The gluon and ghost propagator and the influence of Gribov copies

Abstract

The dependence of the Landau gauge gluon and ghost propagators on the choice of Gribov copies is studied in pure SU (3) lattice gauge theory. Whereas the influence on the gluon propagator is small, the ghost propagator becomes clearly affected by the copies in the infrared region. We compare our data with the infrared exponents predicted by the Dyson-Schwinger equation approach.The non-perturbative behaviour of the gluon and ghost propagators in Yang-Mills theories is of interest for the understanding of the mechanism of confinement of gluons and quarks. In particular the infrared behaviour of the ghost propagator in the Landau gauge is related to the so-called Kugo-Ojima confinement criterion [1], which expresses the absence of coloured massless asymptotic states from the spectrum of physical states in terms of the ghost propagator at vanishing momentum. On the other hand the suppression of the gluon propagator in the infrared was argued to be related to the gluon confinement [2].Zwanziger [3] has suggested that the behaviour of both propagators in Landau gauge results from the restriction of the gauge fields to the Gribov region, where the Faddeev-Popov operator is nonnegative. Generically, one gauge orbit has more than one intersection (Gribov copies) within the Gribov region. In this contribution we assess the importance of this ambiguity for the ghost and gluon propagator in SU (3) gauge theory on a finite lattice.In the continuum the gluon and ghost propagators have been computed from a coupled and truncated set of Dyson-Schwinger (DS) equations [4]. Representing the gluon and ghost propagators in the Landau gauge as D ab µν (q 2 ) = δ ab δ µν − q µ q ν /q 2 Z gl (q 2 )/q 2 , G ab (q 2 ) = δ ab Z gh (q 2 )/q 2

Infrared behavior of gluon and ghost propagators from asymmetric lattices

“…In this work we did not do a systematic study of Gribov-copy effects [24,50,51,52,53,54,55,56,57] for the two propagators, since here we are interested in possible systematic effects due to the use of asymmetric lattices. Let us recall that evidences of Gribov-copy effects in lattice Landau gauge have been found by various authors [24,54,55,56,57] for the ghost propagator and, recently, also for the gluon propagator [53,57], these effects being usually stronger at small momenta. Such effects have also been found [50,54] for the horizon tensor (and for the horizon function), for the smallest eigenvalue of the Faddeev-Popov matrix, for the Kugo-Ojima parameter and for the running coupling constant (defined using gluon and ghost propagators).…”

Low-momentum ghost dressing function and the gluon mass

“…In contrast, alternative DSE solutions were also predicted to give a massive gluon propagator [2,3]. Lattice QCD (LQCD) estimates for those propagators appeared to be also in contradiction with a gluon propagator that vanishes at zero-momentum or with a ghost dressing function that diverges [4][5][6][7]. We addressed this issue in two recent papers [8,9] and tried to clarify the contradiction.…”

Three-gluon running coupling from lattice QCD at N f = 2 + 1 + 1: a consistency check of the OPE approach

“…Such an ambiguity on the gauge-fixing may introduce disrupting deviations for the confrontation of continuum and Landau-gauge lattice quantities. On the lattice, this ambiguity has been scrutinized by comparing the results from a "best copy", selected as the minimum of the functional for a sample of random copies, with the ones from the "first copy" resulting from the minimisation [52][53][54]. The selection of the "best copy" has been also improved in recent investigations by the application of the so-called simulated annealing (SA) gaugefixing algorithm [55][56][57].…”