Sum-rule for large-Nc QCD and application to heavy quarkonia

Abstract

We introduce a 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.