2017/11/30 by Xiao Liu, Yan-Qing Ma, Chenyu Wang +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Classical mechanics #Decomposition #Differential (mechanical device) #Differential equation #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #Geometry #Integral equation #Kinematics #Loop (graph theory) #Mathematical analysis #Mathematics #Numerical methods for differential equations #Order of integration (calculus) #Ordinary differential equation #Physics #Product (mathematics) #Quantum mechanics #Scalar (mathematics) #Slater integrals #Volume integral #hep-ph
paper · pdf · doi:10.1016/j.physletb.2018.02.026
published as Phys.Lett. B779 (2018) 353-357 · references added, version published in PLB
openalex publication_date 2018/02/19 · arxiv created 2018/02/27 · arxiv updated 2018/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems with arbitrary kinematic configurations. Numerical tests show that our method can not only achieve results with high precision, but also be much faster than the only existing systematic method sector decomposition. As a by product, we find a new strategy to compute scalar one-loop integrals without reducing them to master integrals.