The meson spectrum in a covariant quark model

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 - γ^μ⊗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 - γ^μ⊗γ) are in excellent agreement with the K-matrix poles deduced from experiment by Anisovich and coworkers.