Sum-rule for large-$N_c$ QCD and application to heavy quarkonia
Abstract
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.
Cite
@article{arxiv.hep-ph/9710324,
title = {Sum-rule for large-$N_c$ QCD and application to heavy quarkonia},
author = {Dean Lee and Howard Georgi},
journal= {arXiv preprint arXiv:hep-ph/9710324},
year = {2009}
}
Comments
14 pages, Latex, Pictex --- revised version corrects minor typos in formulas and includes minor changes in exposition