20 research outputs found
The strong-coupling limit of lattice Landau gauge
We report on our recent study of the gluon and ghost propagators of pure
SU(2) minimal lattice Landau gauge in the strong-coupling limit. In this limit,
we find evidence of the conformal infrared behaviour of these propagators as
predicted by functional continuum methods. However, in the strong-coupling
limit this happens for lattice momenta with a^2q^2>1, in units of the lattice
spacing a. Deviations from conformal scaling for a^2q^2<1 are well
parameterised by a transverse gluon mass. A comparison of various lattice
definitions of gauge potentials, all equivalent in the continuum limit, shows
that (a) both the critical exponent and coupling can be extracted unambiguously
from the high-momentum data in the strong-coupling limit, in good agreement
with the continuum predictions; but that on the other hand (b) the massive
branch depends on the definition of lattice gluon fields and is thus not
unambiguously defined. We demonstrate that this ambiguity is also present in
the low-momentum region for commonly used values of the lattice coupling in
SU(2).Comment: 5 pages, talk presented at the 8th Conference Quark Confinement and
the Hadron Spectrum, September 1-6, 2008, Mainz, German
The infrared behavior of lattice QCD Green's functions
We investigate different aspects of lattice QCD in Landau gauge using Monte Carlo simulations. In particular, we focus on the low momentum behavior of gluon and ghost propagators. The gauge group is SU(3). Different systematic effects on the gluon and ghost propagators are studied, e.g. the dependence on the choice of Gribov copies or the influence of dynamical Wilson fermions. We compare our data with results from studies of Dyson-Schwinger equations for the gluon and ghost propagators. We demonstrate that the infrared behavior of both propagators, as found in this thesis, is consistent with different criteria for confinement. However, the running coupling constant, given as a renormalization-group-invariant combination of the gluon and ghost dressing functions, does not expose a finite infrared fixed point. We also report on a first nonperturbative computation of the SU(3) ghost-gluon-vertex renormalization constant and on an investigation of the spectral properties of the Faddeev-Popov operator.http://www.arxiv.org/abs/hep-lat/060901
Coulomb gauge studies of SU(3) Yang-Mills theory on the lattice
We study the infrared behaviour of lattice SU(3) Yang-Mills theory in Coulomb
gauge in terms of the ghost propagator, the Coulomb potential and the
transversal and the time-time component of the equal-time gluon propagator. In
particular, we focus on the Gribov problem and its impact on the observables.
We observe that the simulated annealing method is advantageous for fixing the
Coulomb gauge in large volumes. We study finite size and discretization
effects. While finite size effects can be controlled by the cone cut, and the
ghost propagator and the Coulomb potential become scaling functions with the
cylinder cut, the equal-time gluon propagator does not show scaling in the
considered range of the inverse coupling constant. The ghost propagator is
infrared enhanced. The Coulomb potential is now extended to considerably lower
momenta and shows a more complicated infrared regime. The Coulomb string
tension satisfies Zwanziger's inequality, but its estimate can be considered
only preliminary because of the systematic Gribov effect that is particularly
strong for the Coulomb potential.Comment: 7 pages, 5 pictures, poster presented at the XXV International
Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg,
Germany; corrected value for fitting parameter
Using NSPT for the Removal of Hypercubic Lattice Artifacts
The treatment of hypercubic lattice artifacts is essential for the
calculation of non-perturbative renormalization constants of RI-MOM schemes. It
has been shown that for the RI'-MOM scheme a large part of these artifacts can
be calculated and subtracted with the help of diagrammatic Lattice Perturbation
Theory (LPT). Such calculations are typically restricted to 1-loop order, but
one may overcome this limitation and calculate hypercubic corrections for any
operator and action beyond the 1-loop order using Numerical Stochastic
Perturbation Theory (NSPT). In this study, we explore the practicability of
such an approach and consider, as a first test, the case of Wilson fermion
bilinear operators in a quenched theory. Our results allow us to compare
boosted and unboosted perturbative corrections up to the 3-loop order.Comment: 7 pages, 6 figures, talk presented at the 32nd International
Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, New York,
USA; PoS(LATTICE2014)29
Discretization Errors for the Gluon and Ghost Propagators in Landau Gauge using NSPT
The subtraction of hypercubic lattice corrections, calculated at 1-loop order
in lattice perturbation theory (LPT), is common practice, e.g., for
determinations of renormalization constants in lattice hadron physics.
Providing such corrections beyond 1-loop order is however very demanding in
LPT, and numerical stochastic perturbation theory (NSPT) might be the better
candidate for this. Here we report on a first feasibility check of this method
and provide (in a parametrization valid for arbitrary lattice couplings) the
lattice corrections up to 3-loop order for the SU(3) gluon and ghost
propagators in Landau gauge. These propagators are ideal candidates for such a
check, as they are available from lattice simulations to high precision and can
be combined to a renormalization group invariant product (Minimal MOM coupling)
for which a 1-loop LPT correction was found to be insufficient to remove the
bulk of the hypercubic lattice artifacts from the data. As a bonus, we also
compare our results with the ever popular H(4) method.Comment: 7 pages, 5 figures, presented at the 31st International Symposium on
Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German