# TTP05-01 Heavy Quarkonium Spectrum and Production/Annihilation Rates to order $\beta_0^3\alpha_s^3$

TTP05-01 Heavy Quarkonium Spectrum and Production/Annihilation Rates to order $\beta_0^3\alpha_s^3$

TTP05-01 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 Nucl.Phys. B716 303-318 2005 PDF PostScript arXiv
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