Perturbative heavy quarkonium spectrum at next-to-next-to-next-to-leading order

We compute the energy levels of some of the lower-lying heavy quarkonium states perturbatively up to O(αs5m) and O(αs5mlogαs). Stability of the predictions depends crucially on the unknown 4-loop pole-MS¯ mass relation. We discuss the current status of the predictions with respect to the observed bottomonium spectrum.