On triple-cut of scattering amplitudes

2006/11/08 by Pierpaolo Mastrolia · 100 citations
Mathematics · Physics and Astronomy · #Amplitude #Anomaly (physics) #Black Holes and Theoretical Physics #Combinatorics #Covariant transformation #Feynman diagram #Helicity #Holomorphic function #Loop (graph theory) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #Physics #Propagator #Pure mathematics #Quantum mechanics #Scattering amplitude #Spinor #Triple point #hep-th

paper · pdf · doi:10.1016/j.physletb.2006.11.037

published in Physics Letters B 644(4), 272-283 (Elsevier BV) · 17 pages, 8 figures

arxiv created 2006/11/08 · openalex publication_date 2006/12/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

It is analysed the triple-cut of one-loop amplitudes in dimensional regularisation within spinor-helicity representation. The triple-cut is defined as a difference of two double-cuts with the same particle contents, and a same propagator carrying, respectively, causal and anti-causal prescription in each of the two cuts. That turns out into an effective tool for extracting the coefficients of three-point functions (and higher-point ones) from one-loop amplitudes. The phase-space integration is oversimplified by using residues theorem to perform the integration on the spinor variables, via the holomorphic anomaly, and a trivial integration on the Feynman parameter. The results are valid for arbitrary values of dimensions.

Citations

• Holomorphic Anomaly Of Unitarity Cuts And One-Loop Gauge Theory Amplitudes
• Higgs boson production at hadron colliders in NNLO QCD
• One-loop self-dual and N = 4 super Yang-Mills
• Inherited twistor-space structure of gravity amplitudes
• Computing one-loop amplitudes from the holomorphic anomaly of unitarity cuts
• New recursion relations for tree amplitudes of gluons
• Connection between Feynman integrals having different values of the space-time dimension
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Loop amplitudes in pure Yang-Mills from generalised unitarity
• Perturbative Gauge Theory As A String Theory In Twistor Space
• The no-triangle hypothesis for Script N = 8 supergravity

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