English

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

High Energy Physics - Phenomenology 2017-03-08 v2

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 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.

Keywords

Cite

@article{arxiv.1701.01404,
  title  = {The five-loop beta function of Yang-Mills theory with fermions},
  author = {F. Herzog and B. Ruijl and T. Ueda and J. A. M. Vermaseren and A. Vogt},
  journal= {arXiv preprint arXiv:1701.01404},
  year   = {2017}
}

Comments

19 pages, LaTex, 4 figures. FORM file of the main results available with the source. v2: version accepted by JHEP: minor text changes, a few additional references, typos corrected

R2 v1 2026-06-22T17:42:12.893Z