Approach to the Continuum Limit of the Quenched Hermitian Wilson-Dirac Operator

We investigate the approach to the continuum limit of the spectrum of the Hermitian Wilson-Dirac operator in the supercritical mass region for pure gauge SU(2) and SU(3) backgrounds. For this we study the spectral flow of the Hermitian Wilson-Dirac operator in the range $0\le m\le 2$. We find that the spectrum has a gap for $0 < m \le m_1$ and that the spectral density at zero, $\rho(0;m)$, is non-zero for $m_1\le m\le 2$. We find that $m_1\to 0$ and, for $m \ne 0, \rho(0;m)\to 0$ (exponential in the lattice spacing) as one goes to the continuum limit. We also compute the topological susceptibility and the size distribution of the zero modes. The topological susceptibility scales well in the lattice spacing for both SU(2) and SU(3). The size distribution of the zero modes does not appear to show a peak at a physical scale.Comment: 19 pages revtex with 9 postscript figures included by eps

Are Topological Charge Fluctuations in QCD Instanton Dominated?

We consider a recent proposal by Horv\'ath {\em et al.} to address the question whether topological charge fluctuations in QCD are instanton dominated via the response of fermions using lattice fermions with exact chiral symmetry, the overlap fermions. Considering several volumes and lattice spacings we find strong evidence for chirality of a finite density of low-lying eigenvectors of the overlap-Dirac operator in the regions where these modes are peaked. This result suggests instanton dominance of topological charge fluctuations in quenched QCD.Comment: LaTeX, 15 pages, 8 postscript figures, minor improvements, version to appear in PR

Non-Reversibility of Molecular Dynamics Trajectories

We study the non-reversibility of molecular dynamics trajectories arising from the amplification of rounding errors. We analyse the causes of such behaviour and give arguments, indicating that this does not pose a significant problem for Hybrid Monte Carlo computations. We present data for pure SU(3) gauge theory and for QCD with dynamical fermions on small lattices to illustrate and to support some of our ideas.Comment: 3 pages LATEX, 4 color figures included using epsf. Talk presented at LATTICE96(algorithms

Nucleon Structure from Lattice QCD

Recent advances in lattice field theory, in computer technology and in chiral perturbation theory have enabled lattice QCD to emerge as a powerful quantitative tool in understanding hadron structure. I describe recent progress in the computation of the nucleon form factors and moments of parton distribution functions, before proceeding to describe lattice studies of the Generalized Parton Distributions (GPDs). In particular, I show how lattice studies of GPDs contribute to building a three-dimensional picture of the proton. I conclude by describing the prospects for studying the structure of resonances from lattice QCD.Comment: 6 pages, invited plenary talk at NSTAR 2007, 5-8 September 2007, Bonn, German

Spectroscopy using the Anisotropic Clover Action

The calculation of the light-hadron spectrum in the quenched approximation to QCD using an anisotropic clover fermion action is presented. The tuning of the parameters of the action is discussed, using the pion and rho dispersion relation. The adoption of an anisotropic lattice provides clear advantages in the determination of the baryonic resonances, and in particular that of the so-called Roper resonance, the lightest radial excitation of the nucleon.Comment: Lattice2002(spectrum), 3 pages, 3 figures, to appear in Proceedings of Lattice 200

Chiral Condensate in the Deconfined Phase of Quenched Gauge Theories

We compute the low lying spectrum of the overlap Dirac operator in the deconfined phase of finite-temperature quenched gauge theory. It suggests the existence of a chiral condensate which we confirm with a direct stochastic estimate. We show that the part of the spectrum responsible for the chiral condensate can be understood as arising from a dilute gas of instantons and anti-instantons.Comment: Revtex, 16 pages, 3 postscript figure

Chiral properties of domain-wall fermions from eigenvalues of 4 dimensional Wilson-Dirac operator

We investigate chiral properties of the domain-wall fermion (DWF) system by using the four-dimensional hermitian Wilson-Dirac operator. We first derive a formula which connects a chiral symmetry breaking term in the five dimensional DWF Ward-Takahashi identity with the four dimensional Wilson-Dirac operator, and simplify the formula in terms of only the eigenvalues of the operator, using an ansatz for the form of the eigenvectors. For a given distribution of the eigenvalues, we then discuss the behavior of the chiral symmetry breaking term as a function of the fifth dimensional length. We finally argue the chiral property of the DWF formulation in the limit of the infinite fifth dimensional length, in connection with spectra of the hermitian Wilson-Dirac operator in the infinite volume limit as well as in the finite volume.Comment: Added a reference and modified the acknowledgmen

A Comparison of Clover and Wilson Spectroscopy in the Presence of Dynamical Quarks

We present preliminary results of light hadron spectroscopy using valence, tadpole-improved, Clover fermions on an ensemble of gauge configurations generated with 2 flavors of staggered fermions at a beta of 5.6. We compare the slope and intercept of the curve M_V vs. M_PS^2 for Clover and Wilson fermions. We show that a higher order chiral perturbation theory ansatz works very well for chiral extrapolations.Comment: 4 pages latex with 4 Postscript figures, to be published in the Proceedings of Lattice 9

Another determination of the quark condensate from an overlap action

I use the technique of Hernandez, et al (hep-lat/0106011) to convert a recent calculation of the lattice-regulated quark condensate from an overlap action to a continuum-regulated number. I find Sigma(MSbar)(mu = 2 GeV) = (282(6) MeV)-cubed times (a-inverse/1766 MeV)-cubed from a calculation with the Wilson gauge action at beta=5.9.Comment: 3 pages, Revtex, 1 postscript figure. References added. COLO-HEP-47

Schroedinger functional formalism with domain-wall fermion

Finite volume renormalization scheme is one of the most fascinating scheme for non-perturbative renormalization on lattice. By using the step scaling function one can follow running of renormalized quantities with reasonable cost. It has been established the Schroedinger functional is very convenient to define a field theory in a finite volume for the renormalization scheme. The Schroedinger functional, which is characterized by a Dirichlet boundary condition in temporal direction, is well defined and works well for the Yang-Mills theory and QCD with the Wilson fermion. However one easily runs into difficulties if one sets the same sort of the Dirichlet boundary condition for the overlap Dirac operator or the domain-wall fermion. In this paper we propose an orbifolding projection procedure to impose the Schroedinger functional Dirichlet boundary condition on the domain-wall fermion.Comment: 32 page