Bottom Quark Mass from $Υ$ Sum Rules to ${\cal O}(α_s^3)$

We use the ${\cal O}(α_s^3)$ approximation of the heavy-quark vacuum polarization function in the threshold region to determine the bottom quark mass from nonrelativistic $Υ$ sum rules. We find very good stability and convergence of the perturbative series for the bottom quark mass in $\rm\overline{MS}$ renormalization scheme. Our final result is $\overline{m}_b(\overline{m}_b)=4.169\pm 0.008_{th}\pm 0.002_{α_s}\pm 0.002_{exp}$.

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