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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.10287 |
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| _version_ | 1866915082940710912 |
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| author | Feng, Tai-Fu Zhou, Yang Zhang, Hai-Bin |
| author_facet | Feng, Tai-Fu Zhou, Yang Zhang, Hai-Bin |
| contents | Embedding Feynman integrals in Grassmannians, we can write Feynman integrals as some finite linear combinations of generalized hypergeometric functions. In this paper we present a general method to obtain Gauss relations among those generalized hypergeometric functions. The hypergeometric expressions of Feynman integral are continued from a connected component to another by the inverse Gauss relations, then continued to the whole domain of definition by the Gauss-Kummer relations. The Laurent series of the Feynman integral around the space-time dimension $D=4$ is obtained by the Gauss adjacent relations where the coefficient of the term with power of $D-4$ is given as the linear combinations of hypergeometric functions with integer parameters. As examples, we illustrate how to obtain the expressions for the Feynman integrals of the 1-loop self-energy and a 2-loop massless triangle diagram in the domains of definition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gauss Relations in Feynman Integrals Feng, Tai-Fu Zhou, Yang Zhang, Hai-Bin High Energy Physics - Theory Embedding Feynman integrals in Grassmannians, we can write Feynman integrals as some finite linear combinations of generalized hypergeometric functions. In this paper we present a general method to obtain Gauss relations among those generalized hypergeometric functions. The hypergeometric expressions of Feynman integral are continued from a connected component to another by the inverse Gauss relations, then continued to the whole domain of definition by the Gauss-Kummer relations. The Laurent series of the Feynman integral around the space-time dimension $D=4$ is obtained by the Gauss adjacent relations where the coefficient of the term with power of $D-4$ is given as the linear combinations of hypergeometric functions with integer parameters. As examples, we illustrate how to obtain the expressions for the Feynman integrals of the 1-loop self-energy and a 2-loop massless triangle diagram in the domains of definition. |
| title | Gauss Relations in Feynman Integrals |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.10287 |