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

Research output: Contribution to journalArticle

  • F. Herzog
  • B. Ruijl
  • T. Ueda
  • J. A. M. Vermaseren
  • A. Vogt

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Original languageEnglish
Article number90
JournalJournal of High Energy Physics
Publication statusPublished - 17 Feb 2017


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 MSbar 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.

    Research areas

  • hep-ph

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