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In a previous paper Crater and Van Alstine applied the Two Body Diracequations of constraint dynamics to the meson quark-antiquark bound statesusing a relativistic extention of the Adler-Piran potential and compared theirspectral results to those from other approaches, ones which also consideredmeson spectroscopy as a whole and not in parts. In this paper we explore inmore detail the differences and similarities in an important subset of thoseapproaches, the quasipotential approach. In the earlier paper, thetransformation properties of the quark-antiquark potentials were limited to ascalar and an electromagnetic-like four vector, with the former accounting forthe confining aspects of the overall potential, and the latter the short rangeportion. A part of that work consisted of developing a way in which the staticAdler-Piran potential was apportioned between those two different types ofpotentials in addition to covariantization. Here we make a change in thisapportionment that leads to a substantial improvement in the resultantspectroscopy by including a time-like confining vector potential over and abovethe scalar confining one and the electromagnetic-like vector potential. Our fitincludes 19 more mesons than the earlier results and we modify the scalarportion of the potential in such a way that allows this formalism to accountfor the isoscalar mesons {\eta} and {\eta}' not included in the previous work.Continuing the comparisons made in the previous paper with other approaches tomeson spectroscopy we examine in this paper the quasipotential approach ofEbert, Faustov, and Galkin for a comparison with our formalism and spectralresults.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Applications of Two-Body Dirac Equations to the Meson Spectrum with  Three versus Two Covariant Interactions, SU(3) Mixing, and Comparison to a  Quasipotential Approach