133 research outputs found
Goldstone Theorem and Diquark Confinement Beyond Rainbow-Ladder Approximation
The quark Dyson-Schwinger equation and meson Bethe-Salpeter equation are
studied in a truncation scheme that extends the rainbow-ladder approximation
such that, in the chiral limit, the isovector, pseudoscalar meson remains
massless. Quark-quark (diquark) correlations, which are bound in rainbow-ladder
approximation, are destabilised by repulsive contributions that only appear at
higher order in the Bethe-Salpeter kernel. The net effect of higher order terms
on the meson bound-state masses is small.Comment: 11 pages, LaTeX, elsart.sty, 3 EPS figure
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
Confinement, DCSB, Bound States, and the Quark-Gluon Vertex
Aspects of the dressed-quark-gluon vertex and their role in the gap and
Bethe-Salpeter equations are briefly surveyed using an intuitive model. The
model allows one to elucidate why a linear extrapolation to the chiral limit of
extant lattice data on the dressed-quark mass-function overestimates this
function and hence the value of the vacuum quark condensate. The diagrammatic
content of the vertex described is explicitly enumerable. This property is
essential to the symmetry preserving study of bound state properties. It
facilitates a realistic analysis of vector and pseudoscalar meson masses, and
also allows the accuracy of standard truncations to be gauged. The splitting
between vector and pseudoscalar meson masses is observed to vanish as the
current-quark mass increases. That argues for the mass of the pseudoscalar
partner of the Upsilon(1S) to be above 9.4GeV. Moreover, in this limit the
rainbow-ladder truncation provides an increasingly accurate estimate of a bound
state's mass.Comment: 6 pages, Contribution to the Proceedings of "QCD Down Under", Special
Centre for the Subatomic Structure of Matter, University of Adelaide,
10-19/March/200
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
QCD Green functions in a gluon field
We formulate a dressed perturbative expansion of QCD, where the standard
diagrams are evaluated in the presence of a constant external gluon field whose
magnitude is gaussian distributed. The approach is Poincar{\'e} and gauge
invariant, and modifies the usual results for hard processes only by power
suppressed contributions. Long distance propagation of quarks and gluons turns
out to be inhibited due to a branch point singularity instead of a pole at
in the quark and gluon propagators. The dressing keeps the (massless)
quarks in q qbar fluctuations of the photon at a finite distance from each
other.Comment: 21 pages, 7 figures. Minor modifications in text. Version to be
published in JHE
Nonperturbative Aspect of Axial Vector Vertex in the Global Color Symmetry Model
It is shown how the axial vector current of current quarks is related to that
of constituent quarks within the framework of the global color symmetry model.
Gluon dressing of the axial vector 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.Comment: 10 page
Quark running mass and vacuum energy density in truncated Coulomb gauge QCD for five orders of magnitude of current masses
We study in detail the effect of the finite current quark mass on chiral
symmetry breaking, in the framework of truncated Coulomb gauge QCD with a
linear confining quark-antiquark potential. In the chiral limit of massless
current quarks, the breaking of chiral symmetry is spontaneous. But for a
finite current quark mass, some dynamical symmetry breaking continues to add to
the explicit breaking caused by the quark mass. Moreover, using as order
parameter the mass gap, i. e. the quark mass at vanishing moment or the quark
condensate, a finite quark mass transforms the chiral symmetry breaking from a
phase transition into a crossover. For the study of the QCD phase diagram it
thus is relevant to determine how the current quark mass affects chiral
symmetry breaking. Since the current quark masses of the six standard flavours
u, d, s, c, b, t span over five orders of magnitude from 1.5 MeV to 171 GeV, we
develop an accurate numerical method to study the running quark mass gap and
the quark vacuum energy density from very small to very large current quark
masses.Comment: 24 pages, 5 figures, 3 table
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
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