New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations
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arXiv
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| Autori principali: | , , , , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918494340120576 |
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| author | Bree, Iris Gasparotto, Federico Matijašić, Antonela Mazloumi, Pouria Melnichenko, Dmytro Pögel, Sebastian Teschke, Toni Wang, Xing Weinzierl, Stefan Wu, Konglong Xu, Xiaofeng |
| author_facet | Bree, Iris Gasparotto, Federico Matijašić, Antonela Mazloumi, Pouria Melnichenko, Dmytro Pögel, Sebastian Teschke, Toni Wang, Xing Weinzierl, Stefan Wu, Konglong Xu, Xiaofeng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations Bree, Iris Gasparotto, Federico Matijašić, Antonela Mazloumi, Pouria Melnichenko, Dmytro Pögel, Sebastian Teschke, Toni Wang, Xing Weinzierl, Stefan Wu, Konglong Xu, Xiaofeng High Energy Physics - Theory High Energy Physics - Phenomenology Mathematical Physics 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. |
| title | New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology Mathematical Physics |
| url | https://arxiv.org/abs/2511.15381 |