As computing resources are limited, choosing the parameters for a full Lattice QCD simulation always amounts to a compromise between the competing objectives of a lattice spacing as small, quarks as light, and a volume as large as possible. Aiming to push unquenched simulations with the Wilson action towards the computationally expensive regime of small quark masses we address the question whether one can possibly save computing time by extrapolating results from small lattices to the infinite volume, prior to the usual chiral and continuum extrapolations. In the present work the systematic volume dependence of simulated pion and nucleon masses is investigated and compared with a long-standing analytic formula by Lüscher and with results from Chiral Perturbation Theory (ChPT). We analyze data from Hybrid Monte Carlo simulations with the standard (unimproved) two-flavor Wilson action at two different lattice spacings of a ≈ 0.08 fm and 0.13 fm. The quark masses considered correspond to approximately 85 and 50% (at the smaller a) and 36% (at the larger a) of the strange quark mass. At each quark mass we study at least three different lattices with L/a =10 to 24 sites in the spatial directions (L =0.85-2.08 fm).
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.
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.
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