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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2404.04644 |
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| _version_ | 1866910772907474944 |
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| author | Li, Tingfei Song, Yuekai Zhang, Liang |
| author_facet | Li, Tingfei Song, Yuekai Zhang, Liang |
| contents | 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04644 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solving arbitrary one-loop reduction via generating function Li, Tingfei Song, Yuekai Zhang, Liang High Energy Physics - Phenomenology 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. |
| title | Solving arbitrary one-loop reduction via generating function |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2404.04644 |