Zimmermann's Forest Formula, Infrared Divergences and the QCD Beta Function

Understand

We review Zimmermann's forest formula, which solves Bogoliubov's recursive $R$-operation for the subtraction of ultraviolet divergences in perturbative Quantum Field Theory.

• We further discuss a generalisation of the $R$-operation which subtracts besides ultraviolet also Euclidean infrared divergences.
• This generalisation, which goes under the name of the $R^*$-operation, can be used efficiently to compute renormalisation constants.
• We will discuss several results obtained by this method with focus on the QCD beta function at five loops as well as the application to hadronic Higgs boson decay rates at N${}^4$LO.