H EP - P H / 97 0 ∣ 4 ∣ 4 * he p - ph / 9 70

A straightforward calculation reveals the essentially nonlocal character of the leading heavy Q Q interaction arising from nonperturbative gluon eld correlations in the model of a uctuating QCD vacuum. In light of this quarkonium spin splitting ratio predictions which have supported the scalar connnement ansatz are reconsidered as a speciic example of possible consequences for spectroscopy. A great deal of work has gone into the eeort to describe the spectrum and high energy scattering of hadrons as bound states of quarks and gluons. It remains an open and interesting problem. Part of the trouble seems to lie in the historical identiication of particle eld theory with its familiar perturbation expansion, while nonperturbative phenomena such as connnement are thought to play an important role in the QCD bound state. The controlling aim to obtain an understanding in a formulation of the fundamental Quantum Field Theory has led to the development of nonperturbative phenomenology reeecting the eeective degrees of freedom for a given arrangement, where those degrees less relevant are frozen or integrated out of the theory. Unfortunately there is no unique well-deened program by which this is done. Two competing points of view among many are given by potential models on one hand and the method of sum rules on the other. The former assumes a local interaction in terms of quark coordinates, while the gluon eld gures in more directly in the later. It was shown some time ago by Voloshin and Leutwyler separately 1] that large scale uctuations of the QCD vacuum cannot be described adequately by local potentials. The conclusion found support in the subsequent leading relativistic interaction Hamiltonian of Eichten and Feinberg 2] (see also Lemma in 3]) and reenement at the hands of Marquard and Dosch 4] who considered two extreme cases for the vacuum eld's correlation length relative to those of the heavy quarks bound in a meson. Roughly, for T g << T q a local description was found to be justiied, though for T g >> T q a nonlocality appears making the sum rule approach more suitable. Potential model builders have taken this to validate the use of local potentials for suuciently heavy quarks, which is quite right. A quantitative sense of the validity in terms familiar to the language of potential models might be obtained by considering the interaction as a double expansion in the ratios of the two time scales …