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

Universal behaviour of the SU(2) running coupling constant in the continuum limit

We present data from the ALPHA Collaboration about lattice calculation of SU(2) pure--gauge running coupling constant, obtained with two different definitions of the coupling itself, which show universality of the continuum limit and clarify the applicability of renormalized perturbation theory.Comment: 3 pages, postscript, contribution to LAT94 also available at http://sutova.roma2.infn.it/preprints/TovApe/lat94m.ps (eq. (3) corrected

Resonance Scattering on the Lattice with Non-Zero Total Momentum

Most hadronic particles are resonances: for example, the rho meson appears as a resonance in the elastic scattering of two pions. A method by Luescher enables one to measure the properties of the resonance particles from finite lattices. We present here a more general method which includes scattering processes where the total momentum of the particles is non-zero. The main advantage is that the resonance scattering can be observed in a considerably smaller spatial volume. We test the method with a simple 3+1 dimensional spin model, and find excellent agreement between the zero momentum and the non-zero momentum scattering sectors.Comment: 4 pages uuencoded postscript, contribution to LATTICE 9

Monte Carlo Calculation of Phase Shift in Four Dimensional O(4) ϕ4\phi^4 Theory

The phase shift of the O(4) symmetric $\phi^4$ theory in the symmetric phase is calculated numerically using the relation between phase shift and energy levels of two-particle states recently derived by L\"{u}scher. The results agree with the prediction of perturbation theory. A practical difficulty of the method for a reliable extraction of the phase shift for large momenta due to the necessity of a precise determination of excited two-particle energy levels is pointed out.Comment: 10 pages, 3 figures (not included but available by mail), UT-61

Two Loop Computation of a Running Coupling in Lattice Yang-Mills Theory

We compute the two loop coefficient in the relation between the lattice bare coupling and the running coupling defined through the Schroedinger functional for the case of pure SU(2) gauge theory. This result is needed as one computational component to relate the latter to the MSbar-coupling, and it allows us to implement O(a) improvement of the Schroedinger functional to two-loop order. In addition, the two-loop beta-function is verified in a perturbative computation on the lattice, and the behavior of an improved bare coupling is investigated beyond one loop.Comment: 26 pages, uuencoded compressed tar file, new: acknowledgement adde

Further one-loop results in O(a) improved lattice QCD

Using the Schr\"odinger functional we have computed a variety of renormalized on-shell correlation functions to one-loop order of perturbation theory. By studying their approach to the continuum limit we have determined the O($a$) counterterms needed to improve the quark mass and a number of isovector quark bilinear operators.Comment: 3 pages Latex using espcrc2.sty, to appear in the conference proceedings of Lattice '97, Edinburg

A Study of PCAC for the Nonperturbative Improvement of the Wilson Action

We present an exploratory study for the nonperturbative determination of the coefficient of the ${\cal O}(a)$ improvement term to the Wilson action, $c_{SW}$. Following the work by L\"{u}scher et al., we impose the PCAC relation as a nonperturbative improvement condition on $c_{SW}$, without, however, using the Schr\"{o}dinger functional in our calculation.Comment: 3 pages, LaTeX (uses espcrc2.sty), 4 postscript figures, to be published in the proceedings of Lattice'9

Computation of the improvement coefficient cswc_{sw} to 1-loop with improved gluon actions

The clover coefficient \csw is computed at one loop order of perturbation theory for improved gluon actions including six-link loops. The O(a) improvement coefficients for the dimension three isovector composite operators bilinear in the quark fields are also calculated.Comment: LATTICE98(improvement), 3 pages, Latex(espcrc2,epsf), 2 figure

The running coupling from the QCD Schr\"odinger functional -- a one-loop analysis

Starting from the Schr\"odinger functional, we give a non-perturbative definition of the running coupling constant in QCD. The spatial boundary conditions for the quark fields are chosen such that the massless Dirac operator in the classical background field has a large smallest eigenvalue. At one-loop order of perturbation theory, we determine the matching coefficient to the \MSbar-scheme and discuss the quark mass effects in the $\beta$-function. To this order, we also compute the Symanzik improvement coefficient necessary to remove the \Oa lattice artefacts originating from the boundaries. For reasonable lattice resolutions and the standard Wilson action, lattice artefacts are found to be only weakly dependent on the lattice spacing $a$, while they vanish quickly with the improved action of Sheikholeslami and Wohlert.Comment: 29 pages; uuencoded, complete postscript fil

Lattice QCD with open boundary conditions and twisted-mass reweighting

Lattice QCD simulations at small lattice spacings and quark masses close to their physical values are technically challenging. In particular, the simulations can get trapped in the topological charge sectors of field space or may run into instabilities triggered by accidental near-zero modes of the lattice Dirac operator. As already noted in ref. [1], the first problem is bypassed if open boundary conditions are imposed in the time direction, while the second can potentially be overcome through twisted-mass determinant reweighting [2]. In this paper, we show that twisted-mass reweighting works out as expected in QCD with open boundary conditions and 2+1 flavours of O(a) improved Wilson quarks. Further algorithmic improvements are tested as well and a few physical quantities are computed for illustration.Comment: Plain TeX source, 27 pages, 7 figure