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Sum-rule for large- QCD and application to heavy quarkonia
We introduce a new sum-rule for large- QCD which relates the density of
heavy quarkonium states, the state-averaged square of the wavefunction at the
origin, and the heavy quark current-current correlator. Focusing on the region
of energy just above perturbative threshold, we calculate the correlator by
incorporating arbitrarily high orders in the QCD coupling . We use
the sum-rule to determine the bottomonium potential using experimentally
measured s-wave leptonic widths and compare the result with the potential
obtained by direct calculation from the measured s-wave spectrum. We discuss
the utility of the sum-rule method for accurate determination of the confining
potential.Comment: 14 pages, Latex, Pictex --- revised version corrects minor typos in
formulas and includes minor changes in expositio
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