Exploring the infrared structure of QCD with the Gribov-Zwanziger Lagrangian

Gracey, J.A.

doi:10.1590/s0103-97332007000200011

Cited by 3 publications

(5 citation statements)

References 35 publications

(84 reference statements)

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“…Thus, as in the scaling solution of the gluon and ghost DSEs, the gluon propagator is null at zero momentum 12 and the ghost propagator is IRenhanced [42]. These tree-level results, also in agreement with the original work by Gribov [35], have been confirmed by one-loop calculations in the three-and fourdimensional cases [81][82][83][84][85].…”

Section: Introductionsupporting

confidence: 81%

No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the2dgluon propagator

2012

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We study general properties of the Landau-gauge Gribov ghost form factor ðp 2 Þ for SUðN c Þ Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d ¼ 3, 4 with respect to the d ¼ 2 case. In particular, considering any (sufficiently regular) gluon propagator Dðp 2 Þ and the one-loop-corrected ghost propagator, we prove in the 2d case that the function ðp 2 Þ blows up in the infrared limit p ! 0 as ÀDð0Þ lnðp 2 Þ. Thus, for d ¼ 2, the no-pole condition ðp 2 Þ < 1 (for p 2 > 0) can be satisfied only if the gluon propagator vanishes at zero momentum, that is, Dð0Þ ¼ 0. On the contrary, in d ¼ 3 and 4, ðp 2 Þ is finite also if Dð0Þ > 0. The same results are obtained by evaluating the ghost propagator Gðp 2 Þ explicitly at one loop, using fitting forms for Dðp 2 Þ that describe well the numerical data of the gluon propagator in two, three and four space-time dimensions in the SU(2) case. These evaluations also show that, if one considers the coupling constant g 2 as a free parameter, the ghost propagator admits a one-parameter family of behaviors ( labeled by g 2 ), in agreement with previous works by Boucaud et al. In this case the condition ð0Þ 1 implies g 2 g 2 c , where g 2 c is a ''critical'' value. Moreover, a freelike ghost propagator in the infrared limit is obtained for any value of g 2 smaller than g 2 c , while for g 2 ¼ g 2 c one finds an infrared-enhanced ghost propagator. Finally, we analyze the Dyson-Schwinger equation for ðp 2 Þ and show that, for infrared-finite ghost-gluon vertices, one can bound the ghost form factor ðp 2 Þ. Using these bounds we find again that only in the d ¼ 2 case does one need to impose Dð0Þ ¼ 0 in order to satisfy the no-pole condition. The d ¼ 2 result is also supported by an analysis of the Dyson-Schwinger equation using a spectral representation for the ghost propagator. Thus, if the no-pole condition is imposed, solving the d ¼ 2 Dyson-Schwinger equations cannot lead to a massive behavior for the gluon propagator. These results apply to any Gribov copy inside the so-called first Gribov horizon; i.e., the 2d result Dð0Þ ¼ 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.

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Section: Introductionsupporting

confidence: 81%

No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the2dgluon propagator

2012

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“…This result is confirmed by one-loop calculations [46,47]. The above expression for the gluon propagator implies that D(p 2 ) is null at zero momentum, which in turn indicates maximal violation of reflection positivity for the real-space gluon propagator D(x) [45].…”

Section: The Gribov-zwanziger Actionsupporting

confidence: 57%

Modeling the gluon propagator in Landau gauge: Lattice estimates of pole masses and dimension-two condensates

et al. 2012

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We present an analytic description of numerical results for the Landau-gauge SU(2) gluon propagator D(p 2 ), obtained from lattice simulations (in the scaling region) for the largest lattice sizes to date, in d = 2, 3 and 4 space-time dimensions. Fits to the gluon data in 3d and in 4d show very good agreement with the tree-level prediction of the Refined Gribov-Zwanziger (RGZ) framework, supporting a massive behavior for D(p 2 ) in the infrared limit. In particular, we investigate the propagator's pole structure and provide estimates of the dynamical mass scales that can be associated with dimension-two condensates in the theory. In the 2d case, fitting the data requires a non-integer power of the momentum p in the numerator of the expression for D(p 2 ). In this case, an infinite-volume-limit extrapolation gives D(0) = 0. Our analysis suggests that this result is related to a particular symmetry in the complex-pole structure of the propagator and not to purely imaginary poles, as would be expected in the original Gribov-Zwanziger scenario.

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“…For a detailed discussion of how the dressings are related to gauge fixings we refer the reader to references [27,28]. To connect our discussion to those of [13,16,17] we shall take space time to be Euclidian so that the Laplacian = ∂ µ ∂ µ has a unique Green's function.…”

Section: Dressing and The Residual Abelian Gauge Structurementioning

confidence: 99%

“…Having identified the role of the field strength F µν (16) in defining a non-abelian mass term (24), and having defined the gauge covariant inverse Laplacian thus allowing for a perturbative definition of the Zwanziger term (48), we now connect these descriptions by identifying the common role played by the dressed field strength F h µν (17).…”

Section: The Role Of the Dressed Field Strengthmentioning

confidence: 99%

“…The construction of potentially physical mass terms has generated an interesting debate about gauge invariant expansions. This has a long history [7,8], even in QED [9], but has had a resurgence in pure gauge theory over the past decade [10][11][12][13][14][15][16][17] which can be traced to a large extent to a seminal paper by Zwanziger [18] where the gauge invariance of this construction was addressed. In particular Zwanziger introduced an expansion for a non-abelian mass term as a sum of separately gauge invariant terms.…”

Section: Introductionmentioning

confidence: 99%

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Factorization of glue and mass terms inSU(N)gauge theories

2012

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In this paper we investigate the structure of the glue in Zwanziger's gauge invariant expansion for the A 2 -type mass term in Yang-Mills theory. We show how to derive this expansion, in terms of the inverse covariant Laplacian, and extend it to higher orders. In particular, we give an explicit expression, for the first time, for the next to next to leading order term. We further show that the expansion is not unique and give examples of the resulting ambiguity.

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Exploring the infrared structure of QCD with the Gribov-Zwanziger Lagrangian

Abstract: We review recent one and two loop MS Landau gauge calculations using the Gribov-Zwanziger Lagrangian. The behaviour of the gluon and Faddeev-Popov ghost propagators as well as the renormalization group invariant effective coupling constant is examined in the infrared limit.

Cited by 3 publications

References 35 publications

No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the2dgluon propagator

No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the2dgluon propagator

Modeling the gluon propagator in Landau gauge: Lattice estimates of pole masses and dimension-two condensates

Factorization of glue and mass terms inSU(N)gauge theories

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