈ 0.1. We here provide the details of our analysis and an extended discussion. a

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“…8. Momentum-dependence of the effective gauge coupling (in a particular finitevolume scheme) in the pure SU(3) gauge theory [23][24][25] and in QCD with two flavours of massless quarks [26].…”

Section: Simulation Resultsmentioning

confidence: 99%

“…We may choose some particular boundary conditions, for example, and take the response of the system to a change in the boundary values of the fields as a measure for the interaction strength [23]. The important point to note is that the final results (such as f π /Λ) do not depend on any of these details.…”

Section: Finite-size Scalingmentioning

confidence: 99%

Lattice QCD — from Quark Confinement to Asymptotic Freedom

Lüscher

2003

International Conference on Theoretical Physics

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According to the present understanding, the observed diversity of the strong interaction phenomena is described by Quantum Chromodynamics, a gauge field theory with only very few parameters. One of the fundamental questions in this context is how precisely the world of mesons and nucleons is related to the properties of the theory at high energies, where quarks and gluons are the important degrees of freedom. The lattice formulation of QCD combined with numerical simulations and standard perturbation theory are the tools that allow one to address this issue at a quantitative level.

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A precise determination of the running coupling in the SU(3) Yang-Mills theory

Cited by 371 publications

References 27 publications

Propagators and running coupling from SU(2) lattice gauge theory

Propagators and running coupling from SU(2) lattice gauge theory

A non-perturbative exploration of the high energy regime in $$N_{\mathrm{f}}=3$$ N f = 3 QCD

Lattice QCD — from Quark Confinement to Asymptotic Freedom

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