The infrared behavior of lattice QCD Green’s functions

Within the framework of lattice QCD we investigate different aspects of QCD in Landau gauge using Monte Carlo simulations. In particular, we focus on the low momentum behavior of gluon and ghost propagators. The gauge group is that of QCD, namely SU(3). For our study of the lattice gluodynamic, simulations were performed on several lattice sizes ranging from 12 to 48 at the three values of the inverse coupling constant β = 5.8, 6.0 and 6.2. Different systematic effects on the gluon and ghost propagators are studied. We demonstrate that the ghost dressing function systematically depends on the choice of Gribov copies at low momentum, while the influence on the gluon dressing function is not resolvable. Also the eigenvalue distribution of the Faddeev-Popov operator is sensitive to Gribov copies. We show that the influence of dynamical Wilson fermions on the ghost propagator is negligible at the momenta available to us. For this we have used gauge configurations which were generated with two dynamical flavors of clover-improved Wilson fermions. On the contrary, fermions affect the gluon propagator at large and intermediate momenta, in particular where the gluon propagator exposes its characteristic enhancement compared to the free propagator. We also analyze data for both propagators obtained on asymmetric lattices. By comparing these results with data obtained on symmetric lattices, we find that both the gluon and the ghost propagator suffer from systematic effects at the lowest on-axis momenta available on asymmetric lattices. We compare our data with the infrared exponents predicted in studies of truncated systems of Dyson-Schwinger equations for the gluon and ghost propagators. We cannot confirm neither the values for both exponents nor the relation which is proposed to hold between them. In any case, we demonstrate that the infrared behavior of gluon and ghost propagators, as found in this thesis, is consistent with different criteria for confinement. In fact, we verify that our data of the ghost propagator and also of the Kugo-Ojima confinement parameter satisfy the Kugo-Ojima confinement criterion. The Gribov-Zwanziger horizon condition is satisfied by the ghost propagator. Also the gluon propagator seems to vanish in the zero-momentum limit. However, we cannot judge without doubt on the existence of an infrared vanishing gluon propagator. Furthermore, explicit violation of reflection positivity by the transverse gluon propagator is shown for the quenched and unquenched case of SU(3) gauge theory. The running coupling constant given as a renormalization-group-invariant combination of the gluon and ghost dressing functions does not expose a finite infrared fixed point. Rather the data are in favor of an infrared vanishing coupling constant. This behavior does not change if the Gribov ambiguity or unquenching effects are taken into account. We also report on a first nonperturbative computation of the SU(3) ghost-gluon-vertex renormalization constant. We find that it deviates only weakly from being constant in the momentum subtraction scheme considered here. We present results of an investigation of the spectral properties of the Faddeev-Popov operator at β = 5.8 and 6.2 using the lattice sizes 12, 16 and 24. For this we have calculated the low-lying eigenvalues and eigenmodes of the Faddeev-Popov operator. The larger the volume the more eigenvalues are found accumulated close to zero. Using the eigenmodes for a spectral representation of the ghost propagator it turns out that for our smallest lattice only 200 eigenvalues and eigenmodes are sufficient to saturate the ghost propagator at lowest momentum. We associate exceptionally large values occurring occasionally in the Monte Carlo history of the ghost propagator at larger β to extraordinary contributions of the low-lying eigenmodes.