The spin-dependent interactions in mesons are considered in detail in the framework of the field correlator method. Analytic expressions for the spin-dependent potentials in heavy and light quarkonia are derived with the QCD string moment of inertia taken into account. Recent lattice data are analyzed using these formulae, and the data are shown to be consistent with very small values of the gluonic correlation length $\lesssim 0.1\mathrm{fm}$. The field correlator and the Eichten-Feinberg definitions of the spin-dependent potentials in the lowest, Gaussian approximation for the QCD vacuum are compared with one another, and the two approaches are shown to be equivalent in the limit of a vanishing vacuum correlation length, whereas for finite values of the latter the difference between these two approaches can be explained by the contribution of the higher-order field correlators, starting from the quartic one.

• Received 8 September 2008

DOI:https://doi.org/10.1103/PhysRevD.78.114020