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 non-relativistic 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 $\MS$ bottom quark mass, $\bar{m}_b$, from non-relativistic sum rules. Our final figure reads $\bar{m}_b(\bar{m}_b)=4.19\pm 0.06$ GeV.