Five-loop beta function for gauge theories: computations, results and consequences

TL;DR

This paper reports the calculation of the five-loop beta function in QCD, QED, and non-Abelian gauge theories, providing new insights into high-order perturbative corrections and their implications for particle physics.

Contribution

It presents the first five-loop beta function calculations for gauge theories, advancing computational techniques and extending understanding of perturbative quantum field theory.

Findings

Computed five-loop beta functions for QCD, QED, and non-Abelian gauge theories.

Provided numerical estimates for Higgs decay and quark distribution evolution at N$^4$LO.

Estimated the five-loop contribution to the quark cusp anomalous dimension.

Abstract

At the end of 2016, we computed the five-loop (N$^4$LO) 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 N$^4$LO 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.