Anthony G. Williams

Dyson-Schwinger equations and their application to hadronic physics

We review the current status of nonperturbative studies of gauge field theory using the Dyson-Schwinger equation formalism and its application to hadronic physics. We begin with an introduction to the formalism and a discussion of renormalisation in this approach. We then review the current status of studies of Abelian gauge theories [e.g., strong coupling quantum electrodynamics] before turning our attention to the non-Abelian gauge theory of the strong interaction, quantum chromodynamics. We discuss confinement, dynamical chiral symmetry breaking and the application and contribution of these techniques to our understanding of the strong interactions.

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.

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.

Rho-omega mixing, vector meson dominance and the pion form-factor

Abstract We review the current status of ϱ-ω mixing and discuss its implication for our understanding of charge-symmetry breaking. In order to place this work in context we also review the photon-hadron coupling within the framework of vector meson dominance. This leads naturally to a discussion of the electromagnetic form-factor of the pion and of nuclear shadowing.

Unquenched gluon propagator in Landau gauge

[...] Using lattice quantum chromodynamics ~QCD! we perform an unquenched calculation of the gluon propagator in Landau gauge. We use configurations generated with the AsqTad quark action by the MILC collaboration for the dynamical quarks and compare the gluon propagator of quenched QCD ~i.e., the pure Yang-Mills gluon propagator! with that of 211 flavor QCD. The effects of the dynamical quarks are clearly visible and lead to a significant reduction of the nonperturbative infrared enhancement relative to the quenched case.

Hadron masses from novel fat link fermion actions

The hadron mass spectrum is calculated in lattice QCD using a novel fat-link clover fermion action in which only the irrelevant operators in the fermion action are constructed using smeared links. The simulations are performed on a 16{sup 3} x 32 lattice with a lattice spacing of a=0.125 fm. We compare actions with n=4 and 12 smearing sweeps with a smearing fraction of 0.7. The n=4 Fat-Link Irrelevant Clover (FLIC) action provides scaling which is superior to mean-field improvement, and offers advantages over nonperturbative 0(a) improvement, including a reduced exceptional configuration problem.

Strange electric form factor of the proton.

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 electric charge radii of the baryon octet, we obtain an accurate determination of the strange electric charge radius of the proton. While this analysis provides a value for G(E)(s)(Q(2) = 0.1 GeV(2)) in agreement with the best current data, the theoretical error is comparable with that expected from future HAPPEX results from JLab. Together with the earlier determination of G(M)(s), this result considerably constrains the role of hidden flavor in the structure of the nucleon.

Excited Baryons in Lattice QCD

We present first results for the masses of positive and negative parity excited baryons calculated in lattice QCD using an O(a^2)-improved gluon action and a fat-link irrelevant clover (FLIC) fermion action in which only the irrelevant operators are constructed with APE-smeared links. The results are in agreement with earlier calculations of N^* resonances using improved actions and exhibit a clear mass splitting between the nucleon and its chiral partner. An correlation matrix analysis reveals two low-lying J^P=(1/2)^- states with a small mass splitting. The study of different Lambda interpolating fields suggests a similar splitting between the lowest two Lambda1/2^- octet states. However, the empirical mass suppression of the Lambda^*(1405) is not evident in these quenched QCD simulations, suggesting a potentially important role for the meson cloud of the Lambda^*(1405) and/or a need for more exotic interpolating fields.

Medium modifications to the omega -meson mass in the Walecka model.

We calculate the effective mass of the [omega] meson in nuclear matter in a relativistic random-phase approximation to the Walecka model. The dressing of the meson propagator is driven by its coupling to particle-hole pairs and nucleon-antinucleon ([ital N[bar N]]) excitations. We report a reduction in the [omega]-meson mass of about 170 MeV at nuclear-matter saturation density. This reduction arises from a competition between the density-dependent (particle-hole) dressing of the propagator and vacuum polarization ([ital N[bar N]] pairs). While density-dependent effects lead to an increase in the mass proportional to the classical plasma frequency, vacuum polarization leads to an even larger reduction caused by the reduced effective nucleon mass in the medium.