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On the light massive flavor dependence of the large order asymptotic behavior and the ambiguity of the pole mass

  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 20 September 2017
  • volume 2017, Article number: 99 (2017)
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On the light massive flavor dependence of the large order asymptotic behavior and the ambiguity of the pole mass
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  • André H. Hoang1,2,
  • Christopher Lepenik1 &
  • Moritz Preisser  ORCID: orcid.org/0000-0001-7793-56031,3 
  • 266 Accesses

  • 36 Citations

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A preprint version of the article is available at arXiv.

Abstract

We provide a systematic renormalization group formalism for the mass effects in the relation of the pole mass m pole Q and short-distance masses such as the \( \overline{\mathrm{MS}} \) mass \( {\overline{m}}_Q \) of a heavy quark Q, coming from virtual loop insertions of massive quarks lighter than Q. The formalism reflects the constraints from heavy quark symmetry and entails a combined matching and evolution procedure that allows to disentangle and successively integrate out the corrections coming from the lighter massive quarks and the momentum regions between them and to precisely control the large order asymptotic behavior. With the formalism we systematically sum logarithms of ratios of the lighter quark masses and m Q , relate the QCD corrections for different external heavy quarks to each other, predict the \( \mathcal{O}\left({\alpha}_s^4\right) \) virtual quark mass corrections in the pole-\( \overline{\mathrm{MS}} \) mass relation, calculate the pole mass differences for the top, bottom and charm quarks with a precision of around 20 MeV and analyze the decoupling of the lighter massive quark flavors at large orders. The summation of logarithms is most relevant for the top quark pole mass m pole t , where the hierarchy to the bottom and charm quarks is large. We determine the ambiguity of the pole mass for top, bottom and charm quarks in different scenarios with massive or massless bottom and charm quarks in a way consistent with heavy quark symmetry, and we find that it is 250 MeV. The ambiguity is larger than current projections for the precision of top quark mass measurements in the high-luminosity phase of the LHC.

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Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Authors and Affiliations

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

    André H. Hoang, Christopher Lepenik & Moritz Preisser

  2. Erwin Schrödinger International Institute for Mathematical Physics, University of Vienna, Boltzmanngasse 9, A-1090, Wien, Austria

    André H. Hoang

  3. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, U.S.A.

    Moritz Preisser

Authors
  1. André H. Hoang
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  2. Christopher Lepenik
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Correspondence to Moritz Preisser.

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ArXiv ePrint: 1706.08526

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Hoang, A.H., Lepenik, C. & Preisser, M. On the light massive flavor dependence of the large order asymptotic behavior and the ambiguity of the pole mass. J. High Energ. Phys. 2017, 99 (2017). https://doi.org/10.1007/JHEP09(2017)099

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  • Received: 05 July 2017

  • Accepted: 31 August 2017

  • Published: 20 September 2017

  • DOI: https://doi.org/10.1007/JHEP09(2017)099

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Keywords

  • Heavy Quark Physics
  • Perturbative QCD
  • Quark Masses and SM Parameters
  • Renormalization Regularization and Renormalons

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