SSOR preconditioning in simulations of the QCD Schr\"odinger functional

We report on a parallelized implementation of SSOR preconditioning for O(a) improved lattice QCD with Schr\"odinger functional boundary conditions. Numerical simulations in the quenched approximation at parameters in the light quark mass region demonstrate that a performance gain of a factor $\sim$ 1.5 over even-odd preconditioning can be achieved.Comment: 15 pages, latex2e, 4 Postscript figures, uses packages elsart and epsfi

Renormalization group invariant average momentum of non-singlet parton densities

We compute, within the Schr\"odinger functional scheme, a renormalization group invariant renormalization constant for the first moment of the non-singlet parton distribution function. The matching of the results of our non-perturbative calculation with the ones from hadronic matrix elements allows us to obtain eventually a renormalization group invariant average momentum of non-singlet parton densities, which can be translated into a preferred scheme at a specific scale.Comment: Latex2e file, 4 figures, 12 page

Monte Carlo determination of the critical coupling in ϕ24\phi^4_2 theory

We use lattice formulation of $\phi^4$ theory in order to investigate non--perturbative features of its continuum limit in two dimensions. In particular, by means of Monte Carlo calculations, we obtain the critical coupling constant $g/\mu^2$ in the continuum, where $g$ is the {\em unrenormalised} coupling. Our final result is $g/\mu^2=11.15(6)(3)$.Comment: Version published on Phys. Rev. D. We added a reference and modified a couple of sentence

Universal continuum limit of non-perturbative lattice non-singlet moment evolution

We present evidence for the universality of the continuum limit of the scale dependence of the renormalization constant associated with the operator corresponding to the average momentum of non-singlet parton densities. The evidence is provided by a non-perturbative computation in quenched lattice QCD using the Schr\"odinger Functional scheme. In particular, we show that the continuum limit is independent of the form of the fermion action used, i.e. the Wilson action and the non-perturbatively improved clover action.Comment: Latex2e file, 2 figures, 9 page

Low energy physics from the QCD Schr\"odinger functional

We review recent work by the ALPHA and UKQCD Collaborations where masses and matrix elements were computed in lattice QCD using Schr\"odinger functional boundary conditions and where the strange quark mass was determined in the quenched approximation. We emphasize the general concepts and our strategy for the computation of quark masses.Comment: Talks at LATTICE99 (QCD Spectrum and Quark Masses), 5 pages, latex2e, 5 Postscript figures, uses epsfig, amssymb and espcrc

Non-perturbative results for the coefficients b_m and b_a-b_p in O(a) improved lattice QCD

We determine the improvement coefficients b_m and b_a-bp in quenched lattice QCD for a range of beta-values, which is relevant for current large scale simulations. At fixed beta, the results are rather sensitive to the precise choices of parameters. We therefore impose improvement conditions at constant renormalized parameters, and the coefficients are then obtained as smooth functions of g_0^2. Other improvement conditions yield a different functional dependence, but the difference between the coefficients vanishes with a rate proportional to the lattice spacing. We verify this theoretical expectation in a few examples and are therefore confident that O(a) improvement is achieved for physical quantities. As a byproduct of our analysis we also obtain the finite renormalization constant which relates the subtracted bare quark mass to the bare PCAC mass.Comment: 25 pages, 8 figures, minor change at figure

Hadron masses and matrix elements from the QCD Schr"odinger functional

We explain how masses and matrix elements can be computed in lattice QCD using Schr"odinger functional boundary conditions. Numerical results in the quenched approximation demonstrate that good precision can be achieved. For a statistical sample of the same size, our hadron masses have a precision similar to what is achieved with standard methods, but for the computation of matrix elements such as the pseudoscalar decay constant the Schr"odinger functional technique turns out to be much more efficient than the known alternatives.Comment: 18 pages, late

Precision computation of a low-energy reference scale in quenched lattice QCD

We present results for the reference scale r_0 in SU(3) Lattice Gauge Theory for beta = 6/g_0^2 in the range 5.7 <= beta <= 6.57. The high relative accuracy of 0.3-0.6% in r_0/a was achieved through good statistics, the application of a multi-hit procedure and a variational approach in the computation of Wilson loops. A precise definition of the force used to extract r_0 has been used throughout the calculation which guarantees that r_0/a is a smooth function of the bare coupling and that subsequent continuum extrapolations are possible. The results are applied to the continuum extrapolations of the energy gap Delta in the static quark potential and the scale L_max/r_0 used in the calculation of the running coupling constant.Comment: A single uuencoded-gzipped-tar file: 15 pages, 5 figures small change at the end of the introductio