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We complete the non-perturbative calculations of the strange quark mass and the Lambda parameter in two flavor QCD by the ALPHA collaboration. The missing lattice scale is determined via the kaon decay constant, for whose chiral extrapolation complementary strategies are compared. We also give a value for the scale r_0 in physical units as well as an improved determination of the renormalization constant Z_A.Comment: 46 pages, 11 figures, v2: minor corrections, results unchange

The running of renormalized quark masses is computed in lattice QCD with two flavors of massless O(a) improved Wilson quarks. The regularization and flavor independent factor that relates running quark masses to the renormalization group invariant ones is evaluated in the Schroedinger Functional scheme. Using existing data for the scale r_0 and the pseudoscalar meson masses, we define a reference quark mass in QCD with two degenerate quark flavors. We then compute the renormalization group invariant reference quark mass at three different lattice spacings. Our estimate for the continuum value is converted to the strange quark mass with the help of chiral perturbation theory.Comment: 25 pages, 6 figures; sections 1 and 4 rearranged, minor change to the summary plo

We investigate the static potential in the confinement phase of the SU(2) Higgs model on the lattice, where this model is expected to have properties similar to QCD. We observe that Wilson loops are inadequate to determine the potential at large distances, where the formation of two color-neutral mesons is expected. Introducing smeared fields and a suitable matrix correlation function, we are able to overcome this difficulty. We observe string breaking at a distance r b ≈ 1.8r 0 , where the length scale r 0 has a value r 0 ≈ 0.5 fm in QCD. The method presented here may lead the way towards a treatment of string breaking in QCD.

The energy spectrum of a system containing a static quark anti-quark pair is computed for a wide range of source separations using lattice QCD with N f = 2 + 1 dynamical flavours. By employing a variational method with a basis including operators resembling both the gluon string and systems of two separated static mesons, the first three energy levels are determined up to and beyond the distance where it is energetically favourable for the vacuum to screen the static sources through light-or strange-quark pair creation, enabling both these screening phenomena to be observed. The separation dependence of the energy spectrum is reliably parameterised over this saturation region with a simple model which can be used as input for subsequent investigations of quarkonia above threshold and heavy-light and heavy-strange coupled-channel meson scattering.

We measure the static potential from Wilson loops constructed using hypercubic blocked (HYP) links. The HYP potential agrees with the potential measured using thin links for distances r/a ≥ 2. We calculated the lowest order perturbative expansion of the lattice Coulomb potential of HYP links. These results are used in analyzing the static potential both on quenched and dynamical lattices. The statistical accuracy of the potential with HYP links improves by about an order of magnitude, giving a reliable scale even with limited statistics both on quenched and dynamical lattices.

We address the locality problem arising in simulations, which take the square root of the staggered fermion determinant as a Boltzmann weight to reduce the number of dynamical quark tastes. A definition of such a theory necessitates an underlying local fermion operator with the same determinant and the corresponding Green's functions to establish causality and unitarity. We illustrate this point by studying analytically and numerically the square root of the staggered fermion operator. Although it has the correct weight, this operator is non-local in the continuum limit. Our work serves as a warning that fundamental properties of field theories might be violated when employing blindly the square root trick. The question, whether a local operator reproducing the square root of the staggered fermion determinant exists, is left open.Comment: 24 pages, 7 figures, few remarks added for clarity, accepted for publication in Nucl. Phys.

We present in detail a technique to extract the potential between a static quark and anti-quark pair from Wilson loops measured on dynamical configurations. This technique is based on HYP smearing and leads to an exponential improvement of the noise-to-signal ratio of Wilson loops. We explain why the correct continuum potential is obtained and show numerical evidence that the cut-off effects are small. We present precise results for the non-perturbative potential. As applications, we determine the scale r 0 /a and study the shape of the static potential in the range of distances around r 0 , where it can be compared with phenomenological potential models.