25,457 research outputs found
Closed expression of the interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states
The interaction kernel in the Bethe-Salpeter equation for quark-antiquark
bound states is derived from the Bethe-Salpeter equations satisfied by the
quark-antiquark four-point Green's function. The latter equations are
established based on the equations of motion obeyed by the quark and antiquark
propagators, the four-point Green's function and some other kinds of Green's
functions which follow directly from the QCD generating functional. The B-S
kernel derived is given an exact and explicit expression which contains only a
few types of Green's functions. This expression is not only convenient for
perturbative calculations, but also suitable for nonperturbative
investigations.Comment: 27 pages,no figure
KN and KbarN Elastic Scattering in the Quark Potential Model
The KN and KbarN low-energy elastic scattering is consistently studied in the
framework of the QCD-inspired quark potential model. The model is composed of
the t-channel one-gluon exchange potential, the s-channel one-gluon exchange
potential and the harmonic oscillator confinement potential. By means of the
resonating group method, nonlocal effective interaction potentials for the KN
and KbarN systems are derived and used to calculate the KN and KbarN elastic
scattering phase shifts. By considering the effect of QCD renormalization, the
contribution of the color octet of the clusters (qqbar) and (qqq) and the
suppression of the spin-orbital coupling, the numerical results are in fairly
good agreement with the experimental data.Comment: 20 pages, 8 figure
A general multiblock Euler code for propulsion integration. Volume 1: Theory document
A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution
A general multiblock Euler code for propulsion integration. Volume 3: User guide for the Euler code
This manual explains the procedures for using the general multiblock Euler (GMBE) code developed under NASA contract NAS1-18703. The code was developed for the aerodynamic analysis of geometrically complex configurations in either free air or wind tunnel environments (vol. 1). The complete flow field is divided into a number of topologically simple blocks within each of which surface fitted grids and efficient flow solution algorithms can easily be constructed. The multiblock field grid is generated with the BCON procedure described in volume 2. The GMBE utilizes a finite volume formulation with an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. This user guide provides information on the GMBE code, including input data preparations with sample input files and a sample Unix script for program execution in the UNICOS environment
Dirac-Schr\"odinger equation for quark-antiquark bound states and derivation of its interaction kerne
The four-dimensional Dirac-Schr\"odinger equation satisfied by
quark-antiquark bound states is derived from Quantum Chromodynamics. Different
from the Bethe-Salpeter equation, the equation derived is a kind of first-order
differential equations of Schr\"odinger-type in the position space. Especially,
the interaction kernel in the equation is given by two different closed
expressions. One expression which contains only a few types of Green's
functions is derived with the aid of the equations of motion satisfied by some
kinds of Green's functions. Another expression which is represented in terms of
the quark, antiquark and gluon propagators and some kinds of proper vertices is
derived by means of the technique of irreducible decomposition of Green's
functions. The kernel derived not only can easily be calculated by the
perturbation method, but also provides a suitable basis for nonperturbative
investigations. Furthermore, it is shown that the four-dimensinal
Dirac-Schr\"odinger equation and its kernel can directly be reduced to rigorous
three-dimensional forms in the equal-time Lorentz frame and the
Dirac-Schr\"odinger equation can be reduced to an equivalent
Pauli-Schr\"odinger equation which is represented in the Pauli spinor space. To
show the applicability of the closed expressions derived and to demonstrate the
equivalence between the two different expressions of the kernel, the t-channel
and s-channel one gluon exchange kernels are chosen as an example to show how
they are derived from the closed expressions. In addition, the connection of
the Dirac-Schr\"odinger equation with the Bethe-Salpeter equation is discussed
Renormalization of the Sigma-Omega model within the framework of U(1) gauge symmetry
It is shown that the Sigma-Omega model which is widely used in the study of
nuclear relativistic many-body problem can exactly be treated as an Abelian
massive gauge field theory. The quantization of this theory can perfectly be
performed by means of the general methods described in the quantum gauge field
theory. Especially, the local U(1) gauge symmetry of the theory leads to a
series of Ward-Takahashi identities satisfied by Green's functions and proper
vertices. These identities form an uniquely correct basis for the
renormalization of the theory. The renormalization is carried out in the
mass-dependent momentum space subtraction scheme and by the renormalization
group approach. With the aid of the renormalization boundary conditions, the
solutions to the renormalization group equations are given in definite
expressions without any ambiguity and renormalized S-matrix elememts are
exactly formulated in forms as given in a series of tree diagrams provided that
the physical parameters are replaced by the running ones. As an illustration of
the renormalization procedure, the one-loop renormalization is concretely
carried out and the results are given in rigorous forms which are suitable in
the whole energy region. The effect of the one-loop renormalization is examined
by the two-nucleon elastic scattering.Comment: 32 pages, 17 figure
Strange meson-nucleon states in the quark potential model
The quark potential model and resonating group method are used to investigate
the bound states and/or resonances. The model potential consists of
the t-channel and s-channel one-gluon exchange potentials and the confining
potential with incorporating the QCD renormalization correction and the
spin-orbital suppression effect in it. It was shown in our previous work that
by considering the color octet contribution, use of this model to investigate
the low energy elastic scattering leads to the results which are in pretty
good agreement with the experimental data. In this paper, the same model and
method are employed to calculate the masses of the bound systems.
For this purpose, the resonating group equation is transformed into a standard
Schr\"odinger equation in which a nonlocal effective interaction
potential is included. Solving the Schr\"odinger equation by the variational
method, we are able to reproduce the masses of some currently concerned
states and get a view that these states possibly exist as
molecular states. For the system, the same calculation gives no support to
the existence of the resonance which was announced
recently.Comment: 15 pages, 4 figure
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