Lattice evidence for the family of decoupling solutions of Landau gauge Yang–Mills theory

Sternbeck, André; Müller–Preussker, M.

doi:10.1016/j.physletb.2013.08.017

Cited by 79 publications

(108 citation statements)

References 82 publications

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“…Our motivation is to verify whether a fully consistent, simultaneous numerical solution of the heavy-quark DSE and heavy-light pseudoscalar meson BSE can be obtained with a modern approach to the rainbow-ladder (RL) truncation based on the interaction proposed by Qin et al [41]. This Ansatz produces an infrared behavior of the interaction, commonly described by a "dressing function" G(k 2 ) [32], congruent with the decoupling solution found in DSE and lattice studies of the gluon propagator [7][8][9][10][11][12][13][14][15][16][17]21]. Indeed, the gluon propagator is found to be a bounded and regular function of spacelike momenta with a maximum value at k 2 = 0.…”

Section: Introductionmentioning

confidence: 61%

Exciting flavored bound states

2014

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We study ground and radial excitations of flavor singlet and flavored pseudoscalar mesons within the framework of the rainbow-ladder truncation using an infrared massive and finite interaction in agreement with recent results for the gluon-dressing function from lattice QCD and DysonSchwinger equations. Whereas the ground-state masses and decay constants of the light mesons as well as charmonia are well described, we confirm previous observations that this truncation is inadequate to provide realistic predictions for the spectrum of excited and exotic states. Moreover, we find a complex conjugate pair of eigenvalues for the excited D (s) mesons, which indicates a nonHermiticity of the interaction kernel in the case of heavy-light systems and the present truncation. Nevertheless, limiting ourselves to the leading contributions of the Bethe-Salpeter amplitudes, we find a reasonable description of the charmed ground states and their respective decay constants.

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Section: Introductionmentioning

confidence: 61%

Exciting flavored bound states

2014

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“…One study was performed by Maas [52], in which the condition on J(0) was mimicked by selecting Gribov copies which at some finite p 2 give large or small values for J(p 2 ). 4 Another lattice study was performed by Michael and myself [53], in which we selected Gribov copies based on the lowest-lying (non-zero) eigenvalue λ 1 of the Faddeev-Popov operator.…”

Section: Infrared Behavior Of the Gluon And Ghost Propagators In Landmentioning

confidence: 99%

“…We [53] chose those copies with the highest (hc) or lowest (lc) value for λ 1 among 200 copies {U g µ (x)} for each configuration {U µ (x)} (note, hc and lc refer to the entries in the legend of Fig. 5).…”

Section: Infrared Behavior Of the Gluon And Ghost Propagators In Landmentioning

confidence: 99%

QCD propagators and vertices from lattice QCD (in memory of Michael Müller-Preußker)

Sternbeck

2017

EPJ Web Conf.

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Abstract. We review lattice calculations of the elementary Greens functions of QCD with a special emphasis on the Landau gauge. These lattice results have been of interest to continuum approaches to QCD over the past 20 years. They are used as reference for Dyson-Schwinger-and functional renormalization group equation calculations as well as for hadronic bound state equations. The lattice provides low-energy data for propagators and three-point vertices in Landau gauge at zero and finite temperature even including dynamical fermions. We summarize Michael Müller-Preußker's important contributions to this field and put them into the perspective of his other research interests.

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“…This procedure has been done in the case of Landau gauge in [26], and something similar, where one chooses the copy that…”

Section: Comparison With the Lattice Datamentioning

confidence: 99%

“…Although in [26] there wasn't strong dependence of their gauge dependent quantities on which Gribov copy was chosen, further studies on lattices with different volumes should be done. Picking the Gribov copy closest to the horizon is likely to be the best way to compare lattice data with calculations of gauge dependent quantities using the GZ action due to the fact that the measure is concentrated on the horizon as is shown in Appendix E.…”

Section: Comparison With the Lattice Datamentioning

confidence: 99%

Spectral decomposition of the ghost propagator and a necessary condition for confinement

Cooper¹,

Zwanziger²

2016

Phys. Rev. D

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In this article we present exact calculations that substantiate a clear picture relating the confining force of QCD to the zero-modes of the Faddeev-Popov (FP) operator M (gA) = −∂ · D(gA). This is done in two steps. First we calculate the spectral decomposition of the FP operator and show that the ghost propagator G(k;gA) = k|M −1 (gA)| k in an external gauge potential A is enhanced at low k in Fourier space for configurations A on the Gribov horizon. This results from the new formula in the low-k regime G ab (k, gA) = δ ab λ −1 | k| (gA), where λ | k| (gA) is the eigenvalue of the FP operator that emerges from λ | k| (0) = k 2 at A = 0. Next we derive a strict inequality signaling the divergence of the color-Coulomb potential at low momentum k namely, V (k) ≥ k 2 G 2 (k) for k → 0, where V (k) is the Fourier transform of the color-Coulomb potential V (r) and G(k) is the ghost propagator in momentum space. Although the color-Coulomb potential is a gauge-dependent quantity, we recall that it is bounded below by the gauge-invariant Wilson potential, and thus its long range provides a necessary condition for confinement. The first result holds in the Landau and Coulomb gauges, whereas the second holds in the Coulomb gauge only.

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Lattice evidence for the family of decoupling solutions of Landau gauge Yang–Mills theory

Cited by 79 publications

References 82 publications

Exciting flavored bound states

Exciting flavored bound states

QCD propagators and vertices from lattice QCD (in memory of Michael Müller-Preußker)

Spectral decomposition of the ghost propagator and a necessary condition for confinement

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