A determination of Aμ2 and the non-perturbative vacuum energy of Yang–Mills theory in the Landau gauge

Dudal, David; Verschelde, Henri; Browne, R. E.; Gracey, J.A.

doi:10.1016/s0370-2693(03)00541-0

Cited by 49 publications

(72 citation statements)

References 41 publications

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“…A nonvanishing condensate due to dimensional transmutation was favoured as it lowered the vacuum energy. Using a resummation of Feynman diagrams, more evidence for A 2 = 0 was given in [67].…”

Section: An Important Asset In the Computation D(pmentioning

confidence: 99%

Indirect lattice evidence for the refined Gribov-Zwanziger formalism and the gluon condensate⟨A2⟩in the Landau gauge

2010

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We consider the gluon propagator D(p 2 ) at various lattice sizes and spacings in the case of pure SU(3) Yang-Mills gauge theories using the Landau gauge fixing. We discuss a class of fits in the infrared region in order to (in)validate the tree level analytical prediction in terms of the (Refined) Gribov-Zwanziger framework. It turns out that an important role is played by the presence of the widely studied dimension two gluon condensate A 2 . Including this effect allows to obtain an acceptable fit up to 1á 1.5 GeV, while corroborating the Refined Gribov-Zwanziger prediction for the gluon propagator. We also discuss the infinite volume extrapolation, leading to the estimate D(0) = 8.3 ± 0.5 GeV −2 . As a byproduct, we can also provide the prediction g 2 A 2 ≈ 3 GeV 2 obtained at the renormalization scale µ = 10 GeV.

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Section: An Important Asset In the Computation D(pmentioning

confidence: 99%

Indirect lattice evidence for the refined Gribov-Zwanziger formalism and the gluon condensate⟨A2⟩in the Landau gauge

2010

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“…The dimension two condensate A 2 µ has received a great deal of attention in the last few years, see for example [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. This condensate was already introduced in [18] in order to analyze the gluon propagator within the Operator Product Expansion (OPE), while in [19] the condensate A 2 i was considered in the Coulomb gauge.…”

Section: Introductionmentioning

confidence: 99%

Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge

et al. 2005

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The local composite operator A 2 µ is added to the Zwanziger action, which implements the restriction to the Gribov region Ω in Euclidean Yang-Mills theories in the Landau gauge. We prove that Zwanziger's action with the inclusion of the operator A 2 µ is renormalizable to all orders of perturbation theory, obeying the renormalization group equations. This allows to study the dimension two gluon condensate A 2 µ by the local composite operator formalism when the restriction to the Gribov region Ω is taken into account. The resulting effective action is evaluated at one-loop order in the MS scheme. We obtain explicit values for the Gribov parameter and for the mass parameter due to A 2 µ , but the expansion parameter turns out to be rather large. Furthermore, an optimization of the perturbative expansion in order to reduce the dependence on the renormalization scheme is performed. The properties of the vacuum energy, with or without the inclusion of the condensate A 2 µ , are investigated. In particular, it is shown that in the original Gribov-Zwanziger formulation, i.e. without the inclusion of the operator A 2 µ , the resulting vacuum energy is always positive at oneloop order, independently from the choice of the renormalization scheme and scale. In the presence of A 2 µ , we are unable to come to a definite conclusion at the order considered. In the MS scheme, we still find a positive vacuum energy, again with a relatively large expansion parameter, but there are renormalization schemes in which the vacuum energy is negative, albeit the dependence on the scheme itself appears to be strong. Concerning the behaviour of the gluon and ghost propagators, we recover the well known consequences of the restriction to the Gribov region, and this in the presence of A 2 µ , i.e. an infrared suppression of the gluon propagator and an enhancement of the ghost propagator. Such a behaviour is in qualitative agreement with the results obtained from the studies of the Schwinger-Dyson equations and from lattice simulations.

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“…(There is a suggestion that such a condensate may be related to the presence of instantons in the vacuum [4].) The importance of that condensate raises the question of gauge invariance and there are now a large number of papers that address that and related issues [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. We will not attempt to review that large body of literature, but will consider how the presence of an < A a µ A µ a > condensate modifies the gluon propagator and the vacuum polarization function in QCD.…”

Section: Introductionmentioning

confidence: 99%

Description of gluon propagation in the presence of anA2condensate

Shakin

2005

Phys. Rev. D

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There is a good deal of current interest in the condensate < A a µ A µ a > which has been seen to play an important role in calculations which make use of the operator product expansion.That development has led to the publication of a large number of papers which discuss how that condensate could play a role in a gauge-invariant formulation. In the present work we consider gluon propagation in the presence of such a condensate which we assume to be present in the vacuum. We show that the gluon propagator has no on-mass-shell pole and, therefore, a gluon cannot propagate over extended distances. That is, the gluon is a nonpropagating mode in the gluon condensate. In the present work we discuss the properties of both the Euclidean-space and Minkowski-space gluon propagator. In the case of the Euclidean-space propagator we can make contact with the results of QCD lattice calculations of the propagator in the Landau gauge. With an appropriate choice of normalization constants, we present a unified representation of the gluon propagator that describes both the Minkowski-space and Euclidean-space dynamics in which the < A a µ A µ a > condensate plays an important role.

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A determination of Aμ2 and the non-perturbative vacuum energy of Yang–Mills theory in the Landau gauge

Cited by 49 publications

References 41 publications

Indirect lattice evidence for the refined Gribov-Zwanziger formalism and the gluon condensate⟨A2⟩in the Landau gauge

Indirect lattice evidence for the refined Gribov-Zwanziger formalism and the gluon condensate⟨A2⟩in the Landau gauge

Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge

Description of gluon propagation in the presence of anA2condensate

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