arXiv subjects

Derek B. Leinweber

Publications and source records attributed to Derek B. Leinweber.

At least 145 records · Page 8Linked to original sources

arXiv2003

The Hamiltonian limit of (3+1)D SU(3) lattice gauge theory on anisotropic lattices

The extreme anisotropic limit of Euclidean SU(3) lattice gauge theory is examined to extract the Hamiltonian limit, using standard path integral Monte Carlo (PIMC) methods. We examine the mean plaquette and string tension and compare them to results obtained within the Hamiltonian framework of Kogut and Susskind. The results are a significant improvement upon previous Hamiltonian estimates, despite the extrapolation procedure necessary to extract observables. We conclude that the PIMC method is a reliable method of obtaining results for the Hamiltonian version of the theory. Our results also clearly demonstrate the universality between the Hamiltonian and Euclidean formulations of lattice gauge theory. It is particularly important to take into account the renormalization of both the anisotropy, and the Euclidean coupling $ β_E $, in obtaining these results.

hep-lat↗

arXiv2003

Comparison of |Q|=1 and |Q|=2 gauge-field configurations on the lattice four-torus

It is known that exactly self-dual gauge-field configurations with topological charge |Q|=1 cannot exist on the untwisted continuum 4-torus. We explore the manifestation of this remarkable fact on the lattice 4-torus for SU(3) using advanced techniques for controlling lattice discretization errors, extending earlier work of De Forcrand et. al. for SU(2). We identify three distinct signals for the instability of |Q|=1 configurations, and show that these manifest themselves early in the cooling process, long before the would-be instanton has shrunk to a size comparable to the lattice discretization threshold. These signals do not appear for our |Q|=2 configurations. This indicates that these signals reflect the truly global nature of the instability, rather than local discretization effects. Monte-Carlo generated SU(3) gauge field configurations are cooled to the self-dual limit using an O(a^4)-improved gauge action chosen to have small but positive O(a^6) errors. This choice prevents lattice discretization errors from destroying instantons provided their size exceeds the dislocation threshold of the cooling algorithm. Lattice discretization errors are evaluated by comparing the O(a^4)-improved gauge-field action with an O(a^4)-improved action constructed from the square of an O(a^4)-improved lattice field-strength tensor, thus having different O(a^6) discretization errors. The number of action-density peaks, the instanton size and the topological charge of configurations is monitored. We observe a fluctuation in the total topological charge of |Q|=1 configurations, and demonstrate that the onset of this unusual behavior corresponds with the disappearance of multiple-peaks in the action density. At the same time discretization errors are minimal.

hep-lat↗

arXiv2002

Panel discussion on chiral extrapolation of physical observables

This is an approximate reconstruction of the panel discussion on chiral extrapolation of physical observables. The session consisted of brief presentations from panelists, followed by responses from the panel, and concluded with questions and comments from the floor with answers from panelists. In the following, the panelists have summarized their statements, and the ensuing discussion has been approximately reconstructed from notes.

hep-lat↗

arXiv2002

Chiral Nonanalytic Behaviour: The Edinburgh Plot

The Edinburgh Plot is a scale independent way of presenting lattice QCD calculations over a wide range of quark masses. In this sense it is appealing as an indicator of how the approach to physical quark masses is progressing. The difficulty remains that even the most state of the art calculations are still at quark masses that are too heavy to apply dimensionally-regulated chiral perturbation theory. We present a method allowing predictions of the behaviour of the Edinburgh plot, in both the continuum, and on the lattice.

hep-lat↗

arXiv2002

Overlap Quark Propagator in Landau Gauge

The properties of the quark propagator in Landau gauge in quenched QCD are examined for the overlap quark action. The overlap quark action satisfies the Ginsparg-Wilson relation and as such provides an exact lattice realization of chiral symmetry. This in turn implies that the quark action is free of ${\cal O}(a)$ errors. We present results using the standard Wilson fermion kernel in the overlap formalism on a $12^3\times 24$ lattice at a spacing of 0.125 fm. We obtain the nonperturbative momentum-dependent wavefunction renormalization function $Z(p)$ and the nonperturbative mass function $M(p)$ for a variety of bare masses. We perform a simple extrapolation to the chiral limit for these functions. We clearly observe the dynamically generated infrared mass and confirm the qualitative behavior found for the Landau gauge quark propagator in earlier studies. We attempt to extract the quark condensate from the asymptotic behavior of the mass function in the chiral limit.

