Geometric Bookkeeping Guide to Feynman Integral Reduction and ϵ -Factorized Differential Equations
Abstract
We report on three improvements in the context of Feynman integral reduction and ϵ-factorized differential equations. First, we show that with a specific choice of prefactors, we trivialize the ϵ dependence of the integration-by-parts identities. Second, 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. Third, we prove that such a differential equation can always be transformed to an ϵ-factorized form. This provides a systematic algorithm to obtain an ϵ-factorized differential equation for any Feynman integral. Furthermore, the choices for the prefactors and the order relation significantly improve the efficiency of the reduction algorithm.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Polynomial and algebraic computation
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Volume
- 136
- Issue
- 24
- Pages
- 241602–241602
- Publication date
- 25 March 2026
- Language
- EN