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

Abstract

We perform an OPE analysis of the flavorless nonperturbative 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 2 MOM should be equal to 1.5(3)×β 2 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.