hep-lat↗

arXiv2002

Improved Smoothing Algorithms for Lattice Gauge Theory

The relative smoothing rates of various gauge field smoothing algorithms are investigated on ${\cal O}(a^2)$-improved $\suthree$ Yang--Mills gauge field configurations. In particular, an ${\cal O}(a^2)$-improved version of APE smearing is motivated by considerations of smeared link projection and cooling. The extent to which the established benefits of improved cooling carry over to improved smearing is critically examined. We consider representative gauge field configurations generated with an ${\cal O}(a^2)$-improved gauge field action on $\1$ lattices at $β=4.38$ and $\2$ lattices at $β=5.00$ having lattice spacings of 0.165(2) fm and 0.077(1) fm respectively. While the merits of improved algorithms are clearly displayed for the coarse lattice spacing, the fine lattice results put the various algorithms on a more equal footing and allow a quantitative calibration of the smoothing rates for the various algorithms. We find the relative rate of variation in the action may be succinctly described in terms of simple calibration formulae which accurately describe the relative smoothness of the gauge field configurations at a microscopic level.

hep-lat↗

arXiv2001

Quenched chiral perturbation theory for baryon form factors

A new intuitive method for the rapid calculation of the leading nonanalytic behavior of hadronic observables in quenched chiral perturbation theory is presented. After proving the technique in a consideration of baryon masses, the quenched magnetic moments of octet baryons are addressed. The technique provides a separation of magnetic moment contributions into full, sea, valence and quenched valence contributions, the latter being the conventional view of the quenched approximation. Both baryon mass and meson mass violations of SU(3)-flavor symmetry are accounted for. A comprehensive examination of the individual quark-sector contributions to octet baryon magnetic moments reveals that the u-quark contribution to the proton magnetic moment provides an optimal opportunity to directly view nonanalytic behavior associated with the quenched meson cloud of baryons in the quenched approximation.

hep-lat↗

arXiv2001

Gluons, quarks, and the transition from nonperturbative to perturbative QCD

Lattice-based investigations of two fundamental QCD quantities are described, namely the gluon and quark propagators in Landau gauge. We have studied the Landau gauge gluon propagator using a variety of lattices with spacings from a = 0.17 to 0.41 fm. We demonstrate that it is possible to obtain scaling behavior over a very wide range of momenta and lattice spacings and to explore the infinite volume and continuum limits. These results confirm that the Landau gauge gluon propagator is infrared finite. We study the Landau gauge quark propagator in quenched QCD using two forms of the O(a)-improved propagator and we find good agreement between these. The extracted value of the infrared quark mass in the chiral limit is found to be 300 +/- 30 MeV. We conclude that the momentum regime where the transition from nonperturbative to perturbative QCD occurs is Q^2 approx 4GeV^2.

hep-ph↗

arXiv2001

Nonperturbative improvement and tree-level correction of the quark propagator

We extend an earlier study of the Landau gauge quark propagator in quenched QCD where we used two forms of the O(a)-improved propagator with the Sheikholeslami-Wohlert quark action. In the present study we use the nonperturbative value for the clover coefficient c_sw and mean-field improvement coefficients in our improved quark propagators. We compare this to our earlier results which used the mean-field c_sw and tree-level improvement coefficients for the propagator. We also compare three different implementations of tree-level correction: additive, multiplicative, and hybrid. We show that the hybrid approach is the most robust and reliable and can successfully deal even with strong ultraviolet behavior and zero-crossing of the lattice tree-level expression. We find good agreement between our improved quark propagators when using the appropriate nonperturbative improvement coefficients and hybrid tree-level correction. We also present a simple extrapolation of the quark mass function to the chiral limit.

hep-lat↗

arXiv2001

Symanzik Improvement In The Static Quark Potential

A systematic investigation of Symanzic improvement in the gauge field action is performed for the static quark potential in quenched QCD. We consider Symanzik improved gauge field configurations on a 16^3 X 32 lattice with a relatively coarse lattice spacing of 0.165(2)fm. A matched set of standard Wilson gauge configurations is prepared at β= 5.74 with the same physical volume and lattice spacing and is studied for comparison. We find that, despite the coarse lattice spacing, the unimproved and less-expensive Wilson action does as well as the Symanzik action in allowing us to extract the static quark potential at large qqbar separations. We have considered novel methods for stepping off-axis in the static quark potential which provides new insights into the extent to which the ground state potential dominates the Wilson loop correlation function.

hep-lat↗

arXiv2001

General Algorithm For Improved Lattice Actions on Parallel Computing Architectures

