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arXiv · 1002.2374

Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate $\braket{A^2}$ in the Landau gauge

D. Dudal·O. Oliveira·N. Vandersickel
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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 $\braket{A^2}$. Including this effect allows to obtain an acceptable fit up to 1 \'{a} 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 $D(0)=8.3\pm0.5\text{GeV}^{-2}$. As a byproduct, we can also provide the prediction $\braket{g^2 A^2}\approx 3\text{GeV}^2$ obtained at the renormalization scale $\mu=10\text{GeV}$.

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D. Dudal, O. Oliveira, N. Vandersickel. 2010-02-11. Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate $\braket{A^2}$ in the Landau gauge. https://doi.org/10.1103/physrevd.81.074505

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