Derek B. Leinweber

Infinite Volume and Continuum Limits of the Landau-Gauge Gluon Propagator

We extend a previous improved action study of the Landau gauge gluon propagator, by using a variety of lattices with spacings from a = 0.17 to 0.41 fm, to more fully explore finite volume and discretization effects. We also extend a previously used technique for minimizing lattice artifacts, the appropriate choice of momentum variable or “kinematic correction”, by considering it more generally as a “tree-level correction”. We demonstrate that by using tree-level correction, determined by the tree-level behavior of the action being considered, it is possible to obtain scaling behavior over a very wide range of momenta and lattice spacings. This makes it possible to explore the infinite volume and continuum limits of the Landau-gauge gluon propagator.

Physical Nucleon Properties from Lattice QCD

We investigate various resummations of the chiral expansion and fit to the extremely accurate lattice QCD data for the mass of the nucleon recently obtained by the CP-PACS group. Using a variety of finite-range regulators, we demonstrate a remarkably robust chiral extrapolation of the nucleon mass. The systematic error associated with the chiral extrapolation alone is estimated to be less than 1%.

Chiral analysis of quenched baryon masses

[...] We extend to quenched QCD an earlier investigation of the chiral structure of the masses of the nucleon and the delta in lattice simulations of full QCD. Even after including the meson-loop self-energies which give rise to the leading and next-to-leading nonanalytic behavior ~and hence the most rapid variation in the region of light quark mass!, we find surprisingly little curvature in the quenched case. Replacing these meson-loop self-energies by the corresponding terms in full QCD yields a remarkable level of agreement with the results of the full QCD simulations. This comparison leads to a very good understanding of the origins of the mass splitting between these baryons.

Unquenched quark propagator in Landau gauge

[...] 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.

Precise determination of the strangeness magnetic moment of the nucleon.

By combining the constraints of charge symmetry with new chiral extrapolation techniques and recent low mass quenched lattice-QCD simulations of the individual quark contributions to the magnetic moments of the nucleon octet, we obtain a precise determination of the strange magnetic moment of the proton. The result, namely, G{sub M}{sup s}=(-0.046{+-}0.019){mu}{sub N} is consistent with the latest experimental measurements but an order of magnitude more precise. This poses a tremendous challenge for future experiments.

QCD sum rules for skeptics

Abstract 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 ρ -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 ρ -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 ⦠ qq ⦔ 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.

Decuplet baryon structure from lattice QCD

The electromagnetic properties of the SU(3)-flavor baryon decuplet are examined within a lattice simulation of quenched QCD. Electric charge radii, magnetic moments, and magnetic radii are extracted from the {ital E}0 and {ital M}1 form factors. Preliminary results for the {ital E}2 and {ital M}3 moments are presented, giving the first model-independent insight to the shape of the quark distribution in the baryon ground state. As in our octet-baryon analysis, the lattice results give evidence of spin-dependent forces and mass effects in the electromagnetic properties. The quark charge distribution radii indicate these effects act in opposing directions. Some baryon dependence of the effective quark magnetic moments is seen. However, this dependence in decuplet baryons is more subtle than that for octet baryons. Of particular interest are the lattice predictions for the magnetic moments of {Omega}{sup {minus}} and {Delta}{sup ++} for which new recent experimental measurements are available. The lattice prediction of the {Delta}{sup ++}/{ital p} ratio appears larger than the experimental ratio, while the lattice prediction for the {Omega}{sup {minus}}/{ital p} magnetic moment ratio is in good agreement with the experimental ratio.

Baryon masses from lattice QCD: Beyond the perturbative chiral regime

Consideration of the analytic properties of pion-induced baryon self-energies leads to new functional forms for the extrapolation of light baryon masses. These functional forms reproduce the leading non-analytic behavior of chiral perturbation theory, the correct non-analytic behavior at the

Convergence of chiral effective field theory

N \pi

Unquenched gluon propagator in Landau gauge

threshold and the appropriate heavy-quark limit. They involve only three unknown parameters, which may be obtained by fitting to lattice data. Recent dynamical fermion results from CP-PACS and UKQCD are extrapolated using these new functional forms. We also use these functions to probe the limit of applicability of chiral perturbation theory to the extrapolation of lattice QCD results.