Quantum field theories underlie all of our understanding of the fundamental forces of nature. The are relatively few first principles approaches to the study of quantum field theories [such as quantum chromodynamics (QCD) relevant to the strong interaction] away from the perturbative (i.e., weak-coupling) regime. Currently the most common method is the use of Monte Carlo methods on a hypercubic space-time lattice. These methods consume enormous computing power for large lattices and it is essential that increasingly efficient algorithms be developed to perform standard tasks in these lattice calculations. Here we present a general algorithm for QCD that allows one to put any planar improved gluonic lattice action onto a parallel computing architecture. High performance masks for specific actions (including non-planar actions) are also presented. These algorithms have been successfully employed by us in a variety of lattice QCD calculations using improved lattice actions on a 128 node Thinking Machines CM-5. {\underline{Keywords}}: quantum field theory; quantum chromodynamics; improved actions; parallel computing algorithms.

hep-lat↗

arXiv2000

Calibration of Smearing and Cooling Algorithms in SU(3)-Color Gauge Theory

The action and topological charge are used to determine the relative rates of standard cooling and smearing algorithms in pure SU(3)-color gauge theory. We consider representative gauge field configurations on $16^3\times 32$ lattices at $β=5.70$ and $24^3\times 36$ lattices at $β=6.00$. We find the relative rate of variation in the action and topological charge under various algorithms may be succinctly described in terms of simple formulae. The results are in accord with recent suggestions from fat-link perturbation theory.

hep-lat↗

arXiv2000

The Sigma Commutator from Lattice QCD

As a direct source of information on chiral symmetry breaking within QCD, the sigma commutator is of considerable importance. Since hadron structure is a non-perturbative problem, numerical calculations on a space-time lattice are currently the only rigorous approach. With recent advances in the calculation of hadron masses within full QCD, it is of interest to see whether the sigma commutator can be calculated directly from the dependence of the nucleon mass on the input quark mass. We show that, provided the correct chiral behaviour of QCD is respected in the extrapolation to realistic quark masses, one can indeed obtain a fairly reliable determination of the sigma commutator using present lattice data. For two-flavour dynamical fermion QCD the sigma commutator lies between 45 and 55 MeV based on recent data from CP-PACS and UKQCD.

nucl-th↗

arXiv2000

Visualizations of the QCD Vacuum

Action and topological charge densities of the Euclidean-space QCD vacuum are visualized in three-dimensional slices of a 24^3 x 36 space-time lattice and an order-a^2 improved 16^3 x 32 lattice. Features include instanton anti-instanton annihilation and a comparison of standard and over-improved actions used in the smoothing of the gauge fields.

hep-lat↗

arXiv1999

A Lattice QCD Analysis of the Strangeness Magnetic Moment of the Nucleon

The outcome of the SAMPLE Experiment suggests that the strange-quark contribution to the nucleon magnetic moment, G_M^s(0), may be greater than zero. This result is very difficult to reconcile with expectations based on the successful baryon magnetic-moment phenomenology of the constituent quark model. We show that careful consideration of chiral symmetry reveals some rather unexpected properties of QCD. In particular, it is found that the valence u-quark contribution to the magnetic moment of the neutron can differ by more than 50% from its contribution to the Xi^0 magnetic moment. This hitherto unforeseen result leads to the value G_M^s(0) = -0.16 +/- 0.18 with a systematic error, arising from the relatively large strange quark mass used in existing lattice calculations, that would tend to shift G_M^s(0) towards small positive values.

hep-lat↗

arXiv1999

Chiral Corrections to Baryon Masses Calculated within Lattice QCD

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 $N π$ threshold and the appropriate heavy-quark limit. They involve only three unknown parameters, which may be obtained by fitting lattice QCD 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.

nucl-th↗

arXiv1999

Baryon Mass Extrapolation

Consideration of the analytical 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 heavy-quark limit and have the advantage of containing information on the extended structure of hadrons. The forms involve only three unknown parameters which may be optimized by fitting to present lattice data. Recent dynamical fermion results from CP-PACS and UK-QCD are extrapolated using these new functional forms. We also use these functions to probe the limit of the chiral perturbative regime and shed light on the applicability of chiral perturbation theory to the extrapolation of present lattice QCD results.

hep-lat↗

arXiv1999

Nucleon Magnetic Moments Beyond the Perturbative Chiral Regime

The quark mass dependence of nucleon magnetic moments is explored over a wide range. Quark masses currently accessible to lattice QCD, which lie beyond the regime of chiral perturbation theory (chiPT), are accessed via the cloudy bag model (CBM). The latter reproduces the leading nonanalytic behavior of chiPT, while modeling the internal structure of the hadron under investigation. We find that the predictions of the CBM are succinctly described by the simple formula, μ_N(m_π) = μ^{(0)}_N / (1 + αm_π+ βm_π^2), which reproduces the lattice data, as well as the leading nonanalytic behavior of chiPT. As this form also incorporates the anticipated Dirac moment behavior in the limit m_π\to \infty, it constitutes a powerful method for extrapolating lattice results to the physical mass regime.

hep-lat↗