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arXiv · 1701.01404

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

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

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F. Herzog, B. Ruijl, T. Ueda, J. A. M. Vermaseren, A. Vogt. 2017-02-09. The five-loop beta function of Yang-Mills theory with fermions. https://doi.org/10.1007/jhep02(2017)090

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