Spin-dependent potentials from lattice QCD
  The spin-dependent corrections to the static inter-quark potential are phenomenologically relevant to describing the fine and hyperfine spin splitting of the heavy quarkonium spectra. We investigate these corrections, which are represented as the field strength correlators on the quark-antiquark source, in SU(3) lattice gauge theory. We use the Polyakov loop correlation function as the quark-antiquark source, and by employing the multi-level algorithm, we obtain remarkably clean signals for these corrections up to intermediate distances of around 0.6 fm. Our observation suggests several new features of the corrections. 
Yoshiaki Koma and Miho Koma