Reducing full one-loop amplitudes to scalar integrals at the integrand level

2006/09/30 by Giovanni Ossola, C.G. Papadopoulos, Costas G. Papadopoulos +2 · 6 citations
Engineering · Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Combinatorics #Geometry #Loop (graph theory) #Mathematical analysis #Mathematics #Particle Accelerators and Free-Electron Lasers #Particle physics theoretical and experimental studies #Physics #Point (geometry) #Quantum mechanics #Scalar (mathematics) #Scattering amplitude #hep-ph

paper · pdf · doi:10.1016/j.nuclphysb.2006.11.012

published as Nucl.Phys.B763:147-169,2007 · updated version

arxiv created 2006/11/29 · openalex publication_date 2006/12/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no information on the analytical structure of the amplitude is required, making our method appealing for an efficient numerical implementation

Citations

• Reduction method for dimensionally regulatedone-loop N-point Feynman integrals
• Bootstrapping one-loop QCD amplitudes with general helicities
• Color-dressed recursive relations for multi-parton amplitudes
• Recursive numerical calculus of one-loop tensor integrals
• Reduction formalism for dimensionally regulated one-loop N-point integrals
• ALPGEN, a generator for hard multiparton processes in hadronic collisions

Cited by

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• Numerical evaluation of six-photon amplitudes
• Dual conformal symmetry, integration-by-parts reduction, differential equations, and the nonplanar sector
• Analytic one-loop amplitudes for a Higgs boson plus four partons
• Manifesting enhanced cancellations in supergravity: integrands versus integrals
• NLO QCD+EW predictions for 2ℓ2ν diboson signatures at the LHC