Five-loop beta function for gauge theories: computations, results and consequences
Abstract
At the end of 2016, we computed the five-loop (NLO) contributions to the beta function in perturbative Quantum Chromodynamics (QCD), its generalization to non-Abelian gauge theories with a simple compact Lie group, and for Quantum Electrodynamics (QED). Here we recall main tools used in and specifically developed for this computation and its main analytic and numerical results. The development work carried out for this project facilitated further even more involved analytic five-loop computations. We briefly summarize also their numerical QCD results for Higgs-boson decay to hadrons in the heavy-top limit and for two NLO splitting functions for the evolution of quark distributions of hadrons. The latter lead to a first realistic estimate of the five-loop contribution to another important quantity in perturbative QCD, the quark cusp anomalous dimension.
Cite
@article{arxiv.2510.21624,
title = {Five-loop beta function for gauge theories: computations, results and consequences},
author = {F. Herzog and B. Ruijl and T. Ueda and J. Vermaseren and A. Vogt},
journal= {arXiv preprint arXiv:2510.21624},
year = {2025}
}
Comments
20 pages, LaTeX, 4 eps-figures. Contributed to the 2025 International Conference of Basic Science, Beijing (China). v2: 3 additional references