814 research outputs found
Spurious divergences in Dyson-Schwinger equations
We revisit the treatment of spurious ultraviolet divergences in the equation
of motion of the gluon propagator caused by a momentum cutoff and the resulting
violation of gauge invariance. With present continuum studies of the gluon
propagator from its Dyson-Schwinger equation reaching the level of
quantitatively accurate descriptions, it becomes increasingly important to
understand how to subtract these spurious divergences in an unambiguous way.
Here we propose such a method. It is based entirely on the asymptotic
perturbative behavior of the QCD Green's functions without affecting
non-perturbative aspects such as mass terms or the asymptotic infrared
behavior. As a particular example, this allows us to assess the possible
influence of the tadpole diagram beyond perturbation theory. Finally, we test
this method numerically by solving the system of Dyson-Schwinger equations of
the gluon and ghost propagators.Comment: 19 pages, 9 figs; agrees with published versio
Going beyond the propagators of Landau gauge Yang-Mills theory
We present results for the propagators and the ghost-gluon vertex of Landau
gauge Yang-Mills theory obtained from Dyson-Schwinger equations. Solving these
three quantities simultaneously constitutes a new step in truncating these
equations. We also introduce a new model for the three-gluon vertex that is
motivated by lattice results. It features a zero crossing which is confirmed a
posteriori by a Dyson-Schwinger calculation. Within our setup we can reproduce
lattice data very well. We establish that also for the ghost-gluon vertex a
difference between decoupling and scaling solutions is present. For the scaling
solution we discuss the possibility of modifying the infrared exponents via an
angle dependence of the ghost-gluon vertex. However, no such dependence is
found in our calculations. Finally, we calculate the Schwinger function for the
gluon propagator.Comment: 8 pages, Confinement X proceeding
On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory
We solve the Dyson-Schwinger equations of the ghost and gluon propagators of
Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex.
The latter plays a central role in many truncation schemes for functional
equations. By including it dynamically we can determine its influence on the
propagators. We also suggest a new model for the three-gluon vertex motivated
by lattice data which plays a crucial role to obtain stable solutions when the
ghost-gluon vertex is included. We find that both vertices have a sizable
quantitative impact on the mid-momentum regime and contribute to the reduction
of the gap between lattice and Dyson-Schwinger equation results. Furthermore,
we establish that the three-gluon vertex dressing turns negative at low momenta
as suggested by lattice results in three dimensions.Comment: 28 pages, 12 figures, matches published versio
On propagators and vertices of Landau gauge Yang-Mills theory
We calculate the three-point functions of pure Landau gauge QCD and
investigate their influence on the propagators. As expected, the ghost-gluon
vertex leads only to minor modifications, while the three-gluon vertex has a
sizeable impact on the mid-momentum regime of the gluon propagator. We describe
an effective model of the three-gluon vertex that includes contributions from
the neglected two-loop diagrams and thus allows to obtain propagators in good
agreement with lattice results. We also determine the three-gluon vertex from
these propagators and find good agreement with lattice results as well. In
turn, these results allow us to assess the effect of the missing two-loop
diagrams in the gluon propagator equation. Finally, we present the first
self-consistent calculation that includes all two-and three-point functions.Comment: 12 pages, 10 figs., contribution to "QCD-TNT-III: From quarks and
gluons to hadronic matter: A bridge too far?", 2-6 Sept 2013, ECT*, Trento,
Ital
A Dyson-Schwinger study of the four-gluon vertex
We present a self-consistent calculation of the four-gluon vertex of Landau
gauge Yang--Mills theory from a truncated Dyson--Schwinger equation. The
equation contains the leading diagrams in the ultraviolet and is solved using
as the only input results for lower Green functions from previous
Dyson--Schwinger calculations that are in good agreement with lattice data. All
quantities are therefore fixed and no higher Green functions enter within this
truncation. Our self-consistent solution resolves the full momentum dependence
of the vertex but is limited to the tree-level tensor structure at the moment.
Calculations of selected dressing functions for other tensor structures from
this solution are used to exemplify that they are suppressed compared to the
tree-level structure except for possible logarithmic enhancements in the deep
infrared. Our results furthermore allow one to extract a qualitative fit for
the vertex and a running coupling.Comment: 23 pages, 14 figs.; more detailed discussion of renormalization,
version accepted by EPJ
- …