Lattice gluon and ghost propagators and the strong coupling in pure SU(3) Yang-Mills theory: Finite lattice spacing and volume effects

Abstract

The dependence of the Landau gauge two-point gluon and ghost correlation functions on the lattice spacing and on the physical volume are investigated for pure SU(3) Yang-Mills theory in four dimensions using lattice simulations. We present data from very large lattices up to 128 4 and for two lattice spacings 0.10 fm and 0.06 fm corresponding to volumes of ∼ð13 fmÞ 4 and ∼ð8 fmÞ 4 , respectively. Our results show that, for sufficiently large physical volumes, both propagators have a mild dependence on the lattice volume. On the other hand, the gluon and ghost propagators change with the lattice spacing a in the infrared region, with the gluon propagator having a stronger dependence on a compared to the ghost propagator. In what concerns the strong coupling constant α s ðp 2 Þ, as defined from gluon and ghost two-point functions, the simulations show a sizeable dependence on the lattice spacing for the infrared region and for momenta up to ∼1 GeV.

A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

“…The ghost propagator, however, is not enhanced anymore in the strong coupling and, for k ≈ 0, it behaves as 1/k 2 . Such behavior of the gluon and ghost propagator is in very good agreement with the most recent lattice simulations in the Landau gauge, see [17,20,[40][41][42][43]. An interesting property of the refinement of the GribovZwanziger action is that its occurrence depends on the spacetime dimension d. In particular, for d = 3, 4, the formation of dimension-two condensates is dynamically favored and the Gribov-Zwanziger action is naturally refined [37,44].…”

Nonperturbative finite-temperature Yang-Mills theory

“…The lattice results are renormalized as in [2]. Newer lattice results [125] agree with [124] if the largest physical volumes are compared.…”

Reply to “Comment on ‘Lattice gluon and ghost propagators and the strong coupling in pureSU(3)Yang-Mills theory: Finite lattice spacing and volume effects’ ”

“…Note that this "uncertainty" is not related to lattice artefacts or to Gribov copies effects. From Table I in [1] the lattice spacing reads a ¼ 0.1838ð11Þ fm for β ¼ 5.7, a ¼ 0.1016ð25Þ fm for β ¼ 6.0 and a ¼ 0.0627ð24Þ fm for β ¼ 6.3 which translates into a relative statistical error of 0.6%, 2.5% and 3.8%.…”

“…A simple procedure for the relative calibration of the lattice spacing in lattice simulations is suggested. The lattice studies of the gluon [1][2][3][4][5][6][7][8][9][10] and ghost [3,4,7,[11][12][13][14][15] propagators in pure Yang-Mills gauge theories have been thoroughly pursued in the past years. The emerging picture is a finite and non-vanishing gluon propagator in the infrared region, a manifestation of a nonperturbative mechanism responsible for the generation of a gluon mass scale, and a ghost propagator which follows closely its tree level value.…”

“…In [1,9,17] an attempt was made to estimate the combined effects of using a finite volume and a finite spacing on the simulations. For hypercubic lattices with a size La ≳ 6.5 fm, in the perturbative scaling window, the lattice propagators associated to simulations with a β ≳ 5.7 collapse into a single curve for momenta p ≳ 1 GeV.…”