Covariant description of mesons as nontopological solitons

We provide a fully covariant analysis of a nontopological soliton model of hadron structure and make an application to the structure of various mesons. We study the ρ and ω mesons, charmonium, and the Υ system. The model describes quarks coupled to a scalar field which plays the role of an order parameter of the QCD vacuum. There are a few parameters in this model: a flavor-dependent constituent quark mass, a mass parameter for the scalar field, a coupling constant which determines the strength of the coupling of the quarks to the scalar field, and a cutoff parameter. The mass parameter of the scalar field and the scalar-quark coupling constant are taken from our study of nucleon structure. Therefore, once a value is chosen for the high-momentum cutoff, only a single parameter is varied in this analysis, the flavor-dependent (constituent) quark mass. A reasonably good fit is obtained to a series of mesonic states of quite different mass in this extremely simple model, indicating that a unified approach to hadron structure may be possible. (At this point, we have not attempted to model the confinement mechanism. Further, our Hamiltonian has continuum solutions and, given our method of calculation, these solutions prevent us from studying all but the low-lying states of charmonium and the Υ system, for example.) We have also modified our Lagrangian in order to study gluon-exchange effects; however, the study of such effects requires the introduction of additional parameters. By fitting these new parameters to the mass splitting of the lowest $0^{\mathrm{-}}$ and $1^{\mathrm{-}}$ states of the charmonium system, we are able to make a prediction for corresponding splitting in the Υ system.