Renormalization group improved bottom mass from upsilon sum rules at NNLL order

We determine the bottom quark mass from non-relativistic large-n Upsilon sum rules with renormalization group improvement at next-to-next-to-leading logarithmic order. We compute the theoretical moments within the vNRQCD formalism and account for the summation of powers of the Coulomb singularities as well as of logarithmic terms proportional to powers of alpha_s ln(n). The renormalization group improvement leads to a substantial stabilization of the theoretical moments compared to previous fixed-order analyses, which did not account for the systematic treatment of the logarithmic alpha_s ln(n) terms, and allows for reliable single moment fits. For the current world average of the strong coupling (alpha_s(M_Z) = 0.1183 +- 0.0010) we obtain M_b^{1S}=4.755 +- 0.057(pert) +- 0.009(alpha_s) +- 0.003(exp) GeV for the bottom 1S mass and m_b(m_b)= 4.235 +- 0.055(pert) +- 0.003(exp) GeV for the bottom MSbar mass, where we have quoted the perturbative error and the uncertainties from the strong coupling and the experimental data.