172 research outputs found
QCD Propagators at non-vanishing temperatures
We investigate the behaviour of the gluon and ghost propagators, especially
their infrared properties, at non-vanishing temperatures. To this end we solve
their Dyson-Schwinger equations on a torus and find an infrared enhanced ghost
propagator and an infrared vanishing gluon propagator.Comment: 2 pages, 2 figures; talk given by B.G. at the Erice summer school on
Nuclear Physics, Sept. 16 -- 24, 2003, Erice, Ital
Temperature Dependence of Gluon and Ghost Propagators in Landau-Gauge Yang-Mills Theory below the Phase Transition
The Dyson-Schwinger equations of Landau-gauge Yang-Mills theory for the gluon
and ghost propagators are investigated. Numerical results are obtained within a
truncation scheme which has proven to be successful at vanishing temperature.
For temperatures up to 250 MeV we find only minor quantitative changes in the
infrared behaviour of the gluon and ghost propagators. The effective action
calculated from these propagators is temperature-independent within the
numerical uncertainty.Comment: 9 pages, 14 figures, submitted to EPJ C, typos corrected, reference
and 2 minor clarifications added, in v3: one paragraph extended, some
references added, version to appear in EPJ
Center phase transition from matter propagators in (scalar) QCD
Novel order parameters for the confinement-deconfinement phase transition of
quenched QCD and fundamentally charged scalar QCD are presented. Similar to the
well-known dual condensate, they are defined via generalized matter propagators
with -valued boundary conditions. The order parameters are easily
accessible with functional methods. Their validity and accessibility is
explicitly demonstrated by numerical studies of the Dyson-Schwinger equations
for the matter propagators. Even in the case of heavy scalar matter, where the
propagator does not show a signature of the phase transition, a discontinuity
due to the transition can be extracted in the order parameters, establishing
also fundamentally charged scalar matter as a probe for color confinement.Comment: accepted versio
High-Temperature Limit of Landau-Gauge Yang-Mills Theory
The infrared properties of the high-temperature limit of Landau-gauge
Yang-Mills theory are investigated. In a first step the high-temperature limit
of the Dyson-Schwinger equations is taken. The resulting equations are
identical to the Dyson-Schwinger equations of the dimensionally reduced theory,
a three-dimensional Yang-Mills theory coupled to an effective adjoint Higgs
field. These equations are solved analytically in the infrared and ultraviolet,
and numerically for all Euclidean momenta. We find infrared enhancement for the
Faddeev-Popov ghosts, infrared suppression for transverse gluons and a mass for
the Higgs. These results imply long-range interactions and over-screening in
the chromomagnetic sector of high temperature Yang-Mills theory while in the
chromoelectric sector only screening is observed.Comment: 21 pages, 23 figures, 3 tables, submitted to EPJ
A study of the influence of the gauge group on the Dyson-Schwinger equations for scalar-Yang-Mills systems
The particular choice of the gauge group for Yang-Mills theory plays an
important role when it comes to the influence of matter fields. In particular,
both the chosen gauge group and the representation of the matter fields yield
structural differences in the quenched case. Especially, the qualitative
behavior of the Wilson potential is strongly dependent on this selection.
Though the algebraic reasons for this observation is clear, it is far from
obvious how this behavior can be described besides using numerical simulations.
