# Fachartikel

### Electromagnetic meson form factors in a covariant Salpeter model

von Claus R. Münz, Jörg Resag, Bernard C. Metsch, Herbert R. PetryPhysical Review C52 (1995) 2110

We present a covariant formulation of the Salpeter equation for *qq¯* states
in order to calculate bound-state transitions between mesons. The corresponding Bethe-Salpeter
amplitudes are reconstructed from equal-time amplitudes which were obtained in a previous
paper 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 ${\mathrm{\pi}}^{0}$,η,
${\mathrm{\eta}}^{\prime}$→γ
${\gamma}^{\mathrm{*}}$.

### Heavy Quarkonia in the Instantaneous Bethe-Salpeter Model

von Jörg Resag, Claus R. MünzNuclear Physics A590 (1995) 735

The heavy quarkonia (Charmonium cc^{−} and Bottomonium bb^{−}) are investigated
in the framework of the instantaneous BS-equation (Salpeter equation). We parametrize
confinement alternatively by a linearly rising scalar or a vector interaction kernel and
take into account the one-gluon-exchange (OGE) interaction in the instantaneous approximation.
Mass spectra as well as leptonic, two-photon, E1 and M1 decay widths are calculated.
Our results show that a reasonable description of the experimental data can be obtained
with both spin structures for the confining kernel. The relativistic treatment leads to an
improved description compared to nonrelativistic results for the two-photon width of the η_{c}
and to some extent for the E1-transition widths. However, characteristic deviations indicate that
within a relativistic framework confinement is not described adequately by a potential.

### Analysis of the instantaneous Bethe-Salpeter equation for Quark-Antiquark-bound-states

von Jörg Resag, Claus R. Münz, Bernard C. Metsch, Herbert R. PetryNuclear Physics A 578, 397 (1994)

We investigate the structure of the instantaneous Bethe-Salpeter equation for quark-antiquark-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 paper (see paper below).

### A Bethe-Salpeter model for light mesons: spectra and decays

von Claus R. Münz, Jörg Resag, Bernard C. Metsch, Herbert R. PetryNuclear Physics A 578, 418 (1994)

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.

### RPA Equations and the instantaneous Bethe-Salpeter Equation

von J. Resag, D. Schüttenucl-th/9312013 (1993)

We give a derivation of the particle-hole RPA equations for an interacting multi-fermion system by applying the instantaneous approximation to the amputated two-fermion propagator of the system. In relativistic field theory the same approximation leads from the fermion-antifermion Bethe-Salpeter equation to the Salpeter equation. We show that RPA equations and Salpeter equation are indeed equivalent.

### Relativistic effects and the constituent quark model of heavy quarkonia

von M. Beyer, U. Bohn, M.G. Huber, B.C. Metsch, J. ResagZ. Phys. C55 (1992) 307-315

Charmonium cc^{−} and bottomonium bb^{−} are investigated in the framework of a constituent quark model.
A scalar confining and a one-gluon exchange (OGE) potential are used in a nonrelativistic
reduction to order (p/m)^{2}. Therefore the model includes spin dependent as well
as spin independent terms. Their influence on the meson mass spectra and decay widths is analysed.
We find that the experimental spectra can be reproduced by using a full model as well as
by using a reduced version neglecting the spin independent terms. For both versions we calculate
leptonic and radiative decay widths including relativistic corrections for the current operators.
We find that for leptonic decays inclusion of all terms of the OGE potential gives better
results than the non-relativistic formulas. For radiative transitions relativistic corrections are important.