The geometric bookkeeping guide to Feynman integral reduction and $\varepsilon$-factorised differential equations
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arXiv
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| Auteurs principaux: | , , , , , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914423503847424 |
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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 | We report on three improvements in the context of Feynman integral reduction and $\varepsilon$-factorised differential equations: Firstly, we show that with a specific choice of prefactors, we trivialise the $\varepsilon$-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 $\varepsilon$ and compatible with a particular filtration. Thirdly, we prove that such a differential equation can always be transformed to an $\varepsilon$-factorised form. This provides a systematic algorithm to obtain an $\varepsilon$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09124 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The geometric bookkeeping guide to 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 We report on three improvements in the context of Feynman integral reduction and $\varepsilon$-factorised differential equations: Firstly, we show that with a specific choice of prefactors, we trivialise the $\varepsilon$-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 $\varepsilon$ and compatible with a particular filtration. Thirdly, we prove that such a differential equation can always be transformed to an $\varepsilon$-factorised form. This provides a systematic algorithm to obtain an $\varepsilon$-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. |
| title | The geometric bookkeeping guide to Feynman integral reduction and $\varepsilon$-factorised differential equations |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2506.09124 |