411 research outputs found
Multiplicative renormalizability and quark propagator
The renormalized Dyson-Schwinger equation for the quark propagator is
studied, in Landau gauge, in a novel truncation which preserves multiplicative
renormalizability. The renormalization constants are formally eliminated from
the integral equations, and the running coupling explicitly enters the kernels
of the new equations. To construct a truncation which preserves multiplicative
renormalizability, and reproduces the correct leading order perturbative
behavior, non-trivial cancellations involving the full quark-gluon vertex are
assumed in the quark self-energy loop. A model for the running coupling is
introduced, with infrared fixed point in agreement with previous
Dyson-Schwinger studies of the gauge sector, and with correct logarithmic tail.
Dynamical chiral symmetry breaking is investigated, and the generated quark
mass is of the order of the extension of the infrared plateau of the coupling,
and about three times larger than in the Abelian approximation, which violates
multiplicative renormalizability. The generated scale is of the right size for
hadronic phenomenology, without requiring an infrared enhancement of the
running coupling.Comment: 17 pages; minor corrections, comparison to lattice results added;
accepted for publication in Phys. Rev.
Multiplicative renormalizability of gluon and ghost propagators in QCD
We reformulate the coupled set of continuum equations for the renormalized
gluon and ghost propagators in QCD, such that the multiplicative
renormalizability of the solutions is manifest, independently of the specific
form of full vertices and renormalization constants. In the Landau gauge, the
equations are free of renormalization constants, and the renormalization point
dependence enters only through the renormalized coupling and the renormalized
propagator functions. The structure of the equations enables us to devise novel
truncations with solutions that are multiplicatively renormalizable and agree
with the leading order perturbative results. We show that, for infrared power
law behaved propagators, the leading infrared behavior of the gluon equation is
not solely determined by the ghost loop, as concluded in previous studies, but
that the gluon loop, the three-gluon loop, the four-gluon loop, and even
massless quarks also contribute to the infrared analysis. In our new Landau
gauge truncation, the combination of gluon and ghost loop contributions seems
to reject infrared power law solutions, but massless quark loops illustrate how
additional contributions to the gluon vacuum polarization could reinstate these
solutions. Moreover, a schematic study of the three-gluon and four-gluon loops
shows that they too need to be considered in more detail before a definite
conclusion about the existence of infrared power behaved gluon and ghost
propagators can be reached.Comment: 13 pages, 1 figure, submitted to Phys. Rev.
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
The , , and electromagnetic form factors
The rainbow truncation of the quark Dyson-Schwinger equation is combined with
the ladder Bethe-Salpeter equation for the meson amplitudes and the dressed
quark-photon vertex in a self-consistent Poincar\'e-invariant study of the pion
and kaon electromagnetic form factors in impulse approximation. We demonstrate
explicitly that the current is conserved in this approach and that the obtained
results are independent of the momentum partitioning in the Bethe-Salpeter
amplitudes. With model gluon parameters previously fixed by the condensate, the
pion mass and decay constant, and the kaon mass, the charge radii and spacelike
form factors are found to be in good agreement with the experimental data.Comment: 8 pages, 6 figures, Revte
Strong Decays of Light Vector Mesons
The vector meson strong decays rho-->pi pi, phi-->KK, and K^star-->pi K are
studied within a covariant approach based on the ladder-rainbow truncation of
the QCD Dyson--Schwinger equation for the quark propagator and the
Bethe--Salpeter equation for the mesons. The model preserves the one-loop
behavior of QCD in the ultraviolet, has two infrared parameters, and implements
quark confinement and dynamical chiral symmetry breaking. The 3-point decay
amplitudes are described in impulse approximation. The Bethe--Salpeter study
motivates a method for estimating the masses for heavier mesons within this
model without continuing the propagators into the complex plane. We test the
accuracy via the rho, phi and K^{star} masses and then produce estimates of the
model results for the a_1 and b_1 masses as well as the mass of the proposed
exotic vector pi_1(1400).Comment: Submitted for publication; 10x2-column pages, REVTEX 4, 3 .eps files
making 3fig
Spontaneous Chiral-Symmetry Breaking in Three-Dimensional QED with a Chern--Simons Term
