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Journal of High Energy Physics

, 2012:188 | Cite as

Renormalization group improved bottom mass from \( \varUpsilon \) sum rules at NNLL order

  • André H. Hoang
  • Pedro Ruiz-FemeníaEmail author
  • Maximilian Stahlhofen
Article

Abstract

We determine the bottom quark mass from non-relativistic large-n \( \varUpsilon \) 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 α 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 α s ln(n) terms, and allows for reliable single moment fits. For the current world average of the strong coupling (α s (M Z) = 0.1183 ± 0.0010) we obtain \( M_{\mathrm{b}}^{1S } \) = 4.755 ± 0.057pert ± 0.009α s  ± 0.003exp GeV for the bottom 1S mass and \( {{\overline{m}}_{\mathrm{b}}}\left( {{{\overline{m}}_{\mathrm{b}}}} \right) \) = 4.235 ± 0.055pert ± 0.003exp GeV for the bottom \( \overline{\mathrm{MS}} \) mass, where we have quoted the perturbative error and the uncertainties from the strong coupling and the experimental data.

Keywords

Heavy Quark Physics Sum Rules QCD 

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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • André H. Hoang
    • 1
  • Pedro Ruiz-Femenía
    • 1
    • 2
    Email author
  • Maximilian Stahlhofen
    • 1
    • 3
  1. 1.University of Vienna, Faculty of PhysicsWienAustria
  2. 2.IFIC, Universitat de València — CSICValenciaSpain
  3. 3.DESY Theory GroupHamburgGermany

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