The Landau gauge gluon propagator for the pure gauge theory is evaluated on a 32 3 × 64 lattice with a physical volume of (3.35 3 × 6.7) fm 4 . Comparison with two smaller lattices at different lattice spacings allows an assessment of finite volume and finite lattice spacing errors. Cuts on the data are imposed to minimize these errors. Scaling of the gluon propagator is verified between β = 6.0 and β = 6.2. The tensor structure is evaluated and found to be in good agreement with the Landau gauge form, except at very small momentum values, where some small finite volume errors persist. A number of functional forms for the momentum dependence of the propagator are investigated. The form D(q 2 ) = D IR + D UV , where D IR (q 2 ) ∝ (q 2 + M 2 ) −η and D UV is an infrared regulated one-loop asymptotic form, is found to provide an adequate description of the data over the entire momentum region studied -thereby bridging the gap between the infrared confinement region and the ultraviolet asymptotic region. The best estimate for the exponent η is 3.2−0.3, where the first set of errors represents the uncertainty associated with varying the fitting range, while the second set of errors reflects the variation arising from different choices of infrared regulator in D UV . Fixing the form of D UV , we find that the mass parameter M is (1020 ± 100) MeV.

A new Monte-Carlo based uncertainty analysis is introduced to quantitatively determine the predictive ability of QCD sum rules. A comprehensive analysis of ground state rho-meson and nucleon spectral properties is performed. Many of the findings contradict the conventional wisdom of both practitioners and skeptics alike. Associations between the phenomenological fit parameters are particularly interesting as they reveal how the sum rules resolve the spectral properties. The use of derivative sum rules for the determination of rho-meson spectral properties is shown to be a very unfavorable approach. Most prior nucleon sum rule analyses are based on a sum rule which is found to be invalid; the results are suspect, and should be reevaluated. The ``Ioffe formula'', argued by many to qualitatively encapsulate a description of the nucleon mass in terms of the chiral symmetry breaking order parameter is misleading at best. QCD Sum Rules are found to be self-consistent without contributions from direct instantons. This implies that instanton effects are adequately accounted for in the nonperturbative vacuum condensates. This in-depth examination of QCD sum rule self consistency paints a favorable picture for further quantitative refinements of the QCD sum rule approach.Comment: 70 page RevTeX Manuscript with 40 embedded figures. Revised manuscript accepted for publication. Recent estimates of QCD vacuum condensates are used in the analysis. This and related papers may also be obtained from http://www.phys.washington.edu/~derek/Publications.htm

We present an unquenched calculation of the quark propagator in Landau gauge with 2+1 flavors of dynamical quarks. We use configurations generated with an improved staggered ("Asqtad") action by the MILC collaboration. This quark action has been seen to have excellent rotational symmetry and scaling properties in the quenched quark propagator. Quenched and dynamical calculations are performed on a 20 3 × 64 lattice with a nominal lattice spacing of a = 0.125 fm. The matched quenched and dynamical lattices allow us to investigate the relatively subtle sea quark effects, and even in the quenched case the physical volume of these lattices gives access to lower momenta than our previous study. We calculate the quark mass function and renormalization function for a variety of valence and sea quark masses.

A numerical simulation of quenched QCD on a 24 X 12 X 12 X 24 lattice at /3= 5.9 is used to calculate the electric and magnetic form factors of the baryon octet. General forms of the baryon interpolating fields are considered. Magnetic moments, electric radii, magnetic radii, and magnetic transition moments are extracted from the form factors. The electric properties are found to be consistent with a quark-model picture involving spin-dependent forces. The lattice results for the magnetic properties show a mass and spin dependence of the effective quark moments which is not accounted for in conventional quark models. Lattice calculations underestimate the magnitude of electric radii, magnetic radii, and magnetic moments compared to experimental measurements. The finite volume of the periodic lattice may be responsible for the discrepancies. The pattern of electromagnetic radii in the lattice results are seen to be generally reproduced in the model results that are considered. The only exception is that of Z-which proves to be a sensitive probe of the quark dynamics. Lattice calculations indicate a positive value for the normalized square magnetic radius in Z-which contrasts Skyrme model results. Ratios of the magnetic moments allow a more detailed comparison with the experimental measurements. The lattice calculations are seen to better reproduce the experimental ratios than the model calculations.