Relativistic meson spectroscopy in momentum space

In this paper a relativistic constituent-quark model based on the Ruijgrok–de Groot formalism is presented. The quark model is not defined in configuration space, but in momentum space. The complete meson spectrum, with the exception of the self-conjugate light unflavored mesons, is calculated. The potential used consists of a one-gluon exchange (OGE) part and a confining part. For the confining part a relativistic generalization of the linear plus constant potential was used, which is well defined in momentum space without introducing any singularities. For the OGE part several potentials were investigated. Retardations were included at all places. By the use of a fitting procedure involving 52 well-established mesons, but results were obtained for a potential consisting of a purely vector Richardson potential and a purely scalar confining potential. Reasonable results were also obtained for a modified Richardson potential. Most meson masses, with the exception of the π, the K, and the ${\mathit{K}}_0^{\mathrm{*}}$, were found to be quite well described by the model.