Scattering Amplitudes with Open Loops

2011/11/30 by Fabio Cascioli, Philipp Maierhöfer, Stefano Pozzorini · 1,159 citations
Engineering · Mathematics · Physics and Astronomy · #Amplitude #Closed loop #Combinatorics #Generator (circuit theory) #Loop (graph theory) #Mathematical analysis #Mathematics #Momentum (technical analysis) #Open-loop controller #Particle Accelerators and Free-Electron Lasers #Particle physics theoretical and experimental studies #Physics #Power (physics) #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Range (aeronautics) #Scattering #Scattering amplitude #Tensor (intrinsic definition) #Topology (electrical circuits) #Tree (set theory) #hep-ph

paper · pdf · doi:10.1103/physrevlett.108.111601

published in Physical Review Letters 108(11), 111601 (American Physical Society) · 5 pages, 3 figures; v2: Comment on ordering added after eq. (6); typos in eqs. (14,16,17) corrected; various cosmetic changes; reference added. Accepted for publication in PRL

arxiv created 2012/03/05 · openalex publication_date 2012/03/12 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We introduce a new technique to generate scattering amplitudes at one loop. Traditional tree algorithms, which handle diagrams with fixed momenta, are promoted to generators of loop-momentum polynomials that we call open loops. Combining open loops with tensor-integral and Ossola-Papadopoulos-Pittau reduction results in a fully flexible, very fast, and numerically stable one-loop generator. As demonstrated with nontrivial applications, the open-loop approach will permit us to obtain precise predictions for a very wide range of collider processes.

Citations

• Automated one-loop calculations: a proof of concept
• Multi-gluon one-loop amplitudes using tensor integrals
• Scattering amplitudes from unitarity-based reduction algorithm at the integrand-level

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