QCD, Gauge Fixing, and the Gribov Problem

The standard techniques of gauge-fixing, such as covariant gauge fixing, are entirely adequate for the purposes of studies of perturbative QCD. However, they fail in the nonperturbative regime due to the presence of Gribov copies. These copies arise because standard local gauge fixing methods do not completely fix the gauge. Known Gribov-copy-free gauges, such as Laplacian gauge, are manifestly non-local. These issues are examined and the implications of non-local gauge-fixing for ghost fields, BRST invariance, and the proof of renormalizability of QCD are considered.Comment: 5 pages, 2 figures, talk given at LHP 2001 workshop, Cairns, Australi

Improving the low-lying spectrum of the overlap kernel

The action of the overlap-Dirac operator on a vector is typically implemented in directly through a multi-shift conjugate gradient solver. The compute-time this takes to evaluate depends upon the condition number $\kappa$ of the matrix that is used as the overlap kernel. We examine the low-lying spectra of various candidate kernels in an effort to optimise $\kappa$, thereby speeding up the overlap evaluation.Comment: 5 pages, 8 figure

Sigma and omega meson propagation in a dense nuclear medium

The propagation of the scalar ($\sigma$) and vector ($\omega$) mesons in nuclear matter is studied in detail using the Walecka model over a wide range of densities and including the effects of a finite $\sigma$ width through the inclusion of a two-pion loop. We calculate the dispersion relation and spectral functions of the $\sigma$ and (transverse and longitudinal) $\omega$ mesons, including the effect of $\sigma$-$\omega$ mixing in matter. It is shown that the mixing effect is quite important in the propagation of the (longitudinal) $\omega$ and $\sigma$ mesons above normal nuclear matter density. We find that there is a two-peak structure in the spectral function of the $\sigma$ channel, caused by $\sigma$-$\omega$ mixing.Comment: 17 pages including 6 ps files, submitted to Phys. Lett. B. Acknowledgement is revise

Improved Landau Gauge Fixing and Discretisation Errors

Lattice discretisation errors in the Landau gauge condition are examined. An improved gauge fixing algorithm in which order a^2 errors are removed is presented. Order a^2 improvement of the gauge fixing condition displays the secondary benefit of reducing the size of higher-order errors. These results emphasise the importance of implementing an improved gauge fixing condition.Comment: LATTICE99 (Improvement and Renormalization), 3 pages, 1 figur

The neutron charge form factor in helium-3

In order to measure the charge form factor of the neutron, $G^n_E(Q^2)$, one needs to use a neutron bound in a nuclear target. We calculate the change in the form factor for a neutron bound in $^3He$, with respect to the free case, using several versions of the quark meson coupling model. It is found that the form factor may be suppressed by as much as 12% at $Q^2 = 0.5{GeV}^2$ with respect to that of the free neutron.Comment: 13 pages including 2 ps figure

FLIC-Overlap Fermions and Topology

APE smearing the links in the irrelevant operators of clover fermions (Fat-Link Irrelevant Clover (FLIC) fermions) provides significant improvement in the condition number of the Hermitian-Dirac operator and gives rise to a factor of two savings in computing the overlap operator. This report investigates the effects of using a highly-improved definition of the lattice field-strength tensor F_mu_nu in the fermion action, made possible through the use of APE-smeared fat links in the construction of the irrelevant operators. Spurious double-zero crossings in the spectral flow of the Hermitian-Wilson Dirac operator associated with lattice artifacts at the scale of the lattice spacing are removed with FLIC fermions composed with an O(a^4)-improved lattice field strength tensor. Hence, FLIC-Overlap fermions provide an additional benefit to the overlap formalism: a correct realization of topology in the fermion sector on the lattice.Comment: Lattice2002(chiral

Modelling the gluon propagator

Scaling of the Landau gauge gluon propagator calculated at beta=6.0 and at beta=6.2 is demonstrated. A variety of functional forms for the gluon propagator calculated on a large (32^3x64) lattice at beta=6.0 are investigated.Comment: LATTICE98(confine), 3 pages, 2 figure

Towards the Continuum Limit of the Overlap Quark Propagator in Landau Gauge

The properties of the momentum space quark propagator in Landau gauge are examined for the overlap quark action in quenched lattice QCD. Numerical calculations were done on two lattices with different lattice spacing $a$ and similar physical volumes to explore the quark propagator in the continuum limit. We have calculated the nonperturbative wavefunction renormalization function $Z(p)$ and the nonperturbative mass function $M(p)$ for a variety of bare quark masses and perform a simple linear extrapolation to the chiral limit. We find the behaviour of $Z(p)$ and $M(p)$ in the chiral limit are in good agreement between the two lattices.Comment: 3 pages, 2 figures, talk, Lattice2002(Chiral Fermion

Hybrid and Exotic Mesons from FLIC Fermions

The spectral properties of hybrid meson interpolating fields are investigated. The quantum numbers of the meson are carried by smeared-source fermion operators and highly-improved chromo-electric and -magnetic field operators composed with APE-smeared links. The effective masses of standard and hybrid operators indicate that the ground state meson is effectively isolated using both standard and hybrid interpolating fields. Focus is placed on interpolating fields in which the large spinor components of the quark and antiquark fields are merged. In particular, the effective mass of the exotic $1^{-+}$ meson is reported. Further, we port some values for excited mesonic states using a variational process.Comment: 3 Pages, 3 figures, Lattice2003(Spectrum