In three-dimensional QED with a Chern--Simons term we study the phase
structure associated with chiral-symmetry breaking in the framework of the
Schwinger--Dyson equation. We give detailed analyses on the analytical and
numerical solutions for the Schwinger--Dyson equation of the fermion
propagator, where the nonlocal gauge-fixing procedure is adopted to avoid
wave-function renormalization for the fermion. In the absence of the
Chern--Simons term, there exists a finite critical number of four-component
fermion flavors, at which a continuous (infinite-order) chiral phase transition
takes place and below which the chiral symmetry is spontaneously broken. In the
presence of the Chern--Simons term, we find that the spontaneous
chiral-symmetry-breaking transition continues to exist, but the type of phase
transition turns into a discontinuous first-order transition. A simple
stability argument is given based on the effective potential, whose stationary
point gives the solution of the Schwinger-Dyson equation.Comment: 34 pages, revtex, with 9 postscriptfigures appended (uuencoded
Non-perturbative Propagators, Running Coupling and Dynamical Quark Mass of Landau gauge QCD
The coupled system of renormalized Dyson-Schwinger equations for the quark,
gluon and ghost propagators of Landau gauge QCD is solved within truncation
schemes. These employ bare as well as non-perturbative ansaetze for the
vertices such that the running coupling as well as the quark mass function are
independent of the renormalization point. The one-loop anomalous dimensions of
all propagators are reproduced. Dynamical chiral symmetry breaking is found,
the dynamically generated quark mass agrees well with phenomenological values
and corresponding results from lattice calculations. The effects of unquenching
the system are small. In particular the infrared behavior of the ghost and
gluon dressing functions found in previous studies is almost unchanged as long
as the number of light flavors is smaller than four.Comment: 34 pages, 10 figures, version to be published by Phys. Rev.
Self-consistent solution of the Schwinger-Dyson equations for the nucleon and meson propagators
The Schwinger-Dyson equations for the nucleon and meson propagators are
solved self-consistently in an approximation that goes beyond the Hartree-Fock
approximation. The traditional approach consists in solving the nucleon
Schwinger-Dyson equation with bare meson propagators and bare meson-nucleon
vertices; the corrections to the meson propagators are calculated using the
bare nucleon propagator and bare nucleon-meson vertices. It is known that such
an approximation scheme produces the appearance of ghost poles in the
propagators. In this paper the coupled system of Schwinger-Dyson equations for
the nucleon and the meson propagators are solved self-consistently including
vertex corrections. The interplay of self-consistency and vertex corrections on
the ghosts problem is investigated. It is found that the self-consistency does
not affect significantly the spectral properties of the propagators. In
particular, it does not affect the appearance of the ghost poles in the
propagators.Comment: REVTEX, 7 figures (available upon request), IFT-P.037/93,
DOE/ER/40427-12-N9
The Quark-Photon Vertex and the Pion Charge Radius
The rainbow truncation of the quark Dyson-Schwinger equation is combined with
the ladder Bethe-Salpeter equation for the dressed quark-photon vertex to study
the low-momentum behavior of the pion electromagnetic form factor. With model
gluon parameters previously fixed by the pion mass and decay constant, the pion
charge radius is found to be in excellent agreement with the data. When
the often-used Ball-Chiu Ansatz is used to construct the quark-photon vertex
directly from the quark propagator, less than half of is generated.
The remainder of is seen to be attributable to the presence of the
-pole in the solution of the ladder Bethe-Salpeter equation.Comment: 21 pages, 9 figure
Relation Between Chiral Susceptibility and Solutions of Gap Equation in Nambu--Jona-Lasinio Model
We study the solutions of the gap equation, the thermodynamic potential and
the chiral susceptibility in and beyond the chiral limit at finite chemical
potential in the Nambu--Jona-Lasinio (NJL) model. We give an explicit relation
between the chiral susceptibility and the thermodynamic potential in the NJL
model. We find that the chiral susceptibility is a quantity being able to
represent the furcation of the solutions of the gap equation and the
concavo-convexity of the thermodynamic potential in NJL model. It indicates
that the chiral susceptibility can identify the stable state and the
possibility of the chiral phase transition in NJL model.Comment: 21 pages, 6 figures, misprints are correcte
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