Spin-dependent forces in quantum chromodynamics

Abstract

In a manifestly gauge-independent formalism, all relativistic corrections to the fermion propagation function are determined and the general form of the spin-dependent forces in quantum chromodynamics for heavy-quark-antiquark ($q\overline{q}$) systems is derived. For example, the classical spin-orbit and Thomas-precession terms are found to be simple derivatives of the static potential. In addition to expressing the spin-dependent forces in terms of the minimal number of independent potentials, two new applications of this formulation are presented: (1) The effect of pseudoparticle solutions on the spin-dependent forces is analyzed, and (2) an electric-confinement assumption produces a zero-parameter spin-dependent potential. This potential determines the fine structure in heavy $q\overline{q}$ systems. Spin splittings in the $\Upsilon$ system are predicted and the $\frac{J}{\psi }$ system splittings are compared with the experimentally observed values.