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

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

Quark-gluon vertex in general kinematics

The original publication can be found at www.springerlink.com Submitted to Cornell University’s online archive www.arXiv.org in 2007 by Jon-Ivar Skullerud. Post-print sourced from www.arxiv.org.We compute the quark–gluon vertex in quenched lattice QCD in the Landau gauge, using an off-shell mean-field O(a)-improved fermion action. The Dirac-vector part of the vertex is computed for arbitrary kinematics. We find a substantial infrared enhancement of the interaction strength regardless of the kinematics.Ayse Kizilersu, Derek B. Leinweber, Jon-Ivar Skullerud and Anthony G. William

Scaling behavior 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 are done on three lattices with different lattice spacings and similar physical volumes to explore the approach of the quark propagator toward the continuum limit. We have calculated the nonperturbative momentum-dependent wave function renormalization function Z(p) and the nonperturbative mass function M(p) for a variety of bare quark masses and perform an extrapolation to the chiral limit. We find the behavior of Z(p) and M(p) are in reasonable agreement between the two finer lattices in the chiral limit, however the data suggest that an even finer lattice is desirable. The large momentum behavior is examined to determine the quark condensate.Comment: 9 pages, 5 figures, Revtex 4. Streamlined presentation, additional data. Final versio

Nonperturbative structure of the quark-gluon vertex

The complete tensor structure of the quark--gluon vertex in Landau gauge is determined at two kinematical points (`asymmetric' and `symmetric') from lattice QCD in the quenched approximation. The simulations are carried out at beta=6.0, using a mean-field improved Sheikholeslami-Wohlert fermion action, with two quark masses ~ 60 and 115 MeV. We find substantial deviations from the abelian form at the asymmetric point. The mass dependence is found to be negligible. At the symmetric point, the form factor related to the chromomagnetic moment is determined and found to contribute significantly to the infrared interaction strength.Comment: 16 pages, 11 figures, JHEP3.cl

Gluon Propagator on Coarse Lattices in Laplacian Gauges

The Laplacian gauge is a nonperturbative gauge fixing that reduces to Landau gauge in the asymptotic limit. Like Landau gauge, it respects Lorentz invariance, but it is free of Gribov copies; the gauge fixing is unambiguous. In this paper we study the infrared behavior of the lattice gluon propagator in Laplacian gauge by using a variety of lattices with spacings from $a = 0.125$ to 0.35 fm, to explore finite volume and discretization effects. Three different implementations of the Laplacian gauge are defined and compared. The Laplacian gauge propagator has already been claimed to be insensitive to finite volume effects and this is tested on lattices with large volumes.Comment: RevTex 4.0, 14 pages, 9 colour figures; Correction to Reference

From Euclidean to Minkowski space with the Cauchy-Riemann equations

We present an elementary method to obtain Green's functions in non-perturbative quantum field theory in Minkowski space from calculated Green's functions in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes is many times unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore we suggest to use the Cauchy-Riemann equations, that perform the analytical continuation without assuming global information on the function in the entire complex plane, only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge Quantum Chromodynamics, that is known from lattice and Dyson-Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy-Riemann equations to high-frequency noise, that makes difficult to achieve good accuracy. We also point out a few curiosities related to the Wick rotation.Comment: 12 pages in EPJ double-column format, 16 figures. This version: added paragraph, two reference

Analysis of a quenched lattice-QCD dressed-quark propagator

Quenched lattice-QCD data on the dressed-quark Schwinger function can be correlated with dressed-gluon data via a rainbow gap equation so long as that equation's kernel possesses enhancement at infrared momenta above that exhibited by the gluon alone. The required enhancement can be ascribed to a dressing of the quark-gluon vertex. The solutions of the rainbow gap equation exhibit dynamical chiral symmetry breaking and are consistent with confinement. The gap equation and related, symmetry-preserving ladder Bethe-Salpeter equation yield estimates for chiral and physical pion observables that suggest these quantities are materially underestimated in the quenched theory: |<bar-q q>| by a factor of two and f_pi by 30%.Comment: 9 pages, LaTeX2e, REVTEX4, 6 figure

Looking into the matter of light-quark hadrons

In tackling QCD, a constructive feedback between theory and extant and forthcoming experiments is necessary in order to place constraints on the infrared behaviour of QCD's \beta-function, a key nonperturbative quantity in hadron physics. The Dyson-Schwinger equations provide a tool with which to work toward this goal. They connect confinement with dynamical chiral symmetry breaking, both with the observable properties of hadrons, and hence provide a means of elucidating the material content of real-world QCD. This contribution illustrates these points via comments on: in-hadron condensates; dressed-quark anomalous chromo- and electro-magnetic moments; the spectra of mesons and baryons, and the critical role played by hadron-hadron interactions in producing these spectra.Comment: 11 pages, 7 figures. Contribution to the Proceedings of "Applications of light-cone coordinates to highly relativistic systems - LIGHTCONE 2011," 23-27 May, 2011, Dallas. The Proceedings will be published in Few Body System

A dynamical gluon mass solution in a coupled system of the Schwinger-Dyson equations

We study numerically the Schwinger-Dyson equations for the coupled system of gluon and ghost propagators in the Landau gauge and in the case of pure gauge QCD. We show that a dynamical mass for the gluon propagator arises as a solution while the ghost propagator develops an enhanced behavior in the infrared regime of QCD. Simple analytical expressions are proposed for the propagators, and the mass dependency on the $\Lambda_{QCD}$ scale and its perturbative scaling are studied. We discuss the implications of our results for the infrared behavior of the coupling constant, which, according to fits for the propagators infrared behavior, seems to indicate that $\alpha_s (q^2) \to 0$ as $q^2 \to 0$.Comment: 17 pages, 7 figures - Revised version to be consistent with erratum to appear in JHE