Numerical techniques for lattice QCD in the ϵ\epsilon--regime

In lattice QCD it is possible, in principle, to determine the parameters in the effective chiral lagrangian (including weak interaction couplings) by performing numerical simulations in the $\epsilon$--regime, i.e. at quark masses where the physical extent of the lattice is much smaller than the Compton wave length of the pion. The use of a formulation of the lattice theory that preserves chiral symmetry is attractive in this context, but the numerical implementation of any such approach requires special care in this kinematical situation due to the presence of some very low eigenvalues of the Dirac operator. We discuss a set of techniques (low-mode preconditioning and adapted-precision algorithms in particular) that make such computations numerically safe and more efficient by a large factor.Comment: Plain TeX source, 32 pages, figures include

Center Vortex Model for the Infrared Sector of SU(3) Yang-Mills Theory - Vortex Free Energy

The vortex free energy is studied in the random vortex world-surface model of the infrared sector of SU(3) Yang-Mills theory. The free energy of a center vortex extending into two spatial directions, which is introduced into Yang-Mills configurations when acting with the 't Hooft loop operator, is verified to furnish an order parameter for the deconfinement phase transition. It is shown to exhibit a weak discontinuity at the critical temperature, corresponding to the weak first order character of the transition.Comment: 13 pages, 2 figures containing 3 eps file

Exact results and approximation schemes for the Schwinger model with the overlap Dirac operator

We propose new techniques to implement numerically the overlap-Dirac operator which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger model and the results are very promising. We also present a detailed computation of the spectrum and chiral properties of the Schwinger Model in the overlap lattice formulation.Comment: Lattice 2000 (Chiral Fermions

Excited state baryon spectroscopy from lattice QCD

We present a calculation of the Nucleon and Delta excited state spectrum on dynamical anisotropic clover lattices. A method for operator construction is introduced that allows for the reliable identification of the continuum spins of baryon states, overcoming the reduced symmetry of the cubic lattice. Using this method, we are able to determine a spectrum of single-particle states for spins up to and including J = 7/2, of both parities, the first time this has been achieved in a lattice calculation. We find a spectrum of states identifiable as admixtures of SU(6) x O(3) representations and a counting of levels that is consistent with the non-relativistic $qqq$ constituent quark model. This dense spectrum is incompatible with quark-diquark model solutions to the "missing resonance problem" and shows no signs of parity doubling of states.Comment: 29 pages, 18 figure

Light hadron spectra and wave functions in quenched QCD with overlap quarks on a large lattice

A simulation of quenched QCD with the overlap Dirac operator has been completed using 100 Wilson gauge configurations at beta=6 on an 18^3x64 lattice. We present results for meson and baryon masses, meson final state "wave functions'' and other observables.Comment: 5 LaTeX pages (espcrc2.sty), 13 figures. Combined contributions by J.H., L.L. and C.R. at Lattice2004(spectrum), Fermilab, June 21-26, 200

Chiral behavior of pseudo-Goldstone boson masses and decay constants in 2+1 flavor QCD

We present preliminary results for the chiral behavior of charged pseudo-Goldstone-boson masses and decay constants. These are obtained in simulations with N_f=2+1 flavors of tree-level, O(a)-improved Wilson sea quarks. In these simulations, mesons are composed of either valence quarks discretized in the same way as the sea quarks (unitary simulations) or of overlap valence quarks (mixed-action simulations). We find that the chiral behavior of the pseudoscalar meson masses in the mixed-action calculations cannot be explained with continuum, partially-quenched chiral perturbation theory. We show that the inclusion of O(a^2) unitarity violations in the chiral expansion resolves this discrepancy and that the size of the unitarity violations required are consistent with those which we observe in the zero-momentum, scalar-isotriplet-meson propagator.Comment: 7 pages, 3 figures, talk by L. Lellouch at the XXV International Symposium on Lattice Field Theory (LATTICE 2007), 30 July - 4 August 2007, Regensburg, German