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

By F. Herzog, B. Ruijl, Takahiro Ueda, Jos Vermaseren, A. Vogt. 2017

333 citations recorded by the source corpus.

A bstractWe 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 MS¯$$ \overline{\mathrm{MS}} $$ scheme for QCD with nf 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.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e809beecbae48ee2b355e46db0adf89bb9cd1c62

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Citations in the corpus

Fundamental composite dynamics: A review (2020, methodology): “For models with one species of massless fermions in a single representation of the gauge group, the beta function in the MS scheme has been derived up to four loops in [297, 298, 299], with extensions to five loops in [300, 301].”
Minimally subtracted six loop renormalization of $O(n)$-symmetric $\phi^4$ theory and critical exponents (2017, methodology): “Let us just mention the Gross-Neveu model [74] and the particularly impressive 5-loop renormalization of QCD [6, 110, 136] and generalizations [5, 81, 111].”
FLAG Review 2019 (2019, background): “For example, one considers the MS scheme, matches the 3-flavour theory to the 4-flavour theory at a scale given by the charm-quark mass [668–670], runs with the 5-loop β-function [168, 671–674] of the 4-flavour theory to a scale given by the b-quark mass, and there matches to the 5-flavour theory, a”
Collider physics at the precision frontier (2020, methodology): “[868, 870] the R-operation has been extended to Feynman graphs of arbitrary tensorial rank, serving to calculate the 5-loop beta-function [666, 668], see also Refs.”
The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge (2017, methodology): “Five-loop results have appeared over the last ten years or so, first for the case of Quantum Electrodynamics (QED) [9–11], then for physical QCD with gauge group SU(3) [12, 13], and finally for QCD with more general gauge groups [14, 15].”