Herein, it is investigated how the group structure appears in the
Dyson-Schwinger equations, which as a hierarchy of equations for the
correlation functions have to be satisfied. It is found that there are
differences depending on both the gauge group and the representation of the
matter fields. This provides insight into possible truncation schemes for
practical calculations using these equations.Comment: 47 page
Propagators in Coulomb gauge from SU(2) lattice gauge theory
A thorough study of 4-dimensional SU(2) Yang-Mills theory in Coulomb gauge is
performed using large scale lattice simulations. The (equal-time) transverse
gluon propagator, the ghost form factor d(p) and the Coulomb potential V_{coul}
(p) ~ d^2(p) f(p)/p^2 are calculated. For large momenta p, the gluon propagator
decreases like 1/p^{1+\eta} with \eta =0.5(1). At low momentum, the propagator
is weakly momentum dependent. The small momentum behavior of the Coulomb
potential is consistent with linear confinement. We find that the inequality
\sigma_{coul} \ge \sigma comes close to be saturated. Finally, we provide
evidence that the ghost form factor d(p) and f(p) acquire IR singularities,
i.e., d(p) \propto 1/\sqrt{p} and f(p) \propto 1/p, respectively. It turns out
that the combination g_0^2 d_0(p) of the bare gauge coupling g_0 and the bare
ghost form factor d_0(p) is finite and therefore renormalization group
invariant.Comment: 10 pages, 7 figure
Nonperturbative QCD Coupling and its function from Light-Front Holography
The light-front holographic mapping of classical gravity in AdS space,
modified by a positive-sign dilaton background, leads to a nonperturbative
effective coupling . It agrees with hadron physics data
extracted from different observables, such as the effective charge defined by
the Bjorken sum rule, as well as with the predictions of models with built-in
confinement and lattice simulations. It also displays a transition from
perturbative to nonperturbative conformal regimes at a momentum scale
GeV. The resulting function appears to capture the essential
characteristics of the full function of QCD, thus giving further
support to the application of the gauge/gravity duality to the confining
dynamics of strongly coupled QCD. Commensurate scale relations relate
observables to each other without scheme or scale ambiguity. In this paper we
extrapolate these relations to the nonperturbative domain, thus extending the
range of predictions based on .Comment: 32 pages, 7 figures. Final version published in Phys. Rev.
Dynamical Chiral Symmetry Breaking in Unquenched
We investigate dynamical chiral symmetry breaking in unquenched
using the coupled set of Dyson--Schwinger equations for the fermion and photon
propagators. For the fermion-photon interaction we employ an ansatz which
satisfies its Ward--Green--Takahashi identity. We present self-consistent
analytical solutions in the infrared as well as numerical results for all
momenta. In Landau gauge, we find a phase transition at a critical number of
flavours of . In the chirally symmetric phase the
infrared behaviour of the propagators is described by power laws with
interrelated exponents. For and we find small values for the
chiral condensate in accordance with bounds from recent lattice calculations.
We investigate the Dyson--Schwinger equations in other linear covariant gauges
as well. A comparison of their solutions to the accordingly transformed Landau
gauge solutions shows that the quenched solutions are approximately gauge
covariant, but reveals a significant amount of violation of gauge covariance
for the unquenched solutions.Comment: 33 pages, 8 figures, reference added, version to be published in
Phys. Rev.
Two- and three-point functions in two-dimensional Landau-gauge Yang-Mills theory: Continuum results
We investigate the Dyson-Schwinger equations for the gluon and ghost
propagators and the ghost-gluon vertex of Landau-gauge gluodynamics in two
dimensions. While this simplifies some aspects of the calculations as compared
to three and four dimensions, new complications arise due to a mixing of
different momentum regimes. As a result, the solutions for the propagators are
more sensitive to changes in the three-point functions and the ansaetze used
for them at the leading order in a vertex a expansion. Here, we therefore go
beyond this common truncation by including the ghost-gluon vertex
self-consistently for the first time, while using a model for the three-gluon
vertex which reproduces the known infrared asymptotics and the zeros at
intermediate momenta as observed on the lattice. A separate computation of the
three-gluon vertex from the results is used to confirm the stability of this
behavior a posteriori. We also present further arguments for the absence of the
decoupling solution in two dimensions. Finally, we show how in general the
infrared exponent kappa of the scaling solutions in two, three and four
dimensions can be changed by allowing an angle dependence and thus an essential
singularity of the ghost-gluon vertex in the infrared.Comment: 24 pages; added references, improved choices of parameters for vertex
models; identical to version published in JHE
Schwinger functions and light-quark bound states
We examine the applicability and viability of methods to obtain knowledge
about bound-states from information provided solely in Euclidean space.
Rudimentary methods can be adequate if one only requires information about the
ground and first excited state and assumptions made about analytic properties
are valid. However, to obtain information from Schwinger functions about higher
mass states, something more sophisticated is necessary. A method based on the
correlator matrix can be dependable when operators are carefully tuned and
errors are small. This method is nevertheless not competitive when an
unambiguous analytic continuation of even a single Schwinger function to
complex momenta is available.Comment: 27 pages, 14 figure
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