Sum-rule for large-$N_c$ QCD and application to heavy quarkonia

Details Sum-rule for large-$N_c$ QCD and application to heavy quarkonia Sum-rule for large-$N_c$ QCD and application to heavy quarkonia

1997-10-13

arxiv.org/abs/hep-ph/9710324v2

Phys.Lett.B426:367-374,1998

Physics

High Energy Physics

High Energy Physics - Phenomenology

14 pages, Latex, Pictex --- revised version corrects minor typos in formulas and includes minor changes in exposition

Scientific paper

10.1016/S0370-2693(98)00287-1

We introduce a new sum-rule for large-$N_c$ 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 $\alpha_s$. 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.

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