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

Abstract

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 $R^{\ast }$-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. This article summarizes a talk given at the Wolfhart Zimmermann Memorial Symposium.

17 pages, 5 figures; based on a talk given at the Wolfhart Zimmermann Memorial Symposium on the 22nd of May 2017 in Munich

References in corpus (4)

• Towards the five-loop Beta function for a general gauge group
• Forcer, a FORM program for the parametric reduction of four-loop massless propagator diagrams
• Combinatorics of $\mathbf{R}$-, ${\mathbf{R}}^{-1}$-, and ${\mathbf{R}}^{\ast }$-operations and asymptotic expansions of feynman integrals in the limit of large momenta and masses
• Forcer: a FORM program for 4-loop massless propagators

Cited by in corpus (5)

• Collider Physics at the Precision Frontier
• A brief review of Implicit Regularization and its connection with the BPHZ theorem
• Five loop minimal MOM scheme field and quark mass anomalous dimensions in QCD
• Five loop anomalous dimension of non-singlet quark currents in the RI' scheme
• NNLO QCD corrections to $\gamma \gamma \to Q\bar{Q}$ from Local Unitarity combined with Coulomb resummation and NLO EW effects