2025/06/10 by Iris Bree, Federico Gasparotto, Bree, Iris +19
Computer Science · Physics and Astronomy · Mathematics · #Polynomial and algebraic computation #Nonlinear Waves and Solitons #Algebraic and Geometric Analysis
paper · pdf · doi:10.48550/arxiv.2506.09124
We report on three improvements in the context of Feynman integral reduction and ε-factorised differential equations: Firstly, we show that with a specific choice of prefactors, we trivialise the ε-dependence of the integration-by-parts identities. Secondly, we observe that with a specific choice of order relation in the Laporta algorithm, we directly obtain a basis of master integrals, whose differential equation on the maximal cut is in Laurent polynomial form with respect to ε and compatible with a particular filtration. Thirdly, we prove that such a differential equation can always be transformed to an ε-factorised form. This provides a systematic algorithm to obtain an ε-factorised differential equation for any Feynman integral. Furthermore, the choices for the prefactors and the order relation significantly improve the efficiency of the reduction algorithm.