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

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

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

Meson Decay Constants from the Valence Approximation to Lattice QCD

We evaluate $f_{\pi}/ m_{\rho}$, $f_K/ m_{\rho}$, $1/f_{\rho}$, and $m_{\phi}/(f_{\phi} m_{\rho})$, extrapolated to physical quark mass, zero lattice spacing and infinite volume, for lattice QCD with Wilson quarks in the valence (quenched) approximation. The predicted ratios differ from experiment by amounts ranging from 12\% to 17\% equivalent to between 0.9 and 2.8 times the corresponding statistical uncertainties.Comment: uufiles encoded copy of 40 page Latex article, including 14 figures in Postscript. The long version of hep-lat/9302012, IBM/HET 93-