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

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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.

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Authors and Affiliations

  1. University of Vienna, Faculty of Physics, Boltzmanngasse 5, A-1090, Wien, Austria

    André H. Hoang, Pedro Ruiz-Femenía & Maximilian Stahlhofen

  2. IFIC, Universitat de València — CSIC, Apt. Correus 22085, E-46071, Valencia, Spain

    Pedro Ruiz-Femenía

  3. DESY Theory Group, Notkestraße 85, D-22607, Hamburg, Germany

    Maximilian Stahlhofen

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  1. André H. Hoang
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  2. Pedro Ruiz-Femenía
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  3. Maximilian Stahlhofen
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Correspondence to Pedro Ruiz-Femenía.

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ArXiv ePrint: 1209.0450

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Hoang, A.H., Ruiz-Femenía, P. & Stahlhofen, M. Renormalization group improved bottom mass from \( \varUpsilon \) sum rules at NNLL order. J. High Energ. Phys. 2012, 188 (2012). https://doi.org/10.1007/JHEP10(2012)188

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