On the vanishing of certain cuts or residues of loop integrals with higher powers of the propagators

Abstract

Starting from two-loops, there are Feynman integrals with higher powers of the propagators. They arise from self-energy insertions on internal lines. Within the loop-tree duality approach or within methods based on numerical unitarity one needs (among other things) the residue when a raised propagator goes on-shell. We show that for renormalised quantities in the on-shell scheme these residues can be made to vanish already at the integrand level.

19 pages, v2: version to be published

References in corpus (9)

• Numerical integration of one-loop Feynman diagrams for N-photon amplitudes
• From loops to trees by-passing Feynman's theorem
• A Tree-Loop Duality Relation at Two Loops and Beyond
• Numerical NLO QCD calculations
• On the singular behaviour of scattering amplitudes in quantum field theory
• Universal four-dimensional representation of $H\to \gamma \gamma$ at two loops through the Loop-Tree Duality
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Cited by in corpus (3)

• Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• A new formulation of the loop-tree duality at higher loops