The world's first examination of the odd-parity nucleon spectrum at light quark masses in 2+1 flavor lattice QCD is presented. Configurations generated by the PACS-CS collaboration and made available through the ILDG are used, with the lightest pion mass at 156 MeV. A novel method for tracking the individual energy eigenstates as the quark mass changes is introduced. The success of this approach reveals the flow of the states towards the physical masses. Using the correlation matrix method, the two lowest-energy states revealed are found to be in accord with the physical spectrum of Nature.

A determination of the excited energy eigenstates of the nucleon, s = 1/2, I = 1/2, N+, is presented in full QCD using 2 + 1 flavor PACS-CS gauge configurations. The correlation-matrix method is used and is built using standard nucleon interpolators employing smearings at the fermion sources and sinks. We develop and demonstrate a new technique that allows the eigenvectors obtained to be utilized to track the propagation of the intrinsic nature of energy states from one quark mass to the next. This approach is particularly useful for larger dimension correlation matrices where more near-degenerate energy states can appear in the spectrum.

The low-lying even-parity states of the nucleon are explored in lattice QCD using the PACS-CS collaboration 2 + 1-flavor dynamical-QCD gauge-field configurations made available through the International Lattice Datagrid (ILDG). The established correlation-matrix approach is used, in which various fermion source and sink smearings are utilized to provide an effective basis of interpolating fields to span the space of low-lying energy eigenstates. Of particular interest is the nature of the first excited state of the nucleon, the N1/2(+) Roper resonance of P-11 pion-nucleon scattering. The Roper state of the present analysis approaches the physical mass, displaying significant chiral curvature at the lightest quark mass. These full QCD results, providing the world's first insight into the nucleon mass spectrum in the light-quark regime, are significantly different from those of quenched QCD and provide interesting insights into the dynamics of QCD. (C) 2012 Elsevier B.V. All rights reserved.

The results for the odd-parity nucleon spectrum at light quark masses are presented.The 2 + 1 flavor gauge configurations generated by the PACS-CS collaboration are used and the analysis is performed at the lightest pion mas of 156 MeV.The energy eigenstates are tracked by following the evolution of the eigenvector as the quark mass changes.The two lowest-energy odd-parity states revealed are found to be in accord with the physical N 1 2 -spectrum of Nature.

Here we present exploratory calculations of the light meson radiative transition moment ρ → γπ from lattice QCD.We observe interesting chiral curvature in the form factor and a definite environment sensitivity in the quark sector contributions.Results are compared with the simple quark model and experiment.

Recent developments on the determination of the spin-1/2 spectrum of the nucleon in full QCD are presented.Our focus is on the PACS-CS 2+1 flavor configurations made available through the ILDG.Using correlation matrix techniques, in which a wide variety of gauge-invariant Gaussiansmeared fermion-propagator sources and sinks are considered, excited states are determined.We consider several correlation matrices of various sizes, each constructed with a different set of basis interpolators, in order to demonstrate the invariance of the eigenstates on the basis choice.Of particular interest is the approach to the elusive Roper resonance and we report preliminary results in full QCD.

In Nature the excited states of the hadron spectrum appear as resonances. Consequently, there has been significant interest in studying the excited baryon spectrum using lattice QCD. With this in mind we perform spectroscopic calculations with five-quark interpolating fields. Stochastic estimation techniques are used in order to calculate the loop propagators, with dilution in spin, colour and time implemented as a means of variance reduction. We present effective mass plots extracted from these five-quark interpolators, and examine the contributions from fully-connected and loop-containing pieces of the correlation function, keeping in mind their use in future corre- lation matrix studies.

Our recent first-principles lattice-QCD exploration of the excited states of the nucleon in the positive parity channel is presented.Of particular interest is the first positive-parity excitation of the nucleon; the Roper resonance.Using correlation-matrix methods developed by the CSSM Lattice Collaboration, a low-lying Roper state is observed in our full QCD analysis using the PACS-CS gauge fields made available via the ILDG.A method for tracing the quark-mass flow of energy eigenstates using the eigenvectors of the generalized eigenvalue equations is presented.The results for the Roper display significant curvature as the chiral regime is approached.

We use over-improved stout-link smearing to investigate the presence and nature of instantons on the lattice. We find that smearing can remove short-range effects with little damage to the long-range structure of the gauge field, and that after around 50 sweeps this process is complete. There are more significant risks for very high levels of smearing beyond 100 sweeps. We are thus able to produce gauge configurations dominated by instanton effects. We then calculate the overlap quark propagator on these configurations, and thus the non-perturbative mass function. We find that smeared configurations reproduce the majority of dynamical mass generation, and conclude that instantons are primarily responsible for the dynamical generation of mass.

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, using a Lüscher–Weisz gauge action. 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.

Complex systems consisting of vector or matrix oscillators can synchronize to a common state characterized by a frequency matrix with distinct eigenvalues, leading to multiple frequencies of synchronization. In quantum networked systems the synchronized state is a linear combination of states corresponding to different energy levels. Suitable symmetry-breaking network interactions, however, allow only one or more such frequencies to appear. A specific example in three dimensions, where all trajectories lie on the 2-sphere, is a model of interacting spin-1 quantum angular momentum states, where synchronization to a nontrivial frequency occurs despite the presence of zero-frequency modes of oscillation.

Center vortices are studied in SU(3) gauge theory using Maximal Center Gauge (MCG) fixing. Stout link smearing and over-improved stout link smearing are used to construct a preconditioning gauge field transformation, applied to the original gauge field before fixing to MCG. We find that preconditioning successfully achieves higher gauge fixing maxima. We observe a reduction in the number of identified vortices when preconditioning is used, and also a reduction in the vortex-only string tension.

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.

The properties of the momentum-space quark propagator in the 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 nonperturbative wave-function renormalization function Z(p) and the nonperturbative 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.

A new over-improved stout-link smearing algorithm, designed to stabilize 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 visualizations of the topological charge density. We find the incorporation of improvement in stout-link smearing to be essential for the accurate study of QCD vacuum structure.

We examine how dynamical fermions affect both the UV and infrared structure of the QCD vacuum. We consider large 28(3) x 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 preserves nontrivial topological objects, including instantons. At short distances we focus on the topological charge correlator, < q(x)q(0)>, 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 < q(x)q(0)> correlator and the positive < q(0)(2)> contact term are both increased with the introduction of dynamical fermion degrees of freedom. 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.

Also cited as: Lattice 2007, the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany / Gunnar Bali, Vladimir Braun, Christof Gattringer, Meinulf Gockeler, Andreas Schafer, Peter Weisz, Tilo Wettig (eds.): 383/1-383/7.