Consistent OPE Description of Gluon Two- and Three-point Green Function?

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 $A_μA^μ$ 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 $β_2^{\rm MOM}$ should be equal to $1.5(3)\times β_2^{\widetilde{\rm MOM}}=7400(1500)$ 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.