Five-loop Beta Function Computations Advance Perturbative Chromodynamics and Electrodynamics

The precise calculation of fundamental forces relies on understanding how these forces change with energy, a quantity described by the beta function, and recent work by F. Herzog, B. Ruijl, T. Ueda, J. Vermaseren and A. Vogt represents a major step forward in this area. The team successfully computes the beta function to an unprecedented level of precision, extending calculations to the five-loop order for both Quantum Electrodynamics and the more complex theory of strong interactions, known as Chromodynamics. This achievement significantly refines predictions for particle physics phenomena, including the decay of the Higgs boson and the behaviour of quarks within hadrons, and provides a crucial foundation for future theoretical investigations into the fundamental forces governing the universe. The results demonstrate a mastery of complex calculations and unlock new possibilities for testing the Standard Model of particle physics with greater accuracy than ever before.

We recall the 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, five-loop analytic computations. We briefly summarise also their numerical QCD results for Higgs-boson decay to hadrons in the heavy-top limit and for two N4LO splitting functions for the evolution of quark distributions of hadrons. This work extends the precision of these calculations, pushing the accuracy frontier for analyses of benchmark quantities like Higgs-boson production at the Large Hadron Collider. The team successfully computed these complex contributions, building upon previous four-loop calculations and verifying results obtained by other research groups. The research involved the development of advanced computational techniques, notably the background field method and a novel implementation of the R∗ operation for infrared rearrangement.

This new approach allowed for the calculation of pole terms in five-loop diagrams using four-loop propagator-type integrals, evaluated with the Forcer program in Form. These computational advancements proved crucial, enabling the team to tackle the complexities of high-rank tensor integrals that arise in these calculations. The successful determination of the five-loop beta function not only confirms theoretical expectations but also provides a foundation for further investigations into even more complex quantum field theory calculations. Beyond the beta function, the team leveraged these newly developed tools to compute other five-loop quantities, including results for Higgs-boson decay to hadrons in the heavy-top limit and two N4LO splitting functions governing the evolution of quark distributions within hadrons. These splitting functions, in turn, led to the first realistic estimate of the five-loop contribution to the quark cusp anomalous dimension, a crucial parameter in perturbative QCD. This work extends previous calculations to a higher order of precision, enabling more accurate predictions of particle interactions and properties. The team developed novel methods to tackle the computational complexity inherent in these calculations, paving the way for further investigations into even more challenging scenarios. The research extends beyond the beta function, successfully applying these methods to calculate the decay of the Higgs boson into gluons in the heavy-top limit and determining splitting functions that describe the evolution of quark distributions within hadrons.

These calculations provide a more precise understanding of Higgs boson properties and the internal structure of protons and neutrons. Furthermore, the team determined the five-loop contribution to the quark cusp anomalous dimension, a crucial quantity in perturbative quantum chromodynamics. The authors acknowledge that the computational demands of these calculations increase rapidly with the order of perturbation theory, limiting the scope of some calculations, such as the determination of splitting functions for higher values of N. This work extends the precision of these calculations, pushing the accuracy frontier for analyses of benchmark quantities like Higgs-boson production at the Large Hadron Collider. The research involved the development of advanced computational techniques, notably the background field method and a novel implementation of the R∗ operation for infrared rearrangement. This new approach allowed for the calculation of pole terms in five-loop diagrams using four-loop propagator-type integrals, evaluated with the Forcer program in Form.

These computational advancements proved crucial, enabling the team to tackle the complexities of high-rank tensor integrals that arise in these calculations. Beyond the beta function, the team leveraged these newly developed tools to compute other five-loop quantities, including results for Higgs-boson decay to hadrons in the heavy-top limit and two N4LO splitting functions governing the evolution of quark distributions within hadrons. These splitting functions, in turn, led to the first realistic estimate of the five-loop contribution to the quark cusp anomalous dimension, a crucial parameter in perturbative QCD.