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

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

doi:10.1007/JHEP02(2017)090

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

F. Herzog
(
- NIKHEF, Amsterdam
)
,
B. Ruijl
(
- NIKHEF, Amsterdam and
- Leiden U.
)
,
T. Ueda
(
- NIKHEF, Amsterdam
)
,
J.A.M. Vermaseren
(
- NIKHEF, Amsterdam
)
,
A. Vogt
(
- Liverpool U., Dept. Math.
)

Jan 5, 2017

18 pages

Published in:

JHEP 02 (2017) 090

Published: Feb 17, 2017

e-Print:

1701.01404 [hep-ph]

DOI:

10.1007/JHEP02(2017)090

Report number:

NIKHEF-2017-001,
LTH-1117

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Abstract: (Springer)

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.

Note:

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

Perturbative QCD
Renormalization Group
gauge field theory
fermion: coupling
background field
scale dependence
beta function
infrared
correction: quantum
numerical calculations

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