Blade: A package for block-triangular form improved Feynman integrals decomposition
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912221602250752 |
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| author | Guan, Xin Liu, Xiao Ma, Yan-Qing Wu, Wen-Hao |
| author_facet | Guan, Xin Liu, Xiao Ma, Yan-Qing Wu, Wen-Hao |
| contents | In this article, we present the package {\tt Blade} as the first implementation of the block-triangular form improved Feynman integral reduction method. The block-triangular form has orders of magnitude fewer equations compared to the plain integration-by-parts system, allowing for strictly block-by-block solutions. This results in faster evaluations and reduced resource consumption. We elucidate the algorithms involved in obtaining the block-triangular form along with their implementations. Additionally, we introduce novel algorithms for finding the canonical form and symmetry relations of Feynman integrals, as well as for performing spanning-sector reduction. Our benchmarks for various state-of-the-art problems demonstrate that {\tt Blade} is remarkably competitive among existing reduction tools. Furthermore, the {\tt Blade} package offers several distinctive features, including support for complex kinematic variables or masses, user-defined Feynman prescriptions for each propagator, and general integrands. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_14621 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Blade: A package for block-triangular form improved Feynman integrals decomposition Guan, Xin Liu, Xiao Ma, Yan-Qing Wu, Wen-Hao High Energy Physics - Phenomenology High Energy Physics - Theory In this article, we present the package {\tt Blade} as the first implementation of the block-triangular form improved Feynman integral reduction method. The block-triangular form has orders of magnitude fewer equations compared to the plain integration-by-parts system, allowing for strictly block-by-block solutions. This results in faster evaluations and reduced resource consumption. We elucidate the algorithms involved in obtaining the block-triangular form along with their implementations. Additionally, we introduce novel algorithms for finding the canonical form and symmetry relations of Feynman integrals, as well as for performing spanning-sector reduction. Our benchmarks for various state-of-the-art problems demonstrate that {\tt Blade} is remarkably competitive among existing reduction tools. Furthermore, the {\tt Blade} package offers several distinctive features, including support for complex kinematic variables or masses, user-defined Feynman prescriptions for each propagator, and general integrands. |
| title | Blade: A package for block-triangular form improved Feynman integrals decomposition |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.14621 |