30 research outputs found
Should the Pomeron and imaginary parts be modelled by two gluons and real quarks?
We illustrate that solution of the Schwinger-Dyson equation for the gluon
propagator in QCD does not support an infrared softened behaviour, but only an
infrared enhancement. This has consequences for the modelling of the Pomeron in
terms of dressed gluon exchange. It highlights that an understanding of the
Pomeron within QCD must take account of the bound state nature of hadrons.Comment: 7 pages, latex, 2 figures, replaced ~\epsfig... by \mbox{\epsfig...
QCD Down Under: Building Bridges
The strong coupling regime of QCD is responsible for 99% of hadronic
phenomena. Though considerable progress has been made in solving QCD in this
non-perturbative region, we nevertheless have to rely on a disparate range of
models and approximations. If we are to gain an understanding of the underlying
physics and not just have numerical answers from computing `` black'' boxes, we
must build bridges between the parameter space where models and approximations
are valid to the regime describing experiment, and between the different
modellings of strong dynamics. We describe here how the
Schwinger-Dyson/Bethe-Salpeter approach provides just such a bridge, linking
physics, the lattice and experiment.Comment: 8 pages, 10 figures. Opening talk at Workshop on QCD Down Under,
March 2004, Barossa Valley and Adelaide (to be published in the Proceedings
The Infrared Behavior of Gluon and Ghost Propagators in Landau Gauge QCD
A solvable systematic truncation scheme for the Dyson-Schwinger equations of
Euclidean QCD in Landau gauge is presented. It implements the Slavnov-Taylor
identities for the three-gluon and ghost-gluon vertices, whereas irreducible
four-gluon couplings as well as the gluon-ghost and ghost-ghost scattering
kernels are neglected. The infrared behavior of gluon and ghost propagators is
obtained analytically: The gluon propagator vanishes for small spacelike
momenta whereas the ghost propagator diverges stronger than a massless particle
pole. The numerical solutions are compared with recent lattice data for these
propagators. The running coupling of the renormalization scheme approaches a
fixed point, , in the infrared.Comment: 4 pages, 2 figures, Revtex; revised version accepted for publication
in Physical Review Letter
Study of Quark Propagator Solutions to the Dyson--Schwinger Equation in a Confining Model
We solve the Dyson--Schwinger equation for the quark propagator in a model
with singular infrared behavior for the gluon propagator. We require that the
solutions, easily found in configuration space, be tempered distributions and
thus have Fourier transforms. This severely limits the boundary conditions that
the solutions may satisify. The sign of the dimensionful parameter that
characterizes the model gluon propagator can be either positive or negative. If
the sign is negative, we find a unique solution. It is singular at the origin
in momentum space, falls off like as , and it
is truly nonperturbative in that it is singular in the limit that the
gluon--quark interaction approaches zero. If the sign of the gluon propagator
coefficient is positive, we find solutions that are, in a sense that we
exhibit, unconstrained linear combinations of advanced and retarded
propagators. These solutions are singular at the origin in momentum space, fall
off like asympotically, exhibit ``resonant--like" behavior at the
position of the bare mass of the quark when the mass is large compared to the
dimensionful interaction parameter in the gluon propagator model, and smoothly
approach a linear combination of free--quark, advanced and retarded two--point
functions in the limit that the interaction approaches zero. In this sense,
these solutions behave in an increasingly ``particle--like" manner as the quark
becomes heavy. The Feynman propagator and the Wightman function are not
tempered distributions and therefore are not acceptable solutions to the
Schwinger--Dyson equation in our model. On this basis we advance several
arguments to show that the Fourier--transformable solutions we find are
consistent with quark confinement, even though they have singularities on th
Dynamical symmetry breaking, confinement with flat-bottom potential
In this article, we calculate the dressed quark propagator with the flat
bottom potential in the framework of the rain-bow Schwinger-Dyson equation.
Then based on the nonperturbative dressed quark propagator, we calculate the
decay constant and the quark condensate. The decay constant is an
important parameter in describing the interplay between dynamical symmetry
breaking and confinement, while the quark condensate is an order parameter for
dynamical chiral symmetry breaking. To implement confinement, we prove that the
dressed quark propagator has no poles on the real timelike axial, the
absence of Kallen-Lehmann spectral representation obviously precludes the
existence of free quarks.Comment: 10 pages,3 figure
Nonperturbative Determination of Heavy Meson Bound States
In this paper we obtain a heavy meson bound state equation from the heavy
quark equation of motion in heavy quark effective theory (HQET) and the heavy
meson effective field theory we developed very recently. The bound state
equation is a covariant extention of the light-front bound state equation for
heavy mesons derived from light-front QCD and HQET. We determine the covariant
heavy meson wave function variationally by minimizing the binding energy
. Subsequently the other basic HQET parameters and
, and the heavy quark masses and can also be
consistently determined.Comment: 15 pages, 1 figur
Slavnov-Taylor identities in Coulomb gauge Yang-Mills theory
The Slavnov-Taylor identities of Coulomb gauge Yang-Mills theory are derived
from the (standard, second order) functional formalism. It is shown how these
identities form closed sets from which one can in principle fully determine the
Green's functions involving the temporal component of the gauge field without
approximation, given appropriate input.Comment: 20 pages, no figure
pi-pi scattering in a QCD based model field theory
A model field theory, in which the interaction between quarks is mediated by
dressed vector boson exchange, is used to analyse the pionic sector of QCD. It
is shown that this model, which incorporates dynamical chiral symmetry
breaking, asymptotic freedom and quark confinement, allows one to calculate
, , and the partial wave amplitudes in -
scattering and obtain good agreement with the experimental data, with the
latter being well described up to energies \mbox{ MeV}.Comment: 23 Pages, 4 figures in PostScript format, PHY-7512-TH-93, REVTEX
Available via anonymous ftp in /pub: login anonymou get pipi93.tex Fig1.ps
Fig2.ps Fig3.ps Fig4.p
Dynamical chiral symmetry breaking and confinement with an infrared-vanishing gluon propagator?
We study a model Dyson-Schwinger equation for the quark propagator closed
using an {\it Ansatz} for the gluon propagator of the form \mbox{} and two {\it Ans\"{a}tze} for the quark-gluon vertex: the
minimal Ball-Chiu and the modified form suggested by Curtis and Pennington.
Using the quark condensate as an order parameter, we find that there is a
critical value of such that the model does not support dynamical chiral
symmetry breaking for . We discuss and apply a confinement test which
suggests that, for all values of , the quark propagator in the model {\bf is
not} confining. Together these results suggest that this Ansatz for the gluon
propagator is inadequate as a model since it does not yield the expected
behaviour of QCD.Comment: 21 Pages including 4 PostScript figures uuencoded at the end of the
file. Replacement: slight changes of wording and emphasis. ADP-93-215/T133,
ANL-PHY-7599-TH-93, FSU-SCRI-93-108, REVTEX 3.
Infrared Behaviour of the Gluon Propagator: Confining or Confined?
The possible infrared behaviour of the gluon propagator is studied
analytically, using the Schwinger-Dyson equations, in both the axial and the
Landau gauge. The possibility of a gluon propagator less singular than
when is investigated and found to be
inconsistent, despite claims to the contrary, whereas an infrared enhanced one
is consistent. The implications for confinement are discussed.Comment: 20 pages, latex, 2 figure