Spin-Dependent Forces in Heavy-Quark Systems

For heavy qq̄ bound states in quantum chromodynamics, spin-dependent forces are obtained in a manifestly gauge-invariant formalism. Classical spin-orbit and Thomas precession terms are expressed in general in terms of the static energy, and assuming that the confinement mechanism is electric determines uniquely the spin-dependent forces in terms of the nonrelativistic potential. The Coulomb plus linear potential model gives P-state splittings correct to better than 25% and a mass for the ηc of 3.030±{}0.020 GeV.