Non-perturbative O(a) improvement of the vector current

We discuss non-perturbative improvement of the vector current, using the Schroedinger Functional formalism. By considering a suitable Ward identity, we compute the improvement coefficient which gives the O(a) mixing of the tensor current with the vector one.Comment: 3 pages (LaTeX, 2 ps figures, styles), talk presented at Lattice 9

Non-perturbative renormalization of the axial current with improved Wilson quarks

We present a new normalization condition for the axial current, which is derived from the PCAC relation with non-vanishing mass. Using this condition reduces the O(r_0 m) corrections to the axial current normalization constant Z_A for an easier chiral extrapolation in the cases, where simulations at zero quark-mass are not possible. The method described here also serves as a preparation for a determination of Z_A in the full two-flavor theory.Comment: 3 pages, 3 figures, Lattice2003(improve

Non-Perturbative Improvement of the Anisotropic Wilson QCD Action

We describe the first steps in the extension of the Symanzik O($a$) improvement program for Wilson-type quark actions to anisotropic lattices, with a temporal lattice spacing smaller than the spatial one. This provides a fully relativistic and computationally efficient framework for the study of heavy quarks. We illustrate our method with accurate results for the quenched charmonium spectrum.Comment: LATTICE98(improvement), 3 pages, 4 figure

Moments of parton evolution probabilities on the lattice within the Schroedinger functional scheme

We define, within the Schroedinger functional scheme (SF), the matrix elements of the twist-2 operators corresponding to the first two moments of non-singlet parton densities. We perform a lattice one-loop calculation that fixes the relation between the SF scheme and other common schemes and shows the main source of lattice artefacts. This calculation sets the basis for a numerical evaluation of the non-perturbative running of parton densities.Comment: Latex file, 4 figures, 15 page

A New Way to Set the Energy Scale in Lattice Gauge Theories and its Application to the Static Force and αs\alpha_s in SU(2) Yang--Mills Theory

We introduce a hadronic scale $R_0$ through the force $F(r)$ between static quarks at intermediate distances $r$. The definition $F(R_0)R_0^2=1.65$ amounts to $R_0 \simeq 0.5$~fm in phenomenological potential models. Since $R_0$ is well defined 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 finite 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 significantly. Warning: The preprint is not completely fresh, but maybe you haven't seen it...Comment: accepted in Nucl. Phys. B, 18 pages postscript-file with all figure

A perturbative determination of O(a) boundary improvement coefficients for the Schr\"odinger Functional coupling at 1-loop with improved gauge actions

We determine O($a$) boundary improvement coefficients up to 1-loop level for the Schr\"odinger Functional coupling with improved gauge actions including plaquette and rectangle loops. These coefficients are required to implement 1-loop O($a$) improvement in full QCD simulations for the coupling with the improved gauge actions. To this order, lattice artifacts of step scaling function for each improved gauge action are also investigated. In addition, passing through the SF scheme, we estimate the ratio of $\Lambda$-parameters between the improved gauge actions and the plaquette action more accurately.Comment: 17 pages, 2 figures, 6 table

Lattice QCD without topology barriers

As the continuum limit is approached, lattice QCD simulations tend to get trapped in the topological charge sectors of field space and may consequently give biased results in practice. We propose to bypass this problem by imposing open (Neumann) boundary conditions on the gauge field in the time direction. The topological charge can then flow in and out of the lattice, while many properties of the theory (the hadron spectrum, for example) are not affected. Extensive simulations of the SU(3) gauge theory, using the HMC and the closely related SMD algorithm, confirm the absence of topology barriers if these boundary conditions are chosen. Moreover, the calculated autocorrelation times are found to scale approximately like the square of the inverse lattice spacing, thus supporting the conjecture that the HMC algorithm is in the universality class of the Langevin equation.Comment: Plain TeX source, 26 pages, 4 figures include

A new simulation algorithm for lattice QCD with dynamical quarks

A previously introduced multi-boson technique for the simulation of QCD with dynamical quarks is described and some results of first test runs on a $6^3\times12$ lattice with Wilson quarks and gauge group SU(2) are reported.Comment: 7 pages, postscript file (166 KB

The gradient flow running coupling with twisted boundary conditions

We study the gradient flow for Yang-Mills theories with twisted boundary conditions. The perturbative behavior of the energy density $\langle E(t)\rangle$ is used to define a running coupling at a scale given by the linear size of the finite volume box. We compute the non-perturbative running of the pure gauge $SU(2)$ coupling constant and conclude that the technique is well suited for further applications due to the relatively mild cutoff effects of the step scaling function and the high numerical precision that can be achieved in lattice simulations. We also comment on the inclusion of matter fields.Comment: 27 pages. LaTe

Continuous external momenta in non-perturbative lattice simulations: a computation of renormalization factors

We discuss the usage of continuous external momenta for computing renormalization factors as needed to renormalize operator matrix elements. These kind of external momenta are encoded in special boundary conditions for the fermion fields. The method allows to compute certain renormalization factors on the lattice that would have been very difficult, if not impossible, to compute with standard methods. As a result we give the renormalization group invariant step scaling function for a twist-2 operator corresponding to the average momentum of non-singlet quark densities.Comment: 28 pages, 10 figure