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 $1/2(\text{Id}\otimes \text{Id}-{\gamma }^0\otimes {\gamma }^0)$ as well as the $U_A(1)$-invariant combination $1/2(\text{Id}\otimes \text{Id}-{\gamma }^5\otimes {\gamma }^5-{\gamma }^{\mu }\otimes {\gamma }_{\mu })$, 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 \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. [...]

Comments: 32 pages including 19 figures and 3 tables; submitted to Eur. Phys. A