Renormalization Group Improved Bottom Mass from Upsilon Sum Rules at NNLL Order

Understand

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.