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

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 around 1 to 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 by-product, we can also provide the prediction < g(2)A(2)> approximate to 3 GeV2 obtained at the renormalization scale mu = 10 GeV.