O(αS5m) quarkonium 1S spectrum in large-β0 approximation and renormalon cancellation

Presently the quarkonium spectrum, written in terms of the quark MS-mass, is known at O(αS3m) accuracy. We point out that in order to achieve O(αS4m) accuracy it is sufficient to calculate further (I) the O(αS4m) relation between the MS-mass and the pole-mass, and (II) the binding energy at O(αS5m) in the large-β0 approximation. We calculate the latter correction analytically for the 1S-state and study its phenomenological implications.