Renormalization-group improved sum rule analysis for the bottom-quark mass

We study the effect of resumming large logarithms in the determination of the bottom quark mass through a nonrelativistic sum rule analysis. Our result is complete at next-to-leading-logarithmic accuracy and includes some known contributions at next-to-next-to-leading logarithmic accuracy. Compared to finite order computations, the reliability of the theoretical evaluation is greatly improved, resulting in a substantially reduced scale dependence and a faster convergent perturbative series. This allows us to significantly improve over previous determinations of the $\overline{\mathrm{MS}}$ bottom quark mass, $\overline{m_b}$, from nonrelativistic sum rules. Our final figure reads $\overline{m_b}(\overline{m_b})=4.19\pm 0.06\mathrm{GeV}$.