arXiv subjects
Publications and source records attributed to Derek B. Leinweber.
The lowest-lying negative-parity state of the Lambda is investigated in (2+1)-flavour full-QCD on the PACS-CS configurations made available through the ILDG. We show that a variational analysis using multiple source and sink smearings can extract a state lying lower than that obtained by using a standard fixed smeared source and sink operator alone.
Positive-parity spin-1/2 excitations of the nucleon are explored in lattice QCD. The variational method is used in this investigation and several correlation matrices are employed. As our focus is on the utility and methodology of the variational approach, we work in the quenched approximation to QCD. Various sweeps of Gaussian fermion-field smearing is applied at the source and at the sink of $χ_{1}\barχ_{1}$ and $χ_{1}χ_{2}$ correlation functions to obtain a large basis of operators. Using several different approaches for constructing basis interpolators, we demonstrate how improving the basis can split what otherwise might be interpreted as a single state into multiple eigenstates. Consistency of the extracted excited energy states are explored over various dimensions of the correlation matrices. The use of large correlation matrices is emphasized for the reliable extraction of the excited eigenstates of QCD.
The dependence of the overlap Dirac operator on the Wilson-mass regulator parameter is studied through calculations of the overlap topological charge densities at a variety of Wilson-mass values. In this formulation, the Wilson-mass is used in the negative mass region and acts as a regulator governing the scale at which the Dirac operator is sensitive to topological aspects of the gauge field. We observe a clear dependence on the value of the Wilson-mass and demonstrate how these values can be calibrated against a finite number of stout-link smearing sweeps. The overlap topological charge density is also computed using a pre-smeared gauge field for the input kernel. We show how applying the overlap operator leads to further filtering of the gauge field. The results suggest that the freedom typically associated with smearing algorithms, through the variable number of sweeps, also exists in the overlap operator, through the variable Wilson-mass parameter.
We study the behavior of the AsqTad quark propagator in Landau gauge on SU(3) Yang-Mills gauge configurations under the removal of center vortices. In SU(2) gauge theory, center vortices have been observed to generate chiral symmetry breaking and dominate the infrared behavior of the quark propagator. In contrast, we report a weak dependence on the vortex content of the gauge configurations, including the survival of dynamical mass generation on configurations with vanishing string tension.
We present results for the negative parity low-lying state of the nucleon, $N{\frac{1}{2}}^{-}$ (1535 MeV) ${\rm S}_{11}$, from a variational analysis method. The analysis is performed in quenched QCD with the FLIC fermion action. The principal focus of this paper is to explore the level ordering between the Roper (${\rm{P}}_{11}$) and the negative parity ground (${\rm{S}}_{11}$) states of the nucleon. Evidence of the physical level ordering is observed at light quark masses. A wide variety of smeared-smeared correlation functions are used to construct correlation matrices. A comprehensive correlation matrix analysis is performed to ensure an accurate isolation of the $N{\frac{1}{2}}^{-}$ state.
The utility of chiral effective field theory, constructed in a manner in which loop contributions are suppressed as one moves outside the power-counting regime, is explored for baryon magnetic moments. Opportunities for the study of significant chiral curvature in valence and full QCD and the nontrivial behavior of strange- and light-quark contributions to the magnetic moment of the Lambda baryon are highlighted.
The negative Wilson mass parameter is an input parameter to the overlap Dirac operator. We examine the extent to which the topological charge density, revealed by the overlap definition, depends on the value of the negative Wilson mass. A strong dependence is observed, which can be correlated with the topological charge density obtained from the gluonic definition, with a variable number of stout-link smearing sweeps. The results indicate that the freedom typically associated with fat-link fermion actions, through the number of smearing sweeps, is also present in the overlap formalism, through the freedom in the Wilson mass parameter.
The impact of stout-link smearing in lattice fermion actions is examined through the consideration of the mass and renormalization functions of the overlap quark propagator over a variety of smeared configurations. Up to six sweeps of stout-link smearing are investigated. For heavy quark masses, the quark propagator is strongly affected by the smearing procedure. For moderate masses, the effect appears to be negligible. A small effect is seen for light quark masses, where dynamical mass generation is suppressed through the smearing procedure.
We present an overview of the correlation-matrix methods developed recently by the CSSM Lattice Collaboration for the isolation of excited states of the nucleon. Of particular interest is the first positive-parity excited-state of the nucleon known as the Roper resonance. Using eigenvectors of the correlation matrix we construct parity and eigenstate projected correlation functions which are analysed using standardized methods. The robust nature of this approach for extracting the eigenstate energies is presented. We report the importance of using a variety of source and sink smearings in achieving this. Ultimately the independence of the eigenstate energies from the interpolator basis is demonstrated. In particular we consider $4\times 4$ correlation matrices built from a variety of interpolators and smearing levels. Using FLIC fermions to access the light quark mass regime, we explore the curvature encountered in the energy of the states as the chiral limit is approached. We report a low-lying Roper state contrasting earlier results using correlation matrices. To the best of our knowledge, this is the first time a low-lying Roper resonance has been found using correlation matrix methods. Finally, we present our results in the context of the Roper results reported by other groups.
