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PreprintCC BY 4.0arXiv

SecRed: A program for sector-wise IBP reduction of Feynman integrals

  • Ruichang Niu
  • Chao Zeng
  • Bin Gong
  • Jianxiong Wang
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Abstract

SecRed is a C++ program for the reduction of multi-loop Feynman integrals with integration-by-parts (IBP) identities. It reduces an integral family sector by sector for memory control and parallelism, and adds algorithms designed for that setting: an adaptive seed box with a corner cut, an optional seed truncation, a subsector level filter, and symmetry relations expanded only from the master integrals of a sector. A global stage assembles the retained equations and performs the finite-field reconstruction of the coefficients using FiniteFlow or FireFly, repeating the elimination over a sequence of primes. On the elimination side, a coefficient-free plan records the elimination order once and is replayed at each prime, so that only the arithmetic is repeated, and a head score orders the equations to reduce fill-in during the elimination. The program is demonstrated on a two-loop five-point non-planar family and on a four-loop cut family, where assembling the global equation system as a whole would exceed the memory of a single node.

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Cite

BibTeXRIS
BibTeX
@misc{niu2026secred,
  title = {{SecRed: A program for sector-wise IBP reduction of Feynman integrals}},
  author = {Ruichang Niu and Chao Zeng and Bin Gong and Jianxiong Wang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03703},
  eprint = {2611.03703},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03703},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - SecRed: A program for sector-wise IBP reduction of Feynman integrals
AU  - Ruichang Niu
AU  - Chao Zeng
AU  - Bin Gong
AU  - Jianxiong Wang
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.03703
UR  - https://arxiv.org/abs/2611.03703
AB  - SecRed is a C++ program for the reduction of multi-loop Feynman integrals with integration-by-parts (IBP) identities. It reduces an integral family sector by sector for memory control and parallelism, and adds algorithms designed for that setting: an adaptive seed box with a corner cut, an optional seed truncation, a subsector level filter, and symmetry relations expanded only from the master integrals of a sector. A global stage assembles the retained equations and performs the finite-field reconstruction of the coefficients using FiniteFlow or FireFly, repeating the elimination over a sequence of primes. On the elimination side, a coefficient-free plan records the elimination order once and is replayed at each prime, so that only the arithmetic is repeated, and a head score orders the equations to reduce fill-in during the elimination. The program is demonstrated on a two-loop five-point non-planar family and on a four-loop cut family, where assembling the global equation system as a whole would exceed the memory of a single node.
ER  -