The resonance parameters of the excited $\psi$-family resonances, namely, the $\psi (4040)$, $\psi (4160)$, and $\psi (4415)$, were determined by fitting the $R$ values measured by experiments. It is found that the previously reported leptonic partial widths of these states were merely one possible solution among a four-fold ambiguity. By fitting the most precise experimental data on the $R$ values measured by the BES collaboration, this work presents all four sets of solutions. These results may affect the interpretation of the charmonium and charmonium-like states above $4\mathrm{GeV}/c^2$.

• Received 16 August 2010

DOI:https://doi.org/10.1103/PhysRevD.82.077501