We present preliminary lattice results for the nonperturbative tensor structure of the vector and axial-vector quark-antiquark vertices in QCD. Our lattice calculations are for $N_f=2$ mass-degenerate Wilson fermion flavors whose quark mass values in
clude an almost physical one. We compare our lattice results with the corresponding continuum solutions of the inhomogeneous Bethe-Salpeter equations in a rainbow-ladder truncation. We find similarities in the momentum dependencies of the form factors but also clear deviations at low momentum.
We study the nonperturbative structure of the quark-photon vertex in Landau gauge. To this end, we utilize lattice QCD data for the vector current for two mass-degenerate quark flavours and extract all longitudinal and transverse form factors of the
underlying vertex for two off-shell kinematics. The momentum dependence of the form factors is compared to the solution of the inhomogeneous Bethe-Salpeter equation for the vertex in the rainbow-ladder approximation. Differences but also similarities are seen between our lattice and the truncated continuum results.
We report on preliminary results for the triple-gluon and the quark-gluon vertex in Landau gauge. Our results are based on two-flavor and quenched lattice QCD calculations for different quark masses, lattice spacings and volumes. We discuss the momen
tum dependence of some of the verticess form factors and the deviations from the tree-level form.
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 Dy
son-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 Muller-Preu{ss}kers important contributions to this field and put them into the perspective of his other research interests.
We derive the Dyson-Schwinger equation of a link variable in SU(n) lattice gauge theory in minimal Landau gauge and confront it with Monte-Carlo data for the different terms. Preliminary results for the lattice analog of the Kugo-Ojima confinement criterion is also shown.
The treatment of hypercubic lattice artifacts is essential for the calculation of non-perturbative renormalization constants of RI-MOM schemes. It has been shown that for the RI-MOM scheme a large part of these artifacts can be calculated and subtrac
ted with the help of diagrammatic Lattice Perturbation Theory (LPT). Such calculations are typically restricted to 1-loop order, but one may overcome this limitation and calculate hypercubic corrections for any operator and action beyond the 1-loop order using Numerical Stochastic Perturbation Theory (NSPT). In this study, we explore the practicability of such an approach and consider, as a first test, the case of Wilson fermion bilinear operators in a quenched theory. Our results allow us to compare boosted and unboosted perturbative corrections up to the 3-loop order.
The subtraction of hypercubic lattice corrections, calculated at 1-loop order in lattice perturbation theory (LPT), is common practice, e.g., for determinations of renormalization constants in lattice hadron physics. Providing such corrections beyond
1-loop order is however very demanding in LPT, and numerical stochastic perturbation theory (NSPT) might be the better candidate for this. Here we report on a first feasibility check of this method and provide (in a parametrization valid for arbitrary lattice couplings) the lattice corrections up to 3-loop order for the SU(3) gluon and ghost propagators in Landau gauge. These propagators are ideal candidates for such a check, as they are available from lattice simulations to high precision and can be combined to a renormalization group invariant product (Minimal MOM coupling) for which a 1-loop LPT correction was found to be insufficient to remove the bulk of the hypercubic lattice artifacts from the data. As a bonus, we also compare our results with the ever popular H(4) method.
We study the gluon and ghost propagators of SU(2) lattice Landau gauge theory and find their low-momentum behavior being sensitive to the lowest non-trivial eigenvalue (lambda_1) of the Faddeev-Popov operator. If the gauge-fixing favors Gribov copies
with small (large) values for lambda_1 both the ghost dressing function and the gluon propagator get enhanced (suppressed) at low momentum. For larger momenta no dependence on Gribov copies is seen. We compare our lattice data to the corresponding (decoupling) solutions from the DSE/FRGE study of Fischer, Maas and Pawlowski [Annals Phys. 324 (2009) 2408] and find qualitatively good agreement.
