  We report on a recent determination of the bottom quark mass from
nonrelativistic (large-n) Upsilon sum rules with renormalization group
improvement (RGI) at next-to-next-to-leading logarithmic (NNLL) order. The
comparison to previous fixed-order analyses shows that the RGI computed in the
vNRQCD framework leads to a substantial stabilization of the theoretical sum
rule moments with respect to scale variations. A single moment fit (n=10) to
the available experimental data yields 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. The quoted
uncertainties refer to the perturbative error and the uncertainties associated
with the strong coupling and the experimental input.
