Solving arbitrary one-loop reduction via generating function
Abstract Recently, the concept of generating function has been employed in one-loop reduction. For one-loop integrals encompassing arbitrary tensor ranks and higher-pole contributions, the generating function can be decomposed into a tensor part and a higher-pole part. While the tensor component has...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-025-13848-0 |
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| _version_ | 1823861676850544640 |
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| author | Tingfei Li Yuekai Song Liang Zhang |
| author_facet | Tingfei Li Yuekai Song Liang Zhang |
| author_sort | Tingfei Li |
| collection | DOAJ |
| description | Abstract Recently, the concept of generating function has been employed in one-loop reduction. For one-loop integrals encompassing arbitrary tensor ranks and higher-pole contributions, the generating function can be decomposed into a tensor part and a higher-pole part. While the tensor component has been thoroughly addressed in recent studies, there remains a lack of satisfactory investigations regarding the higher-pole part. In this work, we completely solve the problem. We first establish the partial differential equations governing the higher-pole generating function. Based on these equations, we derive an integration recursion relation and solve it iteratively. This approach enables us to explore the analytical structure of higher-pole reduction and provides a valuable tool for generating reduction coefficients efficiently. |
| format | Article |
| id | doaj-art-ca8648fec3a84969b9b501d4be0526f2 |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-ca8648fec3a84969b9b501d4be0526f22025-02-09T12:51:44ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522025-02-0185211610.1140/epjc/s10052-025-13848-0Solving arbitrary one-loop reduction via generating functionTingfei Li0Yuekai Song1Liang Zhang2Zhejiang Institute of Modern Physics, Zhejiang UniversityZhejiang Institute of Modern Physics, Zhejiang UniversityZhejiang Institute of Modern Physics, Zhejiang UniversityAbstract Recently, the concept of generating function has been employed in one-loop reduction. For one-loop integrals encompassing arbitrary tensor ranks and higher-pole contributions, the generating function can be decomposed into a tensor part and a higher-pole part. While the tensor component has been thoroughly addressed in recent studies, there remains a lack of satisfactory investigations regarding the higher-pole part. In this work, we completely solve the problem. We first establish the partial differential equations governing the higher-pole generating function. Based on these equations, we derive an integration recursion relation and solve it iteratively. This approach enables us to explore the analytical structure of higher-pole reduction and provides a valuable tool for generating reduction coefficients efficiently.https://doi.org/10.1140/epjc/s10052-025-13848-0 |
| spellingShingle | Tingfei Li Yuekai Song Liang Zhang Solving arbitrary one-loop reduction via generating function European Physical Journal C: Particles and Fields |
| title | Solving arbitrary one-loop reduction via generating function |
| title_full | Solving arbitrary one-loop reduction via generating function |
| title_fullStr | Solving arbitrary one-loop reduction via generating function |
| title_full_unstemmed | Solving arbitrary one-loop reduction via generating function |
| title_short | Solving arbitrary one-loop reduction via generating function |
| title_sort | solving arbitrary one loop reduction via generating function |
| url | https://doi.org/10.1140/epjc/s10052-025-13848-0 |
| work_keys_str_mv | AT tingfeili solvingarbitraryoneloopreductionviageneratingfunction AT yuekaisong solvingarbitraryoneloopreductionviageneratingfunction AT liangzhang solvingarbitraryoneloopreductionviageneratingfunction |