We demonstrate the utility of a spectral approximation to fermion loop operators using low-lying eigenmodes of the hermitian Dirac-Wilson matrix, Q = γ5M . The investigation is based on a total of 400 full QCD vacuum configurations, with two degenerate flavors of dynamical Wilson fermions at β = 5.6, at two different sea quark masses. The spectral approach is highly competitive for accessing both topological charge and disconnected diagrams, on large lattices and small quark masses. We propose suitable partial summation techniques that provide sufficient saturation for estimating Tr Q −1 , which is related to the topological charge. In the effective mass plot of the η ′ meson we achieved a consistent early plateau formation, by ground state projecting the connected piece of its propagator. PACS: 11.15.Ha, 12.38.Gc 2 We employ the Arnoldi method as provided by the parallel Arnoldi Package PARPACK [23] from Rice University. The Arnoldi method is designed for non-hermitian matrices, but it reduces, when applied to a hermitian matrix, to the Lanczos method.

We calculate glueball and torelon masses as well as the lowest lying hybrid potential in addition to the static ground state potential in lattice simulations of QCD with two flavours of dynamical Wilson fermions. The results are obtained on lattices with 16 3 × 32 and 24 3 × 40 sites at β = 5.6, corresponding to a lattice spacing, a −1 = 2.65 +5 −8 GeV, as determined from the Sommer force radius, at physical sea quark mass. The range spanned in the present study of five different quark masses is reflected in the ratios, 0.83 ≥ mπ/mρ ≥ 0.57.

We calculate connected and disconnected contributions to the flavour singlet scalar density amplitude of the nucleon in a full QCD lattice simulation with n f = 2 dynamical Wilson fermions at β = 5.6 on a 16 3 × 32 lattice. We find that both contributions are of similar size at the light quark mass. We arrive at the estimate σ πN = 18(5)MeV. Its smallness is directly related to the apparent decrease of u, d quark masses when unquenching QCD lattice simulations. The y parameter can be estimated from a semi-quenched analysis, in which there are no strange quarks in the sea, the result being y = 0.59(13).

Moments of the quark density, helicity, and transversity distributions are calculated in unquenched lattice QCD. Calculations of proton matrix elements of operators corresponding to these moments through operator product expansion have been performed on 16 3 ϫ32 lattices for Wilson fermions at ␤ϭ5.6 using configurations from the SESAM Collaboration and at ␤ϭ5.5 using configurations from SCRI. One-loop perturbative renormalization corrections are included. At quark masses accessible in present calculations, there is no statistically significant difference between quenched and full QCD results, indicating that the contributions of quark-antiquark excitations from the Dirac sea are small. The close agreement between calculations with cooled configurations containing essentially only instantons and the full gluon configurations indicates that quark zero modes associated with instantons play a dominant role. A naive linear extrapolation of the full QCD calculation to the physical pion mass yields results inconsistent with experiment. An extrapolation to the chiral limit including the physics of the pion cloud can resolve this discrepancy and the requirements for a definitive chiral extrapolation are described.

For lattice QCD with two sea quark flavors we study the static quark-antiquark potential V(R) in the regime where string breaking is expected. In order to increase the statistics, we make full use of the lattice information by including all lattice vectors R to any given separation Rϭ͉R͉ in the infrared regime. The corresponding paths between the lattice points are constructed by means of a generalized Bresenham algorithm as known from computer graphics. As a result, we achieve a determination of the Wilson loops in the range 0.8-1.5 fm with hitherto unknown precision. Finally, we discuss the impact of this approach on the signal of the transition matrix element between two-and four-quark states.