The R*-operation for Feynman graphs with generic numerators

Understand

The R*-operation by Chetyrkin, Tkachov, and Smirnov is a generalisation of the BPHZ R-operation, which subtracts both ultraviolet and infrared divergences of euclidean Feynman graphs with non-exceptional 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.