Precision determination of ${\alpha }_s$ and $m_b$ from QCD sum rules for $b\overline{b}$.

Abstract

The QCD sum rules for moments of production cross section of $b\overline{b}$ states in $e^{+}{e}^{-}$ annihilation are extremely sensitive to the values of $m_b$ and ${\alpha }_s$ for moments of large order $n$. This enables one to extract from the existing data on ${\rm Y}$ resonances the values of these parameters with a high precision by using a non-relativistic expansion in $1/n$. It is found that the sum rules fit the data with ${\alpha }_s^{\overline{MS}}(1GeV)=0.336\pm 0.011$ and $m_b=4827\pm 7MeV$, where the estimate of the errors includes the theoretical uncertainty due to subleading in $1/n$ terms and the experimental uncertainty of the $e^{+}{e}^{-}$ annihilation cross section above the $B\overline{B}$ threshold. The found value of ${\alpha }_s$, when evolved in two loops up to the $Z$ mass, gives ${\alpha }_s^{\overline{MS}}(M_Z)=0.109\pm 0.001$. The $b$ quark mass $m_b$ corresponds to the `on shell' value appropriate for one-loop perturbative calculations.

15 pages + 4 figures in LaTeX (FEYNMAN macros used for Fig.3)

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