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The five-loop beta function of Yang-Mills theory with fermions

Journal of High Energy Physics volume 2017, Article number: 90 (2017) Cite this article

A preprint version of the article is available at arXiv.

Abstract

We have computed the five-loop corrections to the scale dependence of the renormalized coupling constant for Quantum Chromodynamics (QCD), its generalization to non-Abelian gauge theories with a simple compact Lie group, and for Quantum Electrodynamics (QED). Our analytical result, obtained using the background field method, infrared rearrangement via a new diagram-by-diagram implementation of the R* operation and the Forcer program for massless four-loop propagators, confirms the QCD and QED results obtained by only one group before. The numerical size of the five-loop corrections is briefly discussed in the standard \( \overline{\mathrm{MS}} \) scheme for QCD with n f flavours and for pure SU(N) Yang-Mills theory. Their effect in QCD is much smaller than the four-loop contributions, even at rather low scales.

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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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Affiliations

  1. Nikhef Theory Group, Science Park 105, 1098 XG, Amsterdam, The Netherlands

    F. Herzog, B. Ruijl, T. Ueda & J. A. M. Vermaseren

  2. Leiden Centre of Data Science, Leiden University, Niels Bohrweg 1, 2333 CA, Leiden, The Netherlands

    B. Ruijl

  3. Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 3BX, United Kingdom

    A. Vogt

Authors
  1. F. Herzog
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  2. B. Ruijl
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  3. T. Ueda
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  4. J. A. M. Vermaseren
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  5. A. Vogt
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Correspondence to A. Vogt.

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ArXiv ePrint: 1701.01404

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Herzog, F., Ruijl, B., Ueda, T. et al. The five-loop beta function of Yang-Mills theory with fermions. J. High Energ. Phys. 2017, 90 (2017). https://doi.org/10.1007/JHEP02(2017)090

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  • DOI: https://doi.org/10.1007/JHEP02(2017)090

Keywords

  • Perturbative QCD
  • Renormalization Group