Including four-gluon interactions into Landau / maximally-Abelian gauge Dyson-Schwinger studies

Mader, Valentin; Alkofer, Reinhard

doi:10.22323/1.171.0063

Cited by 6 publications

(6 citation statements)

References 30 publications

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“…1: The ghost-gluon, the three-gluon and the four-gluon vertices. The latter appears only in the sunset diagram, which was found to be small in all previous calculations [1,[32][33][34]. However, only the tree-level tensor structure has been taken into account so far.…”

Section: The Propagator Equationsmentioning

confidence: 91%

On non-primitively divergent vertices of Yang–Mills theory

Huber

2017

Eur. Phys. J. C

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Two correlation functions of Yang-Mills beyond the primitively divergent ones, the two-ghost-two-gluon and the four-ghost vertices, are calculated and their influence on lower vertices is examined. Their full (transverse) tensor structure is taken into account. As input, a solution of the full two-point equations -including two-loop terms -is used that respects the resummed perturbative ultraviolet behavior. A clear hierarchy is found with regard to the color structure that reduces the number of relevant dressing functions. The impact of the two-ghost-two-gluon vertex on the three-gluon vertex is negligible, which is explained by the fact that all non-small dressing functions drop out due to their color factors. Only in the ghost-gluon vertex a small net effect below 2% is seen. The four-ghost vertex is found to be extremely small in general. Since these two four-point functions do not enter into the propagator equations, these findings establish their small overall effect on lower correlation functions.

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Section: The Propagator Equationsmentioning

confidence: 91%

On non-primitively divergent vertices of Yang–Mills theory

Huber

2017

Eur. Phys. J. C

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“…[40,41].) Due to the considerable complications and technical obstacles induced by the treatment of four-gluon interactions in a self-consistent DSE approach as well as indications of their lack of importance [42] we neglect the two-loop diagrams in the gluon equation. Furthermore, their contribution may be taken into account by adjusting JHEP11(2014)035 Figure 3.…”

Section: The Quark Dyson-schwinger Equationmentioning

confidence: 99%

Running coupling in the conformal window of large-Nf QCD

Hopfer

Fischer

Alkofer

2014

J. High Energ. Phys.

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Quantum Chromodynamics with a relatively large number of fundamentally charged quark flavours in the chiral limit is considered. A self-consistent solution of the quark, gluon and ghost propagator Dyson-Schwinger equations in Landau gauge exhibits a phase transition. Above the critical number of fermion flavours the non-perturbative running coupling develops a plateau over a wide momentum range, and the propagators follow a power law behaviour for these momenta. Hereby, the critical number of quark flavours depends crucially on the beyond-tree-level tensor structures of the quark-gluon vertex.

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“…Also in the maximally Abelian gauge (MAG), the gluon propagator in four dimensions has been investigated using lattice calculations [22][23][24][25] and analytical frameworks [26][27][28][29][30] from the viewpoint of the dual-superconductor picture proposed by Nambu, 't Hooft and Mandelstam [31,32]. The lattice studies in four dimensions show that the diagonal gluon propagator is more largely enhanced than that of the off-diagonal propagator at low momentum, which means that the diagonal gluon plays an important role for the infrared physics (so-called Abelian dominance) [33][34][35].…”

Section: Contents 1 Introductionmentioning

confidence: 99%

Gluon propagators in maximally Abelian gauge in SU(3) lattice QCD

Gongyo

Suganuma

2013

Phys. Rev. D

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In SU(3) lattice QCD, we study diagonal and off-diagonal gluon propagators in the maximally Abelian gauge with Uð1Þ 3 Â Uð1Þ 8 Landau gauge fixing. These propagators are studied both in the coordinate space and in the momentum space. The Monte Carlo simulation is performed on 16 4 at ¼ 6:0 and 32 4 at ¼ 5:8 and 6.0 at the quenched level. In the four-dimensional Euclidean spacetime, the effective mass of diagonal gluons is estimated as M diag ' 0:3 GeV and that of off-diagonal gluons as M off ' 1 GeV in the region of r ¼ 0:4-1:0 fm. In the momentum space, the effective mass of diagonal gluons is estimated as M diag ' 0:3 GeV and that of off-diagonal gluons as M off ' 1 GeV in the region of p < 1:1 GeV. The off-diagonal gluon propagator is relatively suppressed in the infrared region and seems to be finite at zero momentum, while the diagonal gluon propagator is enhanced. Furthermore, we also study the functional form of these propagators in momentum space. These propagators are well fitted by Z=ðp 2 þ m 2 Þ with fit parameters, Z, m, and in the region of p < 3:0 GeV. From the fit results and lattice calculations, all of the spectral functions of diagonal and off-diagonal gluons would have negative regions.

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Including four-gluon interactions into Landau / maximally-Abelian gauge Dyson-Schwinger studies

Cited by 6 publications

References 30 publications

On non-primitively divergent vertices of Yang–Mills theory

On non-primitively divergent vertices of Yang–Mills theory

Running coupling in the conformal window of large-Nf QCD

Gluon propagators in maximally Abelian gauge in SU(3) lattice QCD

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