A systematic large-mass expansion of the quark-antiquark effective Hamiltonian due to instantons is developed. The $O\left(m^{-2\mathrm{}}\right)$ spin-spin and spin-orbit contributions are evaluated in the dilute-gas approximation. These can be expressed in terms of differential operators acting on the spin-independent potential. The three-quark effective Hamiltonian (in a color-singlet state) is shown to be a sum of quark-antiquark Hamiltonians. The structure and numerical value of the effective Hamiltonian is discussed.

• Received 5 July 1978

DOI:https://doi.org/10.1103/PhysRevD.18.4684