We present recent results for the Landau-gauge gluon and ghost propagators in SU (3) lattice gluodynamics obtained on a sequence of lattices with linear extension ranging from L = 64 to L = 96 at β = 5.70, thus reaching "deep infrared" momenta down to 75 MeV. Our gauge-fixing procedure essentially uses a simulated annealing technique which allows us to reach gauge-functional values closer to the global maxima than standard approaches do. Our results are consistent with the so-called decoupling solutions found for Dyson-Schwinger and functional renormalization group equations.

We present recent results on the Landau gauge gluon and ghost propagators in SU(3) pure gauge theory at Wilson β = 5.7 for lattice sizes up to 80 4 corresponding to physical volumes up to (13.2 fm) 4 . In particular, we focus on finite-volume and Gribov-copy effects. We employ a gauge-fixing method that combines a simulated annealing algorithm with finalizing overrelaxation. We find the gluon propagator for the largest volumes to become flat at q 2 ∼ 0.01 GeV 2 . Although not excluded by our data, there is still no clear indication of a gluon propagator tending towards zero in the zero-momentum limit. New data for the ghost propagator are reported, too. The XXV International Symposium on Lattice Field Theory

We introduce the minimal momentum subtraction (MiniMOM) scheme for QCD. Its definition allows the strong coupling to be fixed solely through a determination of the gluon and ghost propagators. In Landau gauge this scheme has been implicit in the early studies of these propagators, especially in relation to their non-perturbative behaviour in the infrared and the associated infrared fixed-point. Here we concentrate on its perturbative use. We give the explicit perturbative definition of the scheme and the relation of its β-function and running coupling to the MS scheme up to 4-loop order in general covariant gauges. We also demonstrate, by considering a selection of N f = 3 examples, that the apparent convergence of the relevant perturbative series can in some (though not all) cases be significantly improved by re-expanding the MS coupling version of this series in terms of the MiniMOM coupling, making the MiniMOM coupling also of potential interest in certain phenomenological applications.

We study the behavior of the gluon and ghost dressing functions in SU (3) Landau gauge at low momenta available on lattice sizes 12 4 − 32 4 at β = 5.8, 6.0 and 6.2. We demonstrate the ghost dressing function to be systematically dependent on the choice of Gribov copies, while the influence on the gluon dressing function is not resolvable. The running coupling given in terms of these functions is found to be decreasing for momenta q < 0.6 GeV. We study also effects of the finite volume and of the lattice discretization.

We compute the axial, scalar, tensor and pseudoscalar isovector couplings of the nucleon as well as the induced tensor and pseudoscalar charges in lattice simulations with N f = 2 massdegenerate non-perturbatively improved Wilson-Sheikholeslami-Wohlert fermions. The simulations are carried out down to a pion mass of 150 MeV and linear spatial lattice extents of up to 4.6 fm at three different lattice spacings ranging from approximately 0.08 fm to 0.06 fm. Possible excited state contamination is carefully investigated and finite volume effects are studied. The couplings, determined at these lattice spacings, are extrapolated to the physical pion mass. In this limit we find agreement with experimental results, where these exist, with the exception of the magnetic moment. A proper continuum limit could not be performed, due to our limited range of lattice constants, but no significant lattice spacing dependence is detected. Upper limits on discretization effects are estimated and these dominate the error budget.

We report on recent numerical computations of the Landau gauge gluon and ghost propagators as well as of the ghost-gluon-vertex function in pure SU(3) Yang-Mills theory and in full QCD on the lattice. Special emphasis is paid to the low momentum region. In particular, we present new data for the gluon propagator at momenta below 300 MeV. We also discuss different systematic effects as there are finite-size, lattice discretization and Gribov copy but also unquenching effects. A MOM-scheme running coupling α s (q 2 ) based on the ghost-gluon vertex is calculated and found to decrease for momenta below 550 MeV, even though the renormalization constant of the vertex deviates only weakly from being constant.

The Landau-gauge gluon propagator is studied using the coarse and fine dynamical MILC configurations. The effects of dynamical quarks are clearly visible and lead to a reduction of the nonperturbative infrared enhancement relative to the quenched case. Lattice spacing effects are studied and found to be small. The gluon spectral function is shown to clearly violate positivity in both quenched and full QCD.

We propose a modified lattice Landau gauge based on stereographically projecting the link variables on the circle S 1 → R for compact U(1) or the 3-sphere S 3 → R 3 for SU(2) before imposing the Landau gauge condition. This can reduce the number of Gribov copies exponentially and solves the Gribov problem in compact U(1) where it is a lattice artifact. Applied to the maximal Abelian subgroup this might be just enough to avoid the perfect cancellation amongst the Gribov copies in a lattice BRST formulation for SU(N), and thus to avoid the Neuberger 0/0 problem. The continuum limit of the Landau gauge remains unchanged.