59 research outputs found
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
Vertices and the CJT Effective Potential
The Cornwall-Jackiw-Tomboulis effective potential is modified to include a
functional dependence on the fermion-gauge particle vertex, and applied to a
quark confining model of chiral symmetry breaking.Comment: 10 pages (latex), PURD-TH-93-1
Approximation of the Schwinger--Dyson and the Bethe--Salpeter Equations and Chiral Symmetry of QCD
The Bethe--Salpeter equation for the pion in chiral symmetric models is
studied with a special care to consistency with low-energy relations. We
propose a reduction of the rainbow Schwinger--Dyson and the ladder
Bethe--Salpeter equations with a dressed gluon propagator. We prove that the
reduction preserves the Ward--Takahashi identity for the axial-vector current
and the PCAC relation.Comment: 10 pages, LaTe
A dynamical, confining model and hot quark stars
We explore the consequences of an equation of state (EOS) obtained in a
confining Dyson-Schwinger equation model of QCD for the structure and stability
of nonstrange quark stars at finite-T, and compare the results with those
obtained using a bag-model EOS. Both models support a temperature profile that
varies over the star's volume and the consequences of this are model
independent. However, in our model the analogue of the bag pressure is
(T,mu)-dependent, which is not the case in the bag model. This is a significant
qualitative difference and comparing the results effects a primary goal of
elucidating the sensitivity of quark star properties to the form of the EOS.Comment: 13 pages, 5 figures, epsfig.sty, elsart.sty. Shortened version to
appear in Phys. Lett. B, qualitatively unmodifie
Nonperturbative aspects of the quark-photon vertex
The electromagnetic interaction with quarks is investigated through a
relativistic, electromagnetic gauge-invariant treatment. Gluon dressing of the
quark-photon vertex and the quark self-energy functions is described by the
inhomogeneous Bethe-Salpeter equation in the ladder approximation and the
Schwinger-Dyson equation in the rainbow approximation respectively. Results for
the calculation of the quark-photon vertex are presented in both the time-like
and space-like regions of photon momentum squared, however emphasis is placed
on the space-like region relevant to electron scattering. The treatment
presented here simultaneously addresses the role of dynamically generated
vector bound states and the approach to asymptotic behavior. The
resulting description is therefore applicable over the entire range of momentum
transfers available in electron scattering experiments. Input parameters are
limited to the model gluon two-point function, which is chosen to reflect
confinement and asymptotic freedom, and are largely constrained by the obtained
bound-state spectrum.Comment: 8 figures available on request by email, 25 pages, Revtex,
DOE/ER/40561-131-INT94-00-5
Squeezed Gluon Condensate and Quark Confinement in the Global Color Model of QCD
We discuss how the presence of a squeezed gluon vacuum might lead to quark
confinement in the framework of the global colour model of QCD. Using reduced
phase space quantization of massive vector theory we construct a Lorentz
invariant and colourless squeezed gluon condensate and show that it induces a
permanent, nonlocal quark interaction (delta-function in 4-momentum space),
which according to Munczek and Nemirovsky might lead to quark confinement. Our
approach makes it possible to relate the strength of this effective confining
quark interaction to the strength of the physical gluon condensate.Comment: 18 pages LaTeX, to appear in Int. J. Mod. Phys.
Squeezed gluon vacuum and the global colour model of QCD
We discuss how the vacuum model of Celenza and Shakin with a squeezed gluon
condensate can explain the existence of an infrared singular gluon propagator
frequently used in calculations within the global colour model. In particular,
it reproduces a recently proposed QCD-motivated model where low energy chiral
parameters were computed as a function of a dynamically generated gluon mass.
We show how the strength of the confining interaction of this gluon propagator
and the value of the physical gluon condensate may be connected.Comment: 13 pages, LaTe
Is There Only One Solution of the Dyson-Schwinger Equation for Quark Propagator in the Case of Non-zero Current Quark Mass
In this letter it is shown on general ground that there exist two
qualitatively distinct solutions of the Dyson-Schwinger equation for the quark
propagator in the case of non-zero current quark mass. One solution corresponds
to the ``Nambu-Goldstone'' phase and the other one corresponds to the
``Wigner'' phase in the chiral limit.Comment: 7 page
Bethe-Salpeter equation and a nonperturbative quark-gluon vertex
A Ward-Takahashi identity preserving Bethe-Salpeter kernel can always be
calculated explicitly from a dressed-quark-gluon vertex whose diagrammatic
content is enumerable. We illustrate that fact using a vertex obtained via the
complete resummation of dressed-gluon ladders. While this vertex is planar, the
vertex-consistent kernel is nonplanar and that is true for any dressed vertex.
In an exemplifying model the rainbow-ladder truncation of the gap and
Bethe-Salpeter equations yields many results; e.g., pi- and rho-meson masses,
that are changed little by including higher-order corrections. Repulsion
generated by nonplanar diagrams in the vertex-consistent Bethe-Salpeter kernel
for quark-quark scattering is sufficient to guarantee that diquark bound states
do not exist.Comment: 16 pages, 12 figures, REVTEX
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
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