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PreprintarXiv licencearXiv

Analyticity Bootstrap of Feynman Integrals

  • Xiang Li
  • Dao-Ming Mu
  • Yan-Qing Ma
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Abstract

We propose an analyticity bootstrap method to determine the reduction of Feynman integrals (FIs). The key observation is that, at any kinematic point, a dimensionally regularized FI possesses a Taylor expansion region (analytic region), and the finiteness of the Taylor region strongly constrains the integral reduction coefficients, which are rational functions of the kinematic variables. By writing the most general ansatz compatible with the singularity structure and then fixing the remaining parameters with only a few integration-by-parts (IBP) samples or asymptotic expansions, one can obtain the full reduction. We develop the method systematically in both single-variable and multi-variable cases, with many explicit examples. Interestingly, the differential equations (DEs) of the master integrals determine all these analyticity constraints and, conversely, the constraints facilitate the construction of the DEs. In particular, we show that the DEs in the auxiliary mass flow method can be constructed at significantly reduced cost and can even be fully determined without using IBP.

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Cite

BibTeXRIS
BibTeX
@misc{li2026analyticity,
  title = {{Analyticity Bootstrap of Feynman Integrals}},
  author = {Xiang Li and Dao-Ming Mu and Yan-Qing Ma},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01154},
  eprint = {2610.01154},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01154},
}
RIS
TY  - UNPB
TI  - Analyticity Bootstrap of Feynman Integrals
AU  - Xiang Li
AU  - Dao-Ming Mu
AU  - Yan-Qing Ma
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01154
UR  - https://arxiv.org/abs/2610.01154
AB  - We propose an analyticity bootstrap method to determine the reduction of Feynman integrals (FIs). The key observation is that, at any kinematic point, a dimensionally regularized FI possesses a Taylor expansion region (analytic region), and the finiteness of the Taylor region strongly constrains the integral reduction coefficients, which are rational functions of the kinematic variables. By writing the most general ansatz compatible with the singularity structure and then fixing the remaining parameters with only a few integration-by-parts (IBP) samples or asymptotic expansions, one can obtain the full reduction. We develop the method systematically in both single-variable and multi-variable cases, with many explicit examples. Interestingly, the differential equations (DEs) of the master integrals determine all these analyticity constraints and, conversely, the constraints facilitate the construction of the DEs. In particular, we show that the DEs in the auxiliary mass flow method can be constructed at significantly reduced cost and can even be fully determined without using IBP.
ER  -