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arXiv · hep-ph/9710324

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

Dean Lee·Howard Georgi
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Abstract

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 $α_s$. 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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Dean Lee, Howard Georgi. 1997-11-03. Sum-rule for large-$N_c$ QCD and application to heavy quarkonia. https://doi.org/10.1016/s0370-2693(98)00287-1

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