Consistent OPE description of gluon two- and three-point Green functions?

Abstract

We perform an OPE analysis of the flavorless non-perturbative gluon propagator and the symmetric three-gluon vertex in the Landau gauge. The first subdominant operator is A µ A µ which can condensate in the Landau gauge "vacuum" although being a non-gauge invariant operator. We neglect all higher dimension operators. Then the gluon propagator and the symmetric three gluon vertex only depend on one common unknown condensate. We propose a consistency check from lattice data. At two loops for the leading coefficient and with 1/p 2 corrections at tree-level order the two fitted values for the condensate do not agree. At three loops we argue that the today unknown β MOM 2 should be equal to 1.5(3) × β MOM 2 = 7400(1500) to fulfill the OPE relation. Inclusion of the power corrections' anomalous dimensions should improve further the agreement. We show that these techniques cannot be applied to the asymmetric three gluon vertex with one vanishing momentum. P.A.C

ηandη′mesons and dimension 2 gluon condensate⟨A2⟩

“…(6) the lattice result g 2 A 2 = 2.76 GeV 2 of Ref. [8], a value compatible with the bound resulting from the discussions of Gubarev et al [9,10] on the physical meaning of A 2 and its possible importance for confinement. As for the contributions O i (1/Q 2 ) (i = A, G) in Eq.…”

“…(3) below] which the running coupling has in the Landau-gauge DS studies [20,28,29,30,31] and the ideas on the possible relevance of the A 2 gluon condensate [2,3,4,5,8,9,10,11,12,13,14]. In the present paper, we give a simplified and more intuitive derivation thereof as follows.…”

“…After it turned out more recently that the Landau-gauge value of A 2 corresponds to a more general gauge-invariant quantity, it attracted a lot of theoretical attention [8,9,10,11,12,13,14,15,16,17,18], to quote just several of many papers offering evidence that A 2 condensate may be important for the nonperturbative regime of Yang-Mills theories. In Ref.…”

Alpha, Lambda and Gluon condensate: Precision sudies with dynamical charm

“…It can be noted that to calculate the coupling more reliably we combined the bare lattice propagators in such a manner that the cut-off dependence is minimal, which prevents the check for the universality of condensates, as gluon and ghost propagators are not to be independently analyzed. However our previous studies in quenched approximation suggested that such universality (even including the three-gluon vertex) is indeed compatible with the numerical data (N f =0) [20,27,28,6,29,7]. This has been also supported by the calculations with N f =2 dynamical flavours [19,30].…”

“…[7,19] for N f =0 and N f =2 quark flavours respectively, we calculate the running coupling by equating numerical results and the OPE prediction. The OPE is clearly dominated by the landau gauge gluon condensate A 2 which has been elsewhere very much studied (e.g., see [20,21,22,23,24,25,26]). It can be noted that to calculate the coupling more reliably we combined the bare lattice propagators in such a manner that the cut-off dependence is minimal, which prevents the check for the universality of condensates, as gluon and ghost propagators are not to be independently analyzed.…”