346 research outputs found
A systematic approach to sketch Bethe-Salpeter equation
To study meson properties, one needs to solve the gap equation for the quark
propagator and the Bethe-Salpeter (BS) equation for the meson wavefunction,
self-consistently. The gluon propagator, the quark-gluon vertex, and the
quark--anti-quark scattering kernel are key pieces to solve those equations.
Predicted by lattice-QCD and Dyson-Schwinger analyses of QCD's gauge sector,
gluons are non-perturbatively massive. In the matter sector, the modeled gluon
propagator which can produce a veracious description of meson properties needs
to possess a mass scale, accordingly. Solving the well-known longitudinal
Ward-Green-Takahashi identities (WGTIs) and the less-known transverse
counterparts together, one obtains a nontrivial solution which can shed light
on the structure of the quark-gluon vertex. It is highlighted that the
phenomenologically proposed anomalous chromomagnetic moment (ACM) vertex
originates from the QCD Lagrangian symmetries and its strength is proportional
to the magnitude of dynamical chiral symmetry breaking (DCSB). The
color-singlet vector and axial-vector WGTIs can relate the BS kernel and the
dressed quark-gluon vertex to each other. Using the relation, one can truncate
the gap equation and the BS equation, systematically, without violating crucial
symmetries, e.g., gauge symmetry and chiral symmetry.Comment: 4 pages, 21st International Conference on Few-Body Problems in
Physic
Charmonium Spectral Functions and Transport Properties of Quark-Gluon Plasma
We study vacuum masses of charmonia and the charm-quark diffusion coefficient
in the quark-gluon plasma based on the spectral representation for meson
correlators. To calculate the correlators, we solve the quark gap equation and
the inhomogeneous Bethe-Salpeter equation in the rainbow-ladder approximation.
It is found that the ground-state masses of charmonia in the pseudoscalar,
scalar, and vector channels can be well described. For ,
the value of the diffusion coefficient is comparable with that obtained by
lattice QCD and experiments: . Relating the diffusion
coefficient with the ratio of shear viscosity to entropy density of
the quark-gluon plasma, we obtain values in the range .Comment: 5 pages, 4 figure
Temperature Dependence of the Effective Bag Constant and the Radius of a Nucleon in the Global Color Symmetry Model of QCD
We study the temperature dependence of the effective bag constant, the mass,
and the radius of a nucleon in the formalism of the simple global color
symmetry model in the Dyson-Schwinger equation approach of QCD with a
Gaussian-type effective gluon propagator. We obtain that, as the temperature is
lower than a critical value, the effective bag constant and the mass decrease
and the radius increases with the temperature increasing. As the critical
temperature is reached, the effective bag constant and the mass vanish and the
radius tends to infinity. At the same time, the chiral quark condensate
disappears. These phenomena indicate that the deconfinement and the chiral
symmetry restoration phase transitions can take place at high temperature. The
dependence of the critical temperature on the interaction strength parameter in
the effective gluon propagator of the approach is given.Comment: 10 pages, 9 figure
Ward-Green-Takahashi identities and the axial-vector vertex
The colour-singlet axial-vector vertex plays a pivotal role in understanding
dynamical chiral symmetry breaking and numerous hadronic weak interactions, yet
scant model-independent information is available. We therefore use longitudinal
and transverse Ward-Green-Takahashi (WGT) identities, together with kinematic
constraints, in order to ameliorate this situation and expose novel features of
the axial vertex: amongst them, Ward-like identities for elements in the
transverse piece of the vertex, which complement and shed new light on
identities determined previously for components in its longitudinal part. Such
algebraic results are verified via solutions of the Bethe-Salpeter equation for
the axial vertex obtained using two materially different kernels for the
relevant Dyson-Schwinger equations. The solutions also provide insights that
suggest a practical Ansatz for the axial-vector vertex.Comment: 7 pages, 3 figure
Dyson-Schwinger Equations with a Parameterized Metric
We construct and solve the Dyson-Schwinger equation (DSE) of quark propagator
with a parameterized metric, which connects the Euclidean metric with the
Minkowskian one. We show, in some models, the Minkowskian vacuum is different
from the Euclidean vacuum. The usual analytic continuation of Green function
does not make sense in these cases. While with the algorithm we proposed and
the quark-gluon vertex ansatz which preserves the Ward-Takahashi identity, the
vacuum keeps being unchanged in the evolution of the metric. In this case,
analytic continuation becomes meaningful and can be fully carried out.Comment: 10 pages, 7 figures. To appear in Physical Review
- …