QCD structure of quarkonium spin spectra

We show that our QCD calculation of the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ charmonium state can be incorporated into a global description of the fine and hyperfine structure of the charmonium and bottomonium systems. We propose a simple renormalization prescription in which all ambiguities are absorbed into a single strong coupling constant ${\alpha }_s$. We find that the $O\left({\alpha }_s^2\right)$ perturbative QCD potential leads to a consistent description of all splittings. The results are used to predict the unmeasured bottomonium $P$-wave hyperfine splittings.