Abstract
The R*operation by Chetyrkin, Tkachov, and Smirnov is a generalisation of the BPHZ Roperation, which subtracts both ultraviolet and infrared divergences of euclidean Feynman graphs with nonexceptional external momenta. It can be used to compute the divergent parts of such Feynman graphs from products of simpler Feynman graphs of lower loops. In this paper we extend the R*operation to Feynman graphs with arbitrary numerators, including tensors. We also provide a novel way of defining infrared counterterms which closely resembles the definition of its ultraviolet counterpart. We further express both infrared and ultraviolet counterterms in terms of scaleless vacuum graphs with a logarithmic degree of divergence. By exploiting symmetries, integrand and integral relations, which the counterterms of scaleless vacuum graphs satisfy, we can vastly reduce their number and complexity. A FORM implementation of this method was used to compute the five loop beta function in QCD for a general gauge group. To illustrate the procedure, we compute the poles in the dimensional regulator of all toplevel propagator graphs at five loops in four dimensional phi^3 theory.
Original language  English 

Article number  37 
Journal  Journal of High Energy Physics 
DOIs  
Publication status  Published  8 May 2017 
Keywords
 hepth
 hepph
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Franz Herzog
 School of Physics and Astronomy  UKRI Future Leader Fellowship
Person: Academic: Research Active