Spin-dependent interactions in quarkonia

TL;DR

This paper derives analytic expressions for spin-dependent potentials in quarkonia within the Field Correlator Method, analyzing lattice data to confirm small gluonic correlation lengths and comparing different potential definitions.

Contribution

It provides a detailed derivation of spin-dependent potentials considering the QCD string moment of inertia and compares two approaches, showing their equivalence in the zero correlation length limit.

Findings

Lattice data are consistent with gluonic correlation length <0.1 fm.

Derived potentials incorporate the QCD string moment of inertia.

Field Correlator and Eichten-Feinberg approaches are equivalent at zero correlation length.

Abstract

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 analysed using these formulae and the data are shown to be consistent with very small values of the gluonic correlation length, <0.1 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 to 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 corelators, starting from the quartic one.