bquark low-scale running mass fromΥsum rules

The b quark low-scale running mass $m_{\mathrm{kin}}$ is determined from an analysis of the ${\rm Y}$ sum rules in the next-to-next-to-leading order (NNLO). It is demonstrated that using this mass one can significantly improve the convergence of the perturbation series for the spectral density moments. We obtain $m_{\mathrm{kin}}\left(1\mathrm{}\hspace{0.5em}\mathrm{GeV}\right)=4.56\mathrm{}\pm 0.06\hspace{0.5em}\mathrm{GeV}$. Using this result we derive the value of the modified minimal subtraction scheme mass $\overline{m}:\hspace{0.5em}\hspace{0.5em}\overline{m}\left(\overline{m}\right)=4.2\mathrm{}\pm 0.1\hspace{0.5em}\mathrm{GeV}$. Contrary to the low-scale running mass, the pole mass of the b quark cannot be reliably determined from the sum rules. As a by-product of our study we find the NNLO analytical expression for the cross section $e^{+}{e}^{-}\to Q\overline{Q}$ of the quark-antiquark pair production in the threshold region, as well as the energy levels and the wave functions at the origin for the ${}^1{S}_3$ bound states of $Q\overline{Q}$.