2010/08/31 by Gudrun Heinrich, G. Heinrich, G. Ossola +3
Mathematics · Physics and Astronomy · #Amplitude #Applied mathematics #Combinatorics #Computer science #Expression (computer science) #Function (biology) #Geometry #Loop (graph theory) #Mathematical analysis #Mathematics #Momentum (technical analysis) #Numerical integration #Numerical methods for differential equations #Optics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Reduction (mathematics) #Sampling (signal processing) #Scattering amplitude #hep-ph
paper · pdf · doi:10.1007/jhep10(2010)105
published as JHEP 1010:105,2010 · 20 pages, 2 figures
openalex publication_date 2010/10/01 · arxiv created 2010/10/06 · arxiv updated 2010/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We present a new approach to the reduction of one-loop amplitudes obtained by reconstructing the tensorial expression of the scattering amplitudes. The reconstruction is performed at the integrand level by means of a sampling in the integration momentum. There are several interesting applications of this novel method within existing techniques for the reduction of one-loop multi-leg amplitudes: to deal with numerically unstable points, such as in the vicinity of a vanishing Gram determinant; to allow for a sampling of the numerator function based on real values of the integration momentum; to optimize the numerical reduction in the case of long expressions for the numerator functions.