Relativistic description of quark-antiquark bound states. II. spin-dependent treatment

We present the results of a study of light- and heavy-quark-antiquark bound states in the context of the reduced Bethe-Salpeter equation, including the full spin dependence. We obtain good fits to the observed spin splittings in the $b\overline{b}$ and $c\overline{c}$ systems using a short-distance single-gluon-exchange interaction, and a long-distance scalar confining interaction. However, we cannot obtain satisfactory fits to the centers of gravity of the $b\overline{b}$ and $c\overline{c}$ spin multiplets at the same time, and the splittings calculated for $q\overline{Q}$ mesons containing the lighter quarks are very poor. The difficulty appears to be intrinsic to the reduced Salpeter equation for reasons which we discuss.