Nuclear Physics B256 (1985) 717-726 fc) North-Holland Publishing Company THE SPIN-DEPENDENT FORCES BETWEEN HEAVY QUARKS IN LATI'ICE GAUGE THEORIES Massimo CAMPOSTRINI Scuola Normale Superiore, Pisa and INFN, Sezione di Pisa, 1-56100 Pisa, Italy Received 13 November 1984 We discuss the possibility of obtaining the spin-dependent forces between heavy quarks from a lattice Monte Carlo computation. The quantities to be measured are various combinations of Wilson loops with two plaquette insertions. We present a Monte Carlo computation with the U(I) gauge group that reproduces well the perturbative results for the spin-orbit and spin-spin interactions, and suggests that an accurate SU(3) calculation is indeed feasible and meaningful. 1. Introduction One of the most interesting problems in the study of QCD is the calculation of the mass spectrum and various properties of the bound states of the theory (like wave functions, magnetic moments and so on). Lattice Monte Carlo methods are presently the most powerful tool in this analysis [1]; now we have reached the capability of performing the necessary calculations for a pure gauge theory on what is believed to be a large enough lattice [2], while for the much more demanding full QCD we must wait for more powerful computers. The study of the bound states of heavy quarks offers considerable simplifications: these particles can be considered in the first approximation as non-relativistic and a consistent 1/m expansion is possible [3]. The effective hamiltonian for these systems can be obtained from Monte Carlo calculations without explicitly introducing heavy quarks [4]. By using the pure SU(3) gauge theory we obtain an approximation equivalent to the "quenching" for light quarks [5], but numerically much less demanding. When light quarks are introduced into the simulation (with large enough lattice and statistics) this method could take care of the heavy quarks with a small extra numerical effort. It also gives more detailed information than a "brute force" (purely numerical) calculation, like the fermion propagator computation needed to study light-quark bound states. 717