We discuss a robust projection method for the extraction of excited-state masses of the nucleon from a matrix of correlation functions. To illustrate the algorithm in practice, we present results for the positive parity excited states of the nucleon in quenched QCD. Using eigenvectors obtained via the variational method, we construct an eigenstate-projected correlation function amenable to standard analysis techniques. The method displays its utility when comparing results from the fit of the projected correlation function with those obtained from the eigenvalues of the variational method. Standard nucleon interpolators are considered, with $2\times 2$ and $3\times 3$ correlation matrix analyses presented using various combinations of source-smeared, sink-smeared and smeared-smeared correlation functions. Using these new robust methods, we observe a systematic dependency of the nucleon excited-state masses on source- and sink-smearing levels. To the best of our knowledge, this is the first clear indication that a correlation matrix of standard nucleon interpolators is insufficient to isolate the eigenstates of QCD.
We present results for the first positive parity excited state of the nucleon, namely, the Roper resonance ($N^{{1/2}^{+}}$=1440 MeV) from a variational analysis technique. The analysis is performed for pion masses as low as 224 MeV in quenched QCD with the FLIC fermion action. A wide variety of smeared-smeared correlation functions are used to construct correlation matrices. This is done in order to find a suitable basis of operators for the variational analysis such that eigenstates of the QCD Hamiltonian may be isolated. A lower lying Roper state is observed that approaches the physical Roper state. To the best of our knowledge, the first time this state has been identified at light quark masses using a variational approach.
The properties of the momentum space quark propagator in Landau gauge are studied for the overlap quark action in quenched lattice QCD. Numerical calculations are performed over four ensembles of gauge configurations, where three are smeared using either 1, 3, or 6 sweeps of stout-link smearing. We calculate the non-perturbative wave function renormalization function $Z(p)$ and the non-perturbative mass function $M(p)$ for a variety of bare quark masses. We find that the wave-function renormalization function is slightly sensitive to the number of stout-link smearing sweeps. For the mass function we find the effect of the stout-link smearing algorithm to be small for moderate to light bare quark masses. For a heavy bare quark mass we find a strong dependence on the number of smearing sweeps.
Extensive studies have demonstrated that finite-range regularization (FRR) offers significantly improved chiral extrapolations for lattice QCD. These studies have typically relied on selecting the finite-regularization scale based upon phenomenological input. Here we report on a preliminary investigation of a procedure to determine a preferred range of FRR scale based on nonperturbative lattice results -- without any phenomenological prejudice.
We study the behavior of the AsqTad quark propagator in Landau gauge on quenched SU(2) gauge configurations under the removal of center vortices. In contrast to recent results in SU(3), we clearly see the infrared enhancement of the mass function disappear if center vortices are removed, a sign of the intimate relation between center vortices and chiral symmetry breaking in SU(2) gauge-field theory. These results provide a benchmark with which to interpret the SU(3) results. In addition, we consider vortex-only configurations. On those, the quark dressing function behaves roughly as on the full configurations, and the mass function picks up an almost linear momentum dependence.
We examine how dynamical fermions affect both the UV and infrared structure of the QCD vacuum. We consider large $28^3 \times 96$ lattices from the MILC collaboration, using a gluonic definition of the topological charge density, founded on a new over-improved stout-link smearing algorithm. The algorithm reproduces established results from the overlap formalism and is designed to preserve nontrivial topological objects including instantons. At short distances we focus on the topological charge correlator, $ $, where negative values at small $x$ reveal a sign-alternating layered structure to the topological-charge density of the QCD vacuum. We find that the magnitudes of the negative dip in the $ $ correlator and the positive $ $ contact term are both increased with the introduction of dynamical fermion degrees of freedom. This is in accord with expectations based on charge renormalization and the vanishing of the topological susceptibility in the chiral limit. At large distances we examine the extent to which instanton-like objects are found on the lattice, and how their distributions vary between quenched and dynamical gauge fields. We show that dynamical gauge fields contain more instanton-like objects with an average size greater than in the quenched vacuum. Finally, we directly visualize the topological charge density in order to investigate the effects of dynamical sea-quark degrees of freedom on topology.
A new over-improved stout-link smearing algorithm, designed to stabilise instanton-like objects, is presented. A method for quantifying the selection of the over-improvement parameter, $ε$, is demonstrated. The new smearing algorithm is compared with the original stout-link smearing, and Symanzik improved smearing through calculations of the topological charge and visualisations of the topological charge density.
The Landau-gauge gluon propagator is studied using the coarse and fine dynamical MILC configurations. The effects of dynamical quarks are clearly visible and lead to a reduction of the nonperturbative infrared enhancement relative to the quenched case. Lattice spacing effects are studied and found to be small. The gluon spectral function is shown to clearly violate positivity in both quenched and full QCD.
The impact of dynamical fermions on the vacuum structure of QCD is explored. Of particular interest is the topological charge correlator, $ $, where negative values at small $x$ reveal a sign-alternating layered structure to the topological-charge density of the QCD vacuum. We consider large $28^3 \times 96$ lattices from the MILC collaboration, and develop a new gluonic definition of the topological charge density, founded on a new over-improved stout-link smearing algorithm. The algorithm reproduces established results from the overlap formalism and is designed to preserve instantons. We examine the extent to which instanton-like objects are found on the lattice. Finally, we investigate the effects of dynamical sea-quark degrees of freedom on topology and find that the magnitudes of the negative dip in the $ $ correlator and the positive $ $ contact term are both increased with the introduction of dynamical fermion degrees of freedom. This is in accord with expectations based on charge renormalization and the vanishing of the topological susceptibility in the chiral limit.