T matrices and current correlation functions for a relativistic quark model with confinement

We describe some properties of a relativistic model of confinement and show how that model may be used to construct T matrices for quark-antiquark sys tems. [In the absence of the confinement model, our Lagrangian reduces to t hat of the SU(3)-flavor Nambu-Jona-Lasinio model.] If we have absolute conf inement, our T matrix is expressed in terms of bound states (or resonances) , without the presence of quark scattering states. We find that is a straig htforward matter to describe singlet-octet and pseudoscalar-axial-vector mi xing in this formalism. We also demonstrate that the construction of the T matrices of the model allows us to obtain expressions for various current c orrelation functions, once the meson decay constants are calculated. That c alculation is readily made starting with knowledge of the T matrix. The mos t complex situation we consider is that of the eta-eta' system, with both s inglet-octet and pseudoscalar-axial-vector mixing, calculated in the presen ce of a (covariant) confinement model. Values of masses, coupling constants and mixing angles are given for the pi, omega, phi, eta, and eta' mesons a nd for some of their radial excitations. [S0556-2813(99)02102-0].