Abstract:
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 ½(1I⊗ 1I - γ0⊗γ0) as well as the U A(1)-invariant combination ½(1I⊗ 1I - γ5⊗γ5 - γμ⊗γ), 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 U A(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 U A(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 q states in this region. The scalar meson masses calculated with the structure ½(1I⊗ 1I - γ5⊗γ5 - γμ⊗γ) are in excellent agreement with the K-matrix poles deduced from experiment by Anisovich and coworkers.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: 28 August 2000 / Accepted: 12 September 2000
Rights and permissions
About this article
Cite this article
Ricken, R., Koll, M., Merten, D. et al. The meson spectrum in a covariant quark model. Eur Phys J A 9, 221–244 (2000). https://doi.org/10.1007/s100500070041
Issue Date:
DOI: https://doi.org/10.1007/s100500070041