We extend the formalism based on perturbative QCD that was developed in ourprevious work, and compute the hyperfine splittings of the bottomonium spectrumas well as the fine and hyperfine splittings of the charmonium spectrum. Allthe corrections up to O(alpha_s^5 m) are included in the computations. We findagreement (with respect to theoretical uncertainties) with the experimentalvalues whenever available and give predictions for not yet observed splittings.
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