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arXiv · 2511.15381

New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations

Iris Bree·Federico Gasparotto·Antonela Matijašić·Pouria Mazloumi·Dmytro Melnichenko·Sebastian Pögel·Toni Teschke·Xing Wang·Stefan Weinzierl·Konglong Wu·Xiaofeng Xu
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Abstract

In this paper, we give a detailed account of the algorithm outlined in [1] for Feynman integral reduction and $\varepsilon$-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 $\varepsilon$ and compatible with a filtration. This step works entirely with rational functions. In a second step, we provide a method to $\varepsilon$-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.

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Iris Bree, Federico Gasparotto, Antonela Matijašić, Pouria Mazloumi, Dmytro Melnichenko, Sebastian Pögel, Toni Teschke, Xing Wang, Stefan Weinzierl, Konglong Wu, Xiaofeng Xu. 2025-11-19. New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations. https://arxiv.org/abs/2511.15381

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