2025/11/19 by Bree, Iris, Gasparotto, Federico, Matijašić, Antonela +8
Computer Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Polynomial and algebraic computation
paper · doi:10.48550/arxiv.2511.15381
openalex publication_date 2025/11/19 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28
In this paper, we give a detailed account of the algorithm outlined in [1] for Feynman integral reduction and ε-factorised differential equations. The algorithm consists of two steps. In the first step, we use a new geometric order relation in the integration-by-parts reduction to obtain a basis of master integrals, whose differential equations on the maximal cut are of a Laurent polynomial form in the regularisation parameter ε and compatible with a filtration. This step works entirely with rational functions. In a second step, we provide a method to ε-factorise the aforementioned Laurent differential equations. The second step may introduce algebraic and transcendental functions. We illustrate the versatility of the algorithm by applying it to different examples with a wide range of complexity.