We study the potential of a static quark anti-quark pair in the range 0.05fm \leq r \leq 0.8fm, employing a sequence of lattices up to 64^4. Lattice artifacts in potential and force are investigated theoretically as well as numerically and continuum quantities are obtained by extrapolation of the results at finite lattice spacing. Consistency of the numerical results with the form of scaling violations predicted by an analysis `a la Symanzik is found. The scale r_0/a is determined for the Wilson action up to beta=6.92.Comment: 24 pages (incl. tables), Late

We introduce a hadronic scale R 0 through the force F (r) between static quarks at intermediate distances r. The de nition F (R 0 )R 2 0 = 1:65 amounts to R 0 ' 0:5 fm in phenomenological potential models. Since R 0 is well de ned and can be calculated accurately in a Monte Carlo simulation, it is an ideal quantity to set the scale. In SU(2) pure gauge theory, we use new data (and R 0 to set the scale) to extrapolate F (r) to the continuum limit for distances r = 0:18 fm to r = 1:1 fm. Through R 0 we determine the energy scale in the recently calculated running coupling, which used the recursive nite size technique to reach large energy scales. Also in this case, the lattice data can be extrapolated to the continuum limit. The use of one loop Symanzik improvement is seen to reduce the lattice spacing dependence signi cantly.

We review lattice results related to pion, kaon, - and -meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor , arising in semileptonic transition at zero momentum transfer, as well as the decay-constant ratio of decay constants and its consequences for the CKM matrix elements and . Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of and Chiral Perturbation Theory and review the determination of the parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, we focus here on - and -meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant .

The coe cients multiplying the counterterms required for O(a) improvement of the action and the isovector axial current in lattice QCD are computed non-perturbatively, in the quenched approximation and for bare gauge couplings g 0 in the range 0 g 0 1. A nite-size method based on the Schr odinger functional is employed, which enables us to perform all calculations at zero or nearly zero quark mass. As a by-product the critical hopping parameter c is obtained at all couplings considered.

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor , arising in the semileptonic transition at zero momentum transfer, as well as the decay constant ratio and its consequences for the CKM matrix elements and . Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of and Chiral Perturbation Theory. We review the determination of the parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for and (also new compared to the previous review), as well as those for D- and B-meson-decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant .