Two loop effective potential for langleA2μrangle in the Landau gauge in quantum chromodynamics

Browne, R. E.; Gracey, J.A.

doi:10.1088/1126-6708/2003/11/029

Cited by 62 publications

(139 citation statements)

References 54 publications

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“…These clearly extend the analogous results for the original 1 2 A a 2 µ , which were derived in [3,11]. Whilst we follow the same procedures here as [11], there are some novel features associated with treating an operator with free Lorentz indices, especially since it is also traceless.…”

Section: Loop Calculationssupporting

confidence: 77%

“…Whilst we follow the same procedures here as [11], there are some novel features associated with treating an operator with free Lorentz indices, especially since it is also traceless. First, we note that we take the same general point of view as [11] and include N f flavours of massless quarks and for the moment also consider the operator in an arbitrary linear covariant gauge with parameter α. At the end we will return to Yang-Mills and the Landau gauge α = 0.…”

Section: Loop Calculationsmentioning

confidence: 99%

“…Before doing this, we can already check whether for small A, the minimum m 2 = (2.03Λ MS ) 2 from [3,11] is a stable one. A Taylor expansion around A = 0 yields …”

Section: Minimum Of the Potentialmentioning

confidence: 99%

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Asymmetry of the dimension-two gluon condensate: The zero temperature case

Vercauteren

Verschelde

2009

Phys. Rev. D

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We provide an algebraic study of the local composite operators A µ A ν − δ µν d A 2 κ and A 2 µ , with d = 4 the spacetime dimension. We prove that these are separately renormalizable to all orders in the Landau gauge. This corresponds to a renormalizable decomposition of the operator A µ A ν into its trace and traceless part. We present explicit results for the relevant renormalization group functions to three loop order, accompanied with various tests of these results. We then develop a formalism to determine the zero temperature effective potential for the corresponding condensates, and recover the already known result for A 2 µ 0, together with A µ A ν − δ µν d A 2 κ = 0, a nontrivial check that the approach is consistent with Lorentz symmetry. The formalism is such that it is readily generalizable to the finite temperature case, which shall allow a future analytical study of the electric-magnetic symmetry of the A 2 µ condensate, which received strong evidence from recent lattice simulations by Chernodub and Ilgenfritz, who related their results to 3 regions in the Yang-Mills phase diagram.

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Section: Loop Calculationssupporting

confidence: 77%

Section: Loop Calculationsmentioning

confidence: 99%

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Asymmetry of the dimension-two gluon condensate: The zero temperature case

Vercauteren

Verschelde

2009

Phys. Rev. D

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“…In particular the explicit values of all the anomalous dimensions are required as the first step in the extension of the local composite operator (LCO) method for QCD, [18], to the MAG in various colour groups. This would thus open up the possibility of extending the effective potential calculations in the Landau gauge, [18,30], to situations beyond the few one loop SU (2) MAG studies already considered, [19,22,26,32,33]. This is the main aim of this article where we will perform the full MS renormalization of QCD in the MAG for an arbitrary colour group to determine the explicit values of the anomalous dimensions with the renormalizability of the gauge having been discussed in [32,34,35,36,37,38].…”

Section: Introductionmentioning

confidence: 99%

Three loop bar Mbar S renormalization of QCD in the maximal abelian gauge

Gracey

2005

J. High Energy Phys.

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Abstract. We determine the three loop anomalous dimensions of the quark, centre and offdiagonal gluons, centre and off-diagonal ghosts and the gauge fixing parameters in the maximal abelian gauge for an arbitrary colour group in the MS renormalization scheme at three loops. We show that the three loop MS β-function emerges from the renormalization of the centre gluon and also deduce the anomalous dimension of the BRST invariant dimension two mass operator. Moreover, we demonstrate that in the limit that the dimension of the centre of the group tends to zero, the anomalous dimensions of the quarks, off-diagonal gluons and off-diagonal ghosts tend to those of the quarks, gluons and ghosts of the Curci-Ferrari gauge respectively.

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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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Two loop effective potential for langleA²_μrangle in the Landau gauge in quantum chromodynamics

Cited by 62 publications

References 54 publications

Asymmetry of the dimension-two gluon condensate: The zero temperature case

Asymmetry of the dimension-two gluon condensate: The zero temperature case

Three loop bar Mbar S renormalization of QCD in the maximal abelian gauge

Description of gluon propagation in the presence of anA2condensate

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