Heavy Quarkonium Spectrum and Production/Annihilation Rates to order   $\beta_0^3\alpha_s^3$
  We compute the third-order corrections to the heavy quarkonium spectrum and production/annihilation rates due to the leading renormalization group running of the static potential. The previously known complete ${\cal O}(m_q\alpha_s^5)$ result for the heavy quarkonium ground state energy is extended to the exited states. After including the ${\cal O}(\alpha_s^3)$ corrections the perturbative results are in surprisingly good agreement with the experimental data on the masses of the excited $\Upsilon$ resonances and the leptonic width of the $\Upsilon(1S)$ meson. The impact of the corrections on the $\Upsilon$ sum rules and top quark-antiquark threshold production cross section is also discussed. 
A.A. Penin, V.A. Smirnov, M. Steinhauser