QCD propagators and vertices from lattice QCD (in memory of Michael Müller-Preußker)

Abstract

Abstract. We review lattice calculations of the elementary Greens functions of QCD with a special emphasis on the Landau gauge. These lattice results have been of interest to continuum approaches to QCD over the past 20 years. They are used as reference for Dyson-Schwinger-and functional renormalization group equation calculations as well as for hadronic bound state equations. The lattice provides low-energy data for propagators and three-point vertices in Landau gauge at zero and finite temperature even including dynamical fermions. We summarize Michael Müller-Preußker's important contributions to this field and put them into the perspective of his other research interests.

Quenched SU(2) scalar-gluon vertex in minimal Landau gauge

“…This would make the scalars indeed point-like, a feature which is also observed in the unquenched case [15]. This is very different from gluons, which seem to have a dramatically large (imaginary) radius [3,9,24,27,28,37,38], but very similar to ghosts [3,9,[26][27][28][29][30][31][32].…”

“…The presented investigation of the vertices shows, as for the propagators [17,18], unfortunately no obvious sign of how confinement in the Wilson sense acts differently on the fundamental and adjoint charges. In fact, the form factors do not show any substantial deviations from the tree-level at all, similarly to the ghost-gluon vertex [9,[26][27][28][29][30][31][32], but very different from the three-gluon vertex [9,24,27,28,37,38].…”

“…However, at least the fundamental scalar propagator in the unquenched theory shows essentially no dependence on how Gribov copies are treated, in contrast to the gauge propagators [35]. In addition, the only vertex whose has been investigated with respect to the influence of Gribov copies, the ghost-gluon vertex [31], did not show a stronger dependence than the corresponding propagators. It thus seems to be plausible that the treatment of Gribov copies will have only a minor, or even negligible, impact on the results presented here.…”

“…Thus, in total the fundamental scalar-gluon vertex does not show any significant deviation from the tree-level behavior. In fact, it is even less affected than the ghost-gluon vertex, which showed hitherto the smallest deviations from tree-level [26][27][28][29][30][31].…”

“…The technical setup of the employed lattice calculations will be discussed in section 2 and appendix A. It follows closely [17,18,26], utilizing that the scalar-gluon vertex is quite similar to the comparatively well-studied ghostgluon vertex [26][27][28][29][30][31][32]. Renormalization is discussed in section 3.…”