Indirect lattice evidence for the refined Gribov-Zwanziger formalism and the gluon condensate⟨A2⟩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 1á 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 byproduct, we can also provide the prediction g 2 A 2 ≈ 3 GeV 2 obtained at the renormalization scale µ = 10 GeV.

Exciting flavored bound states

“…Incidentally, this approximation bears similarity with common phenomenological Ansätze to the BSA for D mesons [76][77][78][79][80] and this is exactly what the values in Table III represent: masses and decay constants obtained with a model based on the lowest-order approximation for which the eigenvalues and BSA are real. The mass difference, ∆m [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] MeV, between the D and D s mesons is smaller than experimentally observed, i.e. ∆m ∼ 100 MeV.…”

Running gluon mass from a Landau gauge lattice QCD propagator

“…Lattice gluon propagators computed with larger volumes, but with a lattice spacing about twice the spacing considered in the present work, were reported in [24]. The two sets of data were compared in [8]. We will not repeat this exercise but will resume the outcome of the comparison.…”

“…Phenomenology favors a gluon mass between ∼ 0.500 GeV and ∼ 1.2 GeV depending on how the mass is defined -see table 15 in [4]. Furthermore, a dynamically generated gluon mass can be related with the presence of the A 2 gluon condensate, which is associated with the non-perturbative sector of QCD and whose role has been investigated by several authors -see, for example, [6,7,8] and references their in.…”

The Landau gauge gluon propagator at zero and finite temperature: accounting for the combined finite lattice spacing and finite volume effects

“…Note that for Z=1, the above expression is the tree level prediction of the so-called refined Gribov-Zwanziger action and, as shown in [7], it describes the infrared lattice gluon propagator up…”