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

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

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

Scattering in a Simple 2-d Lattice Model

L\"uscher has suggested a method to determine phase shifts from the finite volume dependence of the two-particle energy spectrum. We apply this to two models in d=2: (a) the Ising model, (b) a system of two Ising fields with different mass and coupled through a 3-point term, both considered in the symmetric phase. The Monte Carlo simulation makes use of the cluster updating and reduced variance operator techniques. For the Ising system we study in particular O($a^2$) effects in the phase shift of the 2-particle scattering process.Comment: 4 p + 2 PS-figures, UNIGRAZ-UTP-21-10-9

The running quark mass in the SF scheme and its two-loop anomalous dimension

The non-perturbatively defined running quark mass introduced by the ALPHA collaboration is based on the PCAC relation between correlation functions derived from the Schr\"odinger functional (SF). In order to complete its definition it remains to specify a number of parameters, including the ratio of time to spatial extent, $T/L$, and the angle $\theta$ which appears in the spatial boundary conditions for the quark fields. We investigate the running mass in perturbation theory and propose a choice of parameters which attains two desired properties: firstly the two-loop anomalous dimension \d1SF is reasonably small. This is needed in order to ease matching with the non-perturbative computations and to achieve a precise determination of the renormalization group invariant quark mass. Secondly, to one-loop order of perturbation theory, cut-off effects in the step-scaling function are small in O($a$) improved lattice QCD.Comment: 17 pages, gzipped tar-fil

Hadronic decays from the lattice

We discuss strategies to determine hadronic decay couplings from lattice studies. As an application, we explore the decay of a vector meson to two pseudoscalar mesons with $N_f=2$ flavours of sea quark. Although we are working with quark masses that do not allow a physical decay, we show how the transition rate can be evaluated from the amplitude for $\rho \to \pi \pi$ and from the annihilation component of $\pi \pi \to \pi \pi$. We explore the decay amplitude for two different pion momenta and find consistent results. The coupling strength we find is in agreement with experiment. We also find evidence for a shift in the $\rho$ mass caused by mixing with two pion states.Comment: Proc. Latt03 (spectrum), 3 pages, 4 fig

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