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’ ” (original) (raw)

Infrared behavior of gluon and ghost propagators from asymmetric lattices

Physical Review D, 2006

We present a numerical study of the lattice Landau gluon and ghost propagators in three-dimensional pure SU(2) gauge theory. Data have been obtained using asymmetric lattices (V = 20^2 X 40, 20^2 X 60, 8^2 X 64, 8^2 X 140, 12^2 X 140 and 16^2 X 140) for the lattice coupling beta = 3.4, in the scaling region. We find that the gluon (respectively ghost) propagator is suppressed (respec. enhanced) at small momenta in the limit of large lattice volume V. By comparing these results with data obtained using symmetric lattices (V = 60^3 and 140^3), we find that both propagators suffer from systematic effects in the infrared region (p \lesssim 650 MeV). In particular, the gluon (respec. ghost) propagator is less IR-suppressed (respec. enhanced) than in the symmetric case. We discuss possible implications of the use of asymmetric lattices.

Coulomb-gauge ghost and gluon propagators in SU(3) lattice Yang-Mills theory

Physical Review D, 2009

We study the momentum dependence of the ghost propagator and of the space and time components of the gluon propagator at equal time in pure SU (3) lattice Coulomb gauge theory carrying out a joint analysis of data collected independently at RCNP Osaka and Humboldt University Berlin. We focus on the scaling behavior of these propagators at β = 5.8, . . . , 6.2 and apply a matching technique to relate the data for the different lattice cutoffs. Thereby, lattice artifacts are found to be rather strong for both instantaneous gluon propagators at large momentum. As a byproduct we obtain the respective lattice scale dependences a(β) for the transversal gluon and the ghost propagator which indeed run faster with β than two-loop running, but slightly slower than what is known from the Necco-Sommer analysis of the heavy quark potential. The abnormal a(β) dependence as determined from the instantaneous time-time gluon propagator, D44, remains a problem, though. The role of residual gauge-fixing influencing D44 is discussed.

Infrared gluon and ghost propagators from lattice QCD

The European Physical Journal A, 2007

We report on the infrared limit of the quenched lattice Landau gauge gluon and ghost propagators as well as the strong coupling constant computed from large asymmetric lattices. The infrared lattice propagators are compared with the pure power law solutions from Dyson-Schwinger equations (DSE). For the gluon propagator, the lattice data is compatible with the DSE solution. The preferred measured gluon exponent being ∼ 0.52, favouring a vanishing propagator at zero momentum. The lattice ghost propagator shows finite volume effects and, for the volumes considered, the propagator does not follow a pure power law. Furthermore, the strong coupling constant is computed and its infrared behaviour investigated.

Exploring the infrared gluon and ghost propagators using large asymmetric lattices

Brazilian Journal of Physics, 2007

We report on the infrared limit of the quenched lattice Landau gauge gluon propagator computed from large asymmetric lattices. In particular, the compatibility of the pure power law infrared solution (q 2) 2κ of the Dyson-Schwinger equations is investigated and the exponent κ is measured. The lattice data favours κ ∼ 0.52, which would imply a vanishing zero momentum gluon propagator as predicted by the Kugo-Ojima confinement mechanism and the Zwanziger horizon condition. Results for the ghost propagator and for the running coupling constant are shown.

Infrared gluon and ghost propagator exponents from lattice QCD

The European Physical Journal C, 2009

The compatibility of the pure power law infrared solution of QCD and lattice data for the gluon and ghost propagators in Landau gauge is discussed. For the gluon propagator, the lattice data is well described by a pure power law with an infrared exponent κ ∼ 0.53, in the Dyson-Schwinger notation. κ is measured using a technique that suppresses finite volume effects. This value implies a vanishing zero momentum gluon propagator, in agreement with the Gribov-Zwanziger confinement scenario. For the ghost propagator, the lattice data seem not to follow a pure power law, at least for the range of momenta accessed in our simulation.

Nontrivial ghost-gluon vertex and the match of RGZ, DSE and lattice Yang-Mills propagators

2016

Either by solving the ghost propagator DSE or through a one-loop computation in the RGZ (Refined Gribov-Zwanziger) formalism, we show that a non-trivial ghost-gluon vertex is anyhow required to obtain a ghost propagator prediction compatible with the available corresponding lattice data in the SU(3) case. For the necessary gluon propagator input, we present RGZ tree level fits which account well for the gluon lattice data. Interestingly, this propagator can be rewritten in terms of a running gluon mass. A comparison of both DSE and RGZ results for the ghost propagator is furthermore provided. We also briefly discuss the connection between the RGZ and the OPE d = 2 gluon condensate. UHU-FP/12-010 1

Studying the infrared behaviour of gluon and ghost propagators using large asymmetric lattices

AIP Conference Proceedings, 2007

We report on the infrared limit of the quenched lattice Landau gauge gluon propagator computed from large asymmetric lattices. In particular, the compatibility of the pure power law infrared solution (q 2) 2κ of the Dyson-Schwinger equations is investigated and the exponent κ is measured. Some results for the ghost propagator and for the running coupling constant will also be shown.

Large momentum behavior of the ghost propagator in SU(3) lattice gauge theory

Physical Review D, 2005

We study the asymptotic behavior of the ghost propagator in the quenched SU(3) lattice gauge theory with Wilson action. The study is performed on lattices with a physical volume fixed around 1.6 fm and different lattice spacings: 0.100 fm, 0.070 fm and 0.055 fm. We implement an efficient algorithm for computing the Faddeev-Popov operator on the lattice. We are able to extrapolate the lattice data for the ghost propagator towards the continuum and to show that the extrapolated data on each lattice can be described up to four-loop perturbation theory from 2.0 GeV to 6.0 GeV. The three-loop values are consistent with those extracted from previous perturbative studies of the gluon propagator. However the effective Λ MS scale which reproduces the data does depend strongly upon the order of perturbation theory and on the renormalization scheme used in the parametrization. We show how the truncation of the perturbative series can account for the magnitude of the dependency in this energy range. The contribution of non-perturbative corrections will be discussed elsewhere.

Asymptotic behavior of the ghost propagator in SU3 lattice gauge theory

We study the asymptotic behavior of the ghost propagator in the quenched SU(3) lattice gauge theory with Wilson action. The study is performed on lattices with a physical volume fixed around 1.6 fm and different lattice spacings: 0.100 fm, 0.070 fm and 0.055 fm. We implement an efficient algorithm for computing the Faddeev-Popov operator on the lattice. We are able to extrapolate the lattice data for the ghost propagator towards the continuum and to show that the extrapolated data on each lattice can be described up to four-loop perturbation theory from 2.0 GeV to 6.0 GeV. The three-loop values are consistent with those extracted from previous perturbative studies of the gluon propagator. However the effective Λ MS scale which reproduces the data does depend strongly upon the order of perturbation theory and on the renormalization scheme used in the parametrization. We show how the truncation of the perturbative series can account for the magnitude of the dependency in this energy range. The contribution of non-perturbative corrections will be discussed elsewhere.