The Scalar Quarkonium Spectrum and Quarkonium-Glueball Mixing

We evaluate the valence approximation to the mass of scalar quarkonium and to the mixing energy between scalar quarkonium and the lightest scalar glueball for a range of different lattice sizes and quark masses. Our results support the identification of $f_0(1710)$ as the lightest scalar glueball.Comment: 3 pages, 4 PostScript figures, talk given at Lattice 9

Scalar Quarkonium Masses

We evaluate the valence approximation to the mass of scalar quarkonium for a range of different parameters. Our results strongly suggest that the infinite volume continuum limit of the mass of $s\overline{s}$ scalar quarkonium lies well below the mass of $f_J(1710)$. The resonance $f_0(1500)$ appears to the best candidate for $s\overline{s}$ scalar quarkonium.Comment: 3 pages of Latex, 5 PostScript figures, uses espcrc2.sty which is included, Talk presented at LATTICE96(spectrum

Fermion Determinants

The current status of bounds on and limits of fermion determinants in two, three and four dimensions in QED and QCD is reviewed. A new lower bound on the two-dimensional QED determinant is derived. An outline of the demonstration of the continuity of this determinant at zero mass when the background magnetic field flux is zero is also given.Comment: 10 page

Numerical Evidence for the Observation of a Scalar Glueball

We compute from lattice QCD in the valence (quenched) approximation the partial decay widths of the lightest scalar glueball to pairs of pseudoscalar quark-antiquark states. These predictions and values obtained earlier for the scalar glueball's mass are in good agreement with the observed properties of $f_J(1710)$ and inconsistent with all other observed meson resonances.Comment: 12 pages of Latex, 3 PostsScript figures as separate uufil

Continuum Limit of Scalar Masses and Mixing Energies

We evaluate the continuum limit of the valence approximation to the mass of scalar quarkonium and to the scalar quarkonium-glueball mixing energy for a range of different quark masses. Our results answer several questions raised by the proposed identification of $f_0(1710)$ as composed primarily of the lightest scalar glueball.Comment: 3 pages, 2 PostScript figures, LATTICE98(spectrum), one reference correcte

Improved Error Estimate for the Valence Approximation

We construct a systematic mean-field-improved coupling constant and quark loop expansion for corrections to the valence (quenched) approximation to vacuum expectation values in the lattice formulation of QCD. Terms in the expansion are evaluated by a combination of weak coupling perturbation theory and a Monte Carlo algorithm.Comment: 3 pages, 1 PostScript figure, talk given at Lattice 9

Coupling Constants for Scalar Glueball Decay

We evaluate the partial decay widths of the lightest scalar glueball to pairs of pseudoscalar quark-antiquark states. The calculation is done in the valence (quenched) approximation on a 16^3 \time 24 lattice at $\beta = 5.7$. These predictions and values obtained earlier for the infinite volume continuum limit of the scalar glueball's mass are in good agreement with the observed properties of $f_J(1710)$ and inconsistent with all other observed meson resonances.Comment: 8 pages of Latex, 12 PostScript figures, 2 macros included, plenary talk given by D. Weingarten at Lattice 95, to appear in conference proceeding