Differential equations on unitarity cut surfaces

2017/02/28 by Mao Zeng
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Data Storage Technologies #Cryptography and Residue Arithmetic #Differential equation #Electromagnetic Simulation and Numerical Methods #Feynman diagram #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Momentum (technical analysis) #Physics #Propagator #Quantum mechanics #Reduction (mathematics) #Unitarity #hep-ph #hep-th

paper · pdf · doi:10.1007/jhep06(2017)121

published as JHEP 06 (2017) 121 · 17 pages, 3 figures; v2: added more results and references, final journal version

openalex publication_date 2017/06/01 · arxiv created 2017/06/23 · arxiv updated 2017/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We reformulate differential equations (DEs) for Feynman integrals to avoid doubled propagators in intermediate steps. External momentum derivatives are dressed with loop momentum derivatives to form tangent vectors to unitarity cut surfaces, in a way inspired by unitarity-compatible IBP reduction. For the one-loop box, our method directly produces the final DEs without any integration-by-parts reduction. We further illustrate the method by deriving maximal-cut level differential equations for two-loop nonplanar five-point integrals, whose exact expressions are yet unknown. We speed up the computation using finite field techniques and rational function reconstruction.

Citations

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