Heavy Quarkonium Spectrum and Production/Annihilation Rates to order $β_0^3α_s^3$

Abstract

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 ${\cal O}(m_qα_s^5)$ result for the heavy quarkonium ground state energy is extended to the exited states. After including the ${\cal O}(α_s^3)$ corrections the perturbative results are in surprisingly good agreement with the experimental data on the masses of the excited $Υ$ resonances and the leptonic width of the $Υ(1S)$ meson. The impact of the corrections on the $Υ$ sum rules and top quark-antiquark threshold production cross section is also discussed.