Bottom Mass from Nonrelativistic Sum Rules at NNLL

Abstract

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.