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 ${1/2}(\Id\otimes\Id - γ^0\otimesγ^0)$ as well as the $U_A(1)$-invariant combination ${1/2}(\Id\otimes\Id - γ^5\otimesγ^5 - γ^μ\otimesγ_μ)$, 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 \cite{pap41}), 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 {\sc 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 {\it 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. [...]