Geometric Bookkeeping Guide to Feynman Integral Reduction and ϵ-Factorized Differential Equations.

Authors

Iris Bree, Federico Gasparotto, Antonela Matijašić, Pouria Mazloumi, Dmytro Melnichenko, Sebastian Pögel, Toni Teschke, Xing Wang, Stefan Weinzierl, Konglong Wu, Xiaofeng Xu, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϵ</mi></math> Collaboration

Published in

Physical review letters. Volume 136. Issue 24. Pages 241602. Jun 19, 2026.

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.

PMID:
42412449
Bibliographic data and abstract were imported from PubMed on 07 Jul 2026.

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