Color-magnetic interactions (one-gluon exchange) are incorporated into a semirelativistic quark model and the spectra of ground states and orbital and radial excitations of light mesons, light baryons, charmonium, and $b$-quarkonium are calculated by treating the magnetic splitting exactly by variational methods. The $\pi -\rho$ splitting is fit and the $N-\Delta$ splitting is predicted in excellent agreement with experiment. In general, spin-spin and tensor splittings among light mesons and light baryons are calculated in good agreement with experiment. The splittings in heavy-meson spectroscopy are also predicted accurately, including the $P$-wave states of charmonium and $b$-quarkonium. Some problems and limitations of the quark-model description of the light mesons and baryons are emphasized. Spin-orbit splittings in the light mesons and $P$-wave baryon multiplets are calculated, but a unified understanding of the systematics is not obtained. Radial excitations in the meson and baryon systems are generally in error by 100-150 MeV, and the systematics are not understood.

• Received 13 June 1983

DOI:https://doi.org/10.1103/PhysRevD.28.2807