QCD Calculations of Heavy Quarkonium States

Abstract

Recent results on the QCD analysis of bound states of heavy $\bar{q}q$ quarks are reviewed, paying attention to what can be derived from the theory with a reasonable degree of rigour. We report a calculation of $\bar{b}c$ bound states; a very precise evaluation of $b,c$ quark masses from quarkonium spectrum; the NNLO evaluation of ${\rm Y}\to e^{+}{e}^{-}$; and a discussion of power corrections. For the $b$ quark {\sl pole} mass we get, including $O(m_c^2/m_b^2)$ and $O({\alpha }_s^5\log {\alpha }_s)$ corrections, $m_b=5.020\pm 0.058GeV$; and for the $\overline{MS}$ mass the result, correct to $O({\alpha }_s^3)$, $O(m_c^2/m_b^2)$, ${\bar{m}}_b({\bar{m}}_b)=4.286\pm 0.036GeV$. For the decay ${\rm Y}\to e^{+}{e}^{-}$, higher corrections are too large to permit a reliable calculation, but we can predict a toponium width of $13\pm 1keV$.

Comments: PlainTex file; one figure