On the I=2 channel pi-pi interaction in the chiral limit

An approximate local potential for the residual pi+ pi+ interaction is computed. We use an O(a**2) improved action on a coarse 9x9x9x13 lattice with approximately a=0.4fm. The results present a continuation of previous work: Increasing the number of gauge configurations and quark propagators we attempt extrapolation of the pi+ pi+ potential to the chiral limit.Comment: LATTICE98(spectrum) LaTeX2e, 3 pages, 3 eps figure

Two-body spectra of pseudoscalar mesons with an O(a2)O(a^2)--improved lattice action using Wilson fermions

We extend our calculations with the second-order tree-level and tadpole improved next-nearest-neighbor action to meson-meson systems. Correlation matrices built from interpolating fields representing two pseudoscalar mesons (pion-pion) with relative momenta p are diagonalized, and the mass spectrum is extracted. Link variable fuzzing and operator smearing at both sinks and sources is employed. Calculations are presented for two values of the hopping parameter. The spectrum is used to discuss the residual interaction in the meson-meson system.Comment: 3 pages, 4 EPS figures, Poster presented at "Lattice'97", to appear in the proceeding

Large N reduction in the continuum three dimensional Yang-Mills theory

Numerical and theoretical evidence leads us to propose the following: Three dimensional Euclidean Yang-Mills theory in the planar limit undergoes a phase transition on a torus of side $l=l_c$. For $l>l_c$ the planar limit is $l$-independent, as expected of a non-interacting string theory. We expect the situation in four dimensions to be similar.Comment: 4 pages, latex file, two figures, version to appear in Phys. Rev. Let

String breaking

We numerically investigate the transition of the static quark-antiquark string into a static-light meson-antimeson system. Improving noise reduction techniques, we are able to resolve the signature of string breaking dynamics for Nf=2 lattice QCD at zero temperature. We discuss the lattice techniques used and present results on energy levels and mixing angle of the static two-state system. We visualize the action density distribution in the region of string breaking as a function of the static colour source-antisource separation. The results can be related to properties of quarkonium systems.Comment: 8 pages, Talk given at the Workshop on Computational Hadron Physics, Nicosia, Cyprus, 14--17 September 200

Scalar-gauge dynamics in (2+1) dimensions at small and large scalar couplings

We present the results of a detailed calculation of the excitation spectrum of states with quantum numbers J^{PC}=0++, 1-- and 2++ in the three-dimensional SU(2) Higgs model at two values of the scalar self-coupling and for fixed gauge coupling. In the context of studies of the electroweak phase transition at finite temperature these couplings correpond to tree-level, zero temperature Higgs masses of 35 GeV and 120 GeV, respectively. We also study the properties of Polyakov loop operators, which serve to test the confining properties of the model in the symmetric phase. At both values of the scalar coupling we obtain masses of bound states consisting entirely of gauge degrees of freedom ("W-balls"), which are very close to those obtained in the pure gauge theory. We conclude that the previously observed, approximate decoupling of the scalar and gauge sectors of the theory persists at large scalar couplings. We study the crossover region at large scalar coupling and present a scenario how the confining properties of the model in the symmetric phase are lost inside the crossover by means of flux tube decay. We conclude that the underlying dynamics responsible for the observed dense spectrum of states in the Higgs region at large couplings must be different from that in the symmetric phase.Comment: 36 pages, LaTeX, 13 postscript files, to be included with epsf; improved presentation, updated references, conclusions unchanged; version to appear in Nucl. Phys.

On the Mass Spectrum of the SU(2) Higgs Model in 2+1 Dimensions

We calculate the masses of the low-lying states with quantum numbers $J^{PC}=0^{++},1^{--}$ in the Higgs and confinement regions of the three-dimensional SU(2) Higgs model, which plays an important r\^ole in the description of the thermodynamic properties of the standard model at finite temperatures. We extract the masses from correlation functions of gauge-invariant operators which are calculated by means of a lattice Monte Carlo simulation. The projection properties of our lattice operators onto the lowest states are greatly improved by the use of smearing techniques. We also consider cross correlations between various operators with the same quantum numbers. From these the mass eigenstates are determined by means of a variational calculation. In the symmetric phase, we find that some of the ground state masses are about 30\% lighter than those reported from previous simulations. We also obtain the masses of the first few excited states in the symmetric phase. Remarkable among these is the occurrence of a $0^{++}$ state composed almost entirely of gauge degrees of freedom. The mass of this state, as well as that of its first excitations, is nearly identical to the corresponding glueball states in three-dimensional SU(2) pure gauge theory, indicating an approximate decoupling of the pure gauge sector from the Higgs sector of the model. We perform a detailed study of finite size effects and extrapolate the lattice mass spectrum to the continuum.Comment: 30 pages LATEX, uses epsf.st

The scalar and tensor glueballs in the valence approximation

We evaluate the infinite volume, continuum limit of $0^{++}$ and $2^{++}$ glueball masses in the valence approximation. We find $m_{0^{++}} = 1740 \pm 71$~MeV and $m_{2^{++}} = 2359 \pm 128$~MeV, consistent with the interpretation of $f_0 ( 1710 )$ as the lightest scalar glueball.Comment: (talk presented by A. Vaccarino at Lattice 93) 3 pages of PostScript in uufiles compressed form. IBM-HET-94-

Another determination of the quark condensate from an overlap action

I use the technique of Hernandez, et al (hep-lat/0106011) to convert a recent calculation of the lattice-regulated quark condensate from an overlap action to a continuum-regulated number. I find Sigma(MSbar)(mu = 2 GeV) = (282(6) MeV)-cubed times (a-inverse/1766 MeV)-cubed from a calculation with the Wilson gauge action at beta=5.9.Comment: 3 pages, Revtex, 1 postscript figure. References added. COLO-HEP-47

Bounds on the Wilson Dirac Operator

New exact upper and lower bounds are derived on the spectrum of the square of the hermitian Wilson Dirac operator. It is hoped that the derivations and the results will be of help in the search for ways to reduce the cost of simulations using the overlap Dirac operator. The bounds also apply to the Wilson Dirac operator in odd dimensions and are therefore relevant to domain wall fermions as well.Comment: 16 pages, TeX, 3 eps figures, small corrections and improvement

Three-Quark Potential in SU(3) Lattice QCD

The static three-quark (3Q) potential is measured in the SU(3) lattice QCD with $12^3 \times 24$ and $\beta=5.7$ at the quenched level. From the 3Q Wilson loop, the 3Q ground-state potential $V_{\rm 3Q}$ is extracted using the smearing technique for the ground-state enhancement. With accuracy better than a few %, $V_{\rm 3Q}$ is well described by a sum of a constant, the two-body Coulomb term and the three-body linear confinement term $\sigma_{\rm 3Q} L_{\rm min}$, where $L_{\rm min}$ denotes the minimal length of the color flux tube linking the three quarks. By comparing with the Q-$\bar {\rm Q}$ potential, we find a universal feature of the string tension, $\sigma_{\rm 3Q} \simeq \sigma_{\rm Q \bar Q}$, as well as the one-gluon-exchange result for the Coulomb coefficient, $A_{\rm 3Q} \simeq \frac12 A_{\rm Q \bar Q}$.Comment: 7 pages, 3 figur