General one-loop generating function by integration-by-part relations
In this paper, we have studied the general generating function of reduction for one-loop integrals with arbitrary tensor structure in the numerator and arbitrary power distribution of propagators in the denominator. Using integration-by-part relations, we have established the partial differential equations for these generating functions and solved them analytically with compact form. These results provide useful information for the analytical structure of reduction coefficients and guidance for applying the generating function method to reductions of higher loop integrals.
Authors
- Chang Hu (ORCID: https://orcid.org/0000-0002-6744-949X)
- Yaobo Zhang (ORCID: https://orcid.org/0000-0002-7878-8040)
- Bo Feng (ORCID: https://orcid.org/0000-0001-7980-3567)
- Jiyuan Shen
Institutions
- Chinese Academy of Sciences (CN)
- Ningxia University (CN)
- Peng Huanwu Center for Fundamental Theory (CN)
- Numerical Method (China) (CN)
- Computational Physics (United States) (US)
- Beijing Computational Science Research Center (CN)
- University of Chinese Academy of Sciences (CN)
- Hebei University (CN)
- University College of Applied Science (PS)
Publication Details
- Journal
- Physical review. D/Physical review. D.
- Published
- 2025-04-24
- DOI
- https://doi.org/10.1103/physrevd.111.076026
- Citations
- 2
- Primary Topic
- Algorithms and Data Compression
- Type
- article
- Field-Weighted Citation Impact
- 4.96
Funders
- Ningxia University
- National Natural Science Foundation of China
- Hebei University
- National Safety Academic Fund