Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate $⟨A^2⟩$ in the Landau gauge

Abstract

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 up to 1 á 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 $D(0)=8.3\pm 0.5{\text{GeV}}^{-2}$. As a byproduct, we can also provide the prediction $⟨g^2{A}^2⟩\approx 3{\text{GeV}}^2$ obtained at the renormalization scale $\mu =10\text{GeV}$.

Comments: 17 pages, 10 figures, updated version, accepted for publication in Phs.Rev.D