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Hadrons and Nuclei
Eur. Phys. J. A 9, 221-244

The meson spectrum in a covariant quark model

R. Ricken - M. Koll - D. Merten - B.Ch. Metsch - H.R. Petry

Institut für Theoretische Kernphysik, Nußallee 14-16, D-53115 Bonn, Germany

Received: 28 August 2000
Communicated by V.V. Anisovich

Within the framework of the instantaneous Bethe-Salpeter equation, we present a detailed analysis of light meson spectra with respect to various parameterizations of confinement in Dirac space. Assuming a linearly rising quark-antiquark potential, we investigate two different spinorial forms (Dirac structures), namely $\frac{1}{2}({\rm 1\kern-.3em I}\otimes{\rm 1\kern-.3em I}- \gamma^0\otimes\gamma^0)$ as well as the UA(1)-invariant combination $\frac{1}{2}({\rm 1\kern-.3em I}\otimes{\rm 1\kern-.3em I}- \gamma^5\otimes\gamma^5 - \gamma^\mu\otimes\gamma_\mu)$, both providing a good description of the ground-state Regge trajectories up to highest observed angular momenta. Whereas the first structure is slightly prefered concerning numerous meson decay properties (see M. Koll et al. Eur. Phys. J. A 9, 73 (2000)), we find the UA(1)-invariant force to be much more appropriate for the description of a multitude of higher mass resonances discovered in the data of the Crystal Barrel collaboration during the last few years. Furthermore, this confinement structure has the remarkable feature to yield a linear dependence of masses on their radial excitation number. For many experimental resonances such a trajectory-like behaviour was observed by Anisovich et al. We can confirm that almost the same slope occurs for all trajectories. Adding the UA(1)-breaking instanton induced 't Hooft interaction we can compute the pseudoscalar mass splittings with both Dirac structures and for the scalar mesons a natural mechanism of flavour mixing is achieved. In the scalar sector, the two models provide completely different ground-state and excitation masses, thus leading to different assignments of possible $\bar q q$ states in this region. The scalar meson masses calculated with the structure $\frac{1}{2}({\rm 1\kern-.3em I}\otimes{\rm 1\kern-.3em I}- \gamma^5\otimes\gamma^5 - \gamma^\mu\otimes\gamma_\mu)$ are in excellent agreement with the K-matrix poles deduced from experiment by Anisovich and coworkers.

11.10.St Bound states and Bethe-Salpeter equations - 11.30.Rd Chiral symmetries - 12.39.Ki Relativistic quark model - 12.40.Yx Hadron mass models and calculations

Copyright Società Italiana di Fisica, Springer-Verlag 2000