The R*-operation for Feynman graphs with generic numerators

Abstract

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. 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 top-level propagator graphs at five loops in four dimensional phi^3 theory.

38 pages, lots of graphs; minor typos corrected and references added

References in corpus (3)

• Algorithm FIRE -- Feynman Integral REduction
• The five-loop beta function of Yang-Mills theory with fermions
• Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators

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• On Higgs decays to hadrons and the R-ratio at N^4LO
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• Two- and three-loop anomalous dimensions of Weinberg's dimension-six CP-odd gluonic operator
• The on-shell expansion: from Landau equations to the Newton polytope
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
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• Renormalization and non-renormalization of scalar EFTs at higher orders
• The Hopf algebra structure of the $R^{\ast }$-operation
• Six-loop anomalous dimension of the ${\varphi }^Q$ operator in the $O(N)$ symmetric model
• Renormalization-group equations of the LEFT at two loops: dimension-five effects
• Four-loop large-n_f contributions to the non-singlet structure functions F_2 and F_L
• Tensor Reduction for Feynman Integrals with Lorentz and Spinor Indices
• Renormalization of gluonic leading-twist Operators in covariant Gauges
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