QCD propagators and vertices from lattice QCD (in memory of Michael M\"uller-Preu{\ss}ker)

TL;DR

This paper reviews lattice QCD calculations of propagators and vertices in Landau gauge, highlighting their role as benchmarks for continuum methods and including recent finite temperature and dynamical fermion results.

Contribution

It summarizes key lattice QCD results for QCD Greens functions and emphasizes Michael M"uller-Preu{}ker's contributions to this research area.

Findings

Lattice results serve as benchmarks for continuum QCD approaches.

Provides low-energy propagator and vertex data at zero and finite temperature.

Includes dynamical fermion effects in lattice calculations.

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 M\"uller-Preu{\ss}ker's important contributions to this field and put them into the perspective of his other research interests.