On the infrared behaviour of QCD Green functions in the Maximally Abelian gauge

Alkofer, Reinhard; Huber, Markus Q.; Mader, Valentin; Windisch, Andreas

doi:10.48550/arxiv.1112.6173

Cited by 8 publications

(9 citation statements)

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“…Using the functional renormalization group the propagators can be calculated such that this gap practically vanishes [30], but due to the different structure of the corresponding equations, it can not be inferred how much additional support in the mid-momentum regime is expected from which source in DSEs: two-loop diagrams or the dressing of the three-gluon vertex in the gluon loop. First calculations of two-loop diagrams in DSEs were performed in [74,75].…”

Section: Three-gluon Vertexmentioning

confidence: 99%

On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory

Huber

Smekal

2013

J. High Energ. Phys.

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104

162

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We solve the Dyson-Schwinger equations of the ghost and gluon propagators of Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex. The latter plays a central role in many truncation schemes for functional equations. By including it dynamically we can determine its influence on the propagators. We also suggest a new model for the three-gluon vertex motivated by lattice data which plays a crucial role to obtain stable solutions when the ghost-gluon vertex is included. We find that both vertices have a sizable quantitative impact on the mid-momentum regime and contribute to the reduction of the gap between lattice and Dyson-Schwinger equation results. Furthermore, we establish that the three-gluon vertex dressing turns negative at low momenta as suggested by lattice results in three dimensions.

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Section: Three-gluon Vertexmentioning

confidence: 99%

On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory

Huber

Smekal

2013

J. High Energ. Phys.

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104

162

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“…While the calculation of the spectral dimension as a function of the diffusion time was done numerically, the main results we presented were obtained analytically. Thus, they can be transferred directly to other cases, in particular to unquenched propagators and other gauges like linear covariant, Coulomb or maximally Abelian ones, for which results are available, e.g., [58][59][60][61][62][63][64], thereby extending the here presented study in order to elucidate the (in-)dependence of the results on the chosen gauge. the following ones:…”

Section: Figmentioning

confidence: 89%

Spectral dimension as a tool for analyzing nonperturbative propagators

2019

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We derive general properties of the scale-dependent effective spectral dimensions of nonperturbative gauge boson propagators as they appear as solutions from different methods in Yang-Mills theories. In the ultraviolet and for short timescales the anomalous dimensions of the propagators lead to a slight decrease of the spectral dimension as compared to the one of a free propagator. Lowering the momentum scale, the spectral dimension decreases further. The class of propagators which display a maximum at Euclidean momenta, and thus violate positivity, always approaches a spectral dimension of one for large times. We also show that the longest time intervals are not related to the deep infrared but to the momentum scale defined by the position of the maximum.

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“…In fact, in some cases, like the maximally Abelian gauge, this seems like a requirement for numeric calculations anyway, because no simpler working truncation was found yet, see Refs. [6,53,146] for details. In other cases, though, solutions of simple truncations exist.…”

Section: Discussionmentioning

confidence: 99%

Correlation functions of Landau gauge Yang-Mills theory

Huber

2020

Preprint

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Correlation functions of Yang-Mills theory in the Landau gauge are calculated from their equations of motion. The employed setup is completely parameter-free and leads, within errors, to good quantitative agreement with corresponding lattice results for the ghost and gluon propagators as well as the ghost-gluon and three-gluon vertices. Also the four-gluon vertex is calculated. The present setup allows for the first time for a unique subtraction of quadratic divergences in the gluon propagator Dyson-Schwinger equation. Thus, there are no ambiguities which can arise due to the use of models or auxiliary workarounds. In addition, several self-tests of the results are described that allow assessing the truncation error in a self-consistent way. This enables a new perspective on how to identify limitations of the present setup and develop future improvements.

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On the infrared behaviour of QCD Green functions in the Maximally Abelian gauge

Cited by 8 publications

References 0 publications

On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory

On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory

Spectral dimension as a tool for analyzing nonperturbative propagators

Correlation functions of Landau gauge Yang-Mills theory

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