Sum-rule prediction for the masses ofL≥1levels of quarkonium

We derive sum rules relating the four quarkonium levels for each L≥1 which are valid for a wide class of potentials with a vector or a vector-plus-scalar Lorentz character for five cases of interest. The numerical predictions for the ${}_{}{}^1{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$ mass for the cc¯ and bb¯ systems are given in each case.