Fundamental parameters of QCD

The theory of strong interactions, QCD, is described in terms of a few parameters, namely the strong coupling constant alpha_s and the quark masses. We show how these parameters can be determined reliably using computer simulations of QCD on a space-time lattice, and by employing a finite-size scaling method, which allows to trace the energy dependence of alpha_s and quark masses over several orders of magnitude. We also discuss methods designed to reduce the effects of finite lattice spacing and address the issue of computer resources required.Comment: Contribution to proceedings of NIC Symposium 2001, 13 pages, 7 figures, uses nic-series.cl

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

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 determination of the axial current normalization constant in O(a) improved lattice QCD

A finite-size technique is employed to compute the normalization constant $Z_A$ of the isovector axial current in lattice QCD. The calculation is carried out in the quenched approximation for values of the bare gauge coupling $g_0$ ranging from 0 to 1. In the lattice action and the lattice expression for the axial current we include the counterterms required for O(a) improvement, with non-perturbatively determined coefficients. With little additional work the normalization constant $Z_V$ of the improved isospin current is also obtained

Non-perturbative quark mass renormalization in quenched lattice QCD

The renormalization factor relating the bare to the renormalization group invariant quark masses is accurately calculated in quenched lattice QCD using a recursive finite-size technique. The result is presented in the form of a product of a universal factor times another factor, which depends on the details of the lattice theory but is easy to compute, since it does not involve any large scale differences. As a byproduct the Lambda-parameter of the theory is obtained with a total error of 8%

Some new results in O(a) improved lattice QCD

It is shown how on-shell O(a) improvement can be implemented non-perturbatively in lattice QCD with Wilson quarks. Improvement conditions are obtained by requiring the PCAC relation to hold exactly in certain matrix elements. These are derived from the QCD Schrödinger functional which enables us to simulate directly at vanishing quark masses. In the quenched approximation and for bare couplings in the range $0\leq g_0\leq 1$, we determine the improved action, the improved axial current, the additive renormalization of the quark mass and the isospin current normalization constants Z_A and Z_V

First results on the running coupling in QCD with two massless flavours

We report on the non-perturbative computation of the running coupling of two-flavour QCD in the Schr"odinger functional scheme. The corresponding Lambda-parameter, which describes the coupling strength at high energy, is related to a low energy scale which still remains to be connected to a hadronic ``experimentally'' observable quantity. We find the non-perturbative evolution of the coupling indispensable to avoid untolerable errors in the estimated Lambda-parameter.Comment: 14 pages, 5 figures, 3 tables, some changes in the data analysis after discovery and correction of an error in Nucl. Phys. B 525, 387 (1998) by C. Christou et al. (hep-lat/9801007v2, Erratum to appear

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

The Nf=0 heavy quark potential from short to intermediate distances

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