Tmatrices 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 systems. [In the absence of the confinement model, our Lagrangian reduces to that of the SU(3)-flavor Nambu–Jona-Lasinio model.] If we have absolute confinement, our T matrix is expressed in terms of bound states (or resonances), without the presence of quark scattering states. We find that is a straightforward matter to describe singlet-octet and pseudoscalar-axial-vector mixing in this formalism. We also demonstrate that the construction of the T matrices of the model allows us to obtain expressions for various current correlation functions, once the meson decay constants are calculated. That calculation is readily made starting with knowledge of the T matrix. The most complex situation we consider is that of the $\eta -{\eta }^{\prime }$ system, with both singlet-octet and pseudoscalar-axial-vector mixing, calculated in the presence of a (covariant) confinement model. Values of masses, coupling constants and mixing angles are given for the π, ω, φ, η, and ${\eta }^{\prime }$ mesons and for some of their radial excitations.