64 research outputs found
A Bethe-Salpeter model for light mesons: spectra and decays
The spectra and electroweak decay properties of light mesons are analyzed
within the framework of the instantaneous Bethe-Salpeter equation. The
interaction kernel comprises alternative spin-structures for a parameterization
of confinement and a residual quark-antiquark interaction based on instanton
effects. It is shown that only with a vector confinement the parameters can be
chosen such as to yield an excellent description of the light pseudoscalar and
vector mesons including weak and two photon decays. However it is found that it
is not possible to reconcile this with the Regge behavior of higher lying meson
states with the same parameter set.Comment: 12 pages, RevTeX, TK-93-1
Bound q\bar q Systems in the Framework of the Different Versions of the 3-Dimensional Reductions of the Bethe-Salpeter Equation
Bound q\bar q systems are studied in the framework of different 3-dimensional
relativistic equations derived from the Bethe-Salpeter equation with the
instantaneous kernel in the momentum space. Except the Salpeter equation, all
these equations have a correct one-body limit when one of the constituent quark
masses tends to infinity. The spin structure of the confining qq interaction
potential is taken in the form ,
with . At first stage, the one-gluon-exchange potential is
neglected and the confining potential is taken in the oscillator form. For the
systems (u\bar s), (c\bar u), (c\bar s) and (u\bar u), (s\bar s) a comparative
qualitative analysis of these equations is carried out for different values of
the mixing parameter x and the confining potential strength parameter. We
investigate: 1)the existence/nonexistence of stable solutions of these
equations; 2) the parameter dependence of the general structure of the meson
mass spectum and leptonic decay constants of pseudoscalar and vector mesons. It
is demonstrated that none of the 3-dimensional equations considered in the
present paper does simultaneously describe even general qualitative features of
the whole mass spectrum of q\bar q systems. At the same time, these versions
give an acceptable description of the meson leptonic decay characteristics.Comment: 22 pages, 5 postscript figures, LaTeX-file (revtex.sty
The stability of the spectator, Dirac, and Salpeter equations for mesons
Mesons are made of quark-antiquark pairs held together by the strong force.
The one channel spectator, Dirac, and Salpeter equations can each be used to
model this pairing. We look at cases where the relativistic kernel of these
equations corresponds to a time-like vector exchange, a scalar exchange, or a
linear combination of the two. Since the model used in this paper describes
mesons which cannot decay physically, the equations must describe stable
states. We find that this requirement is not always satisfied, and give a
complete discussion of the conditions under which the various equations give
unphysical, unstable solutions
Electromagnetic Meson Form Factors in the Salpeter Model
We present a covariant scheme to calculate mesonic transitions in the
framework of the Salpeter equation for -states. The full Bethe
Salpeter amplitudes are reconstructed from equal time amplitudes which were
obtained in a previous paper\cite{Mue} by solving the Salpeter equation for a
confining plus an instanton induced interaction. This method is applied to
calculate electromagnetic form factors and decay widths of low lying
pseudoscalar and vector mesons including predictions for CEBAF experiments. We
also describe the momentum transfer dependence for the processes
.Comment: 22 pages including 10 figure
Support of generalized parton distributions in Bethe-Salpeter models of hadrons
The proper support of generalized parton distributions from relativistic
constituent quark models with pointlike constituents is studied. The correct
support is guaranteed when the vertex function does not depend on the relative
minus-momentum. We show that including quark interactions in models with
pointlike constituent quarks might lead to a support problem. A computation of
the magnitude of the support problem in the Bonn relativistic constituent quark
model is presented.Comment: 8 pages, 4 figures. v2: specific calculation included, references and
figure added. Submitted to Phys. Lett.
Analysis of the instantaneous Bethe-Salpeter equation for -bound-states
We investigate the structure of the instantaneous Bethe-Salpeter equation for
-bound states in the general case of unequal quark masses and
develop a numerical scheme for the calculation of mass spectra and
Bethe-Salpeter amplitudes. In order to appreciate the merits of the various
competing models beyond the reproduction of the mass spectra we present
explicit formulas to calculate electroweak decays. The results for an explicit
quark model will be compared to experimental data in a subsequent paperComment: 11 pages, RevTeX, TK-93-1
Instantaneous Bethe-Salpeter equation: utmost analytic approach
The Bethe-Salpeter formalism in the instantaneous approximation for the
interaction kernel entering into the Bethe-Salpeter equation represents a
reasonable framework for the description of bound states within relativistic
quantum field theory. In contrast to its further simplifications (like, for
instance, the so-called reduced Salpeter equation), it allows also the
consideration of bound states composed of "light" constituents. Every
eigenvalue equation with solutions in some linear space may be (approximately)
solved by conversion into an equivalent matrix eigenvalue problem. We
demonstrate that the matrices arising in these representations of the
instantaneous Bethe-Salpeter equation may be found, at least for a wide class
of interactions, in an entirely algebraic manner. The advantages of having the
involved matrices explicitly, i.e., not "contaminated" by errors induced by
numerical computations, at one's disposal are obvious: problems like, for
instance, questions of the stability of eigenvalues may be analyzed more
rigorously; furthermore, for small matrix sizes the eigenvalues may even be
calculated analytically.Comment: LaTeX, 23 pages, 2 figures, version to appear in Phys. Rev.
Spectrum for Heavy Quankonia and Mixture of the Relevant Wave Functions within the Framework of Bethe-Salpeter Equation
Considering the fact that some excited states of the heavy quarkonia
(charmonium and bottomonium) still missing in experimental observations and
potential applications of the relevant wave functions of the bound states, we
re-analyze the spectrum and the relevant wave functions of the heavy quarkonia
within the framework of Bethe-Salpeter (B.S.) equation with a proper
QCD-inspired kernel. Such a kernel for the heavy quarkonia, relating to
potential of non-relativistic quark model, is instantaneous, so we call the
corresponding B.S. equation as BS-In equation throughout the paper.
Particularly, a new way to solve the B.S. equation, which is different from the
traditional ones, is proposed here, and with it not only the known spectrum for
the heavy quarkonia is re-generated, but also an important issue is brought in,
i.e., the obtained solutions of the equation `automatically' include the
'fine', 'hyperfine' splittings and the wave function mixture, such as
wave mixing in states, wave mixing in
states for charmonium and bottomonium etc. It is pointed out that the best
place to test the wave mixture probably is at -factory ( collider
running at -boson pole with extremely high luminosity).Comment: 26 pages, 8 figure
K0 form factor and charge radius in a covariant Salpeter model
The electromagnetic form factor for the is calculated in a covariant
formulation of the Salpeter equation for - bound states, which has
been presented recently for the mass spectrum, decay properties and form
factors of the light pseudoscalar and vector mesons. The charge radius
dependence on the difference between strange and down constituent quark mass is
discussed.Comment: 5 pages including 3 uuencoded figures, RevTe
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