Spin splittings of heavy-quark bound states from lattice QCD

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Abstract
The spin-dependent potentials which determine the spin splittings of heavy-quark bound states are evaluated by a lattice Monte Carlo calculation. One of the spin-orbit potentials is found to have a long-range nonperturbative component, while all other potentials exhibit a short-ranged perturbative behavior. Calculations at two different values of the bare coupling constant demonstrate scaling. The spin splittings that follow from the calculated potentials are evaluated. Good agreement is found with experimental data provided that vacuum-polarization effects from qq¯ pairs at short distances are taken into account.