The l = 1 hyperfine splitting in bottomium as a precise probe of the QCD vacuum

By relating fine and hyperfine splittings for l = 1 states in bottomium we can factor out the less tractable part of the perturbative and nonperturbative effects. Reliable predictions for one of the fine splittings and the hyperfine splitting can then be made by calculating in terms of the remaining fine splitting, which is then taken from experiment; perturbative and nonperturbative corrections to these relations are under full control. The method (which produces reasonable results even for the cc system) predicts a value of 1.5 MeV for the (s = 1) − (s = 0) splitting in bb, opposite in sign to that in cc. For this result the contribution of the gluon condensate 〈αsG2〉 is essential, as any model (in particular potential models) which neglects this would give a negative bb hyperfine splitting.