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.

arXiv comment19 pages, v2: version to be published

References in corpus (29)

• Electroweak corrections to charged-current e+e- --> 4 fermion processes - technical details and further results
• Two-loop Integrand Decomposition into Master Integrals and Surface Terms
• General subtraction method for numerical calculation of one-loop QCD matrix elements
• Numerical integration of one-loop Feynman diagrams for N-photon amplitudes
• Techniques for QCD calculations by numerical integration
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• From loops to trees by-passing Feynman's theorem
• Two-Loop Four-Gluon Amplitudes with the Numerical Unitarity Method
• Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity
• Towards gauge theories in four dimensions
• A Tree-Loop Duality Relation at Two Loops and Beyond
• Numerical NLO QCD calculations
• Four-dimensional unsubtraction from the loop-tree duality
• QCD Calculations by Numerical Integration
• NLO results for five, six and seven jets in electron-positron annihilation
• 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
• Subleading Poles in the Numerical Unitarity Method at Two Loops
• Efficiency improvements for the numerical computation of NLO corrections
• Direct numerical integration for multi-loop integrals
• Direct numerical integration of one-loop Feynman diagrams for N-photon amplitudes
• A simple formula for the infrared singular part of the integrand of one-loop QCD amplitudes
• Direct contour deformation with arbitrary masses in the loop
• Unitarity Cuts of Integrals with Doubled Propagators
• Universal dual amplitudes and asymptotic expansions for $gg\to H$ and $H\to \gamma \gamma$ in four dimensions
• Numerical integration of subtraction terms
• Infrared singularities in one-loop amplitudes
• Tree-Loop Duality Relation beyond simple poles
• NLO corrections to Z production in association with several jets

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• Loop Tree Duality for multi-loop numerical integration
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• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Quantum algorithm for Feynman loop integrals
• Building Bases of Loop Integrands
• Locally finite two-loop QCD amplitudes from IR universality for electroweak production
• Asymptotic expansions through the loop-tree duality
• Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• A new formulation of the loop-tree duality at higher loops