Positive Integrands from Feynman Integrals in the Minkowski Regime
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912458280534016 |
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| author | Jones, Stephen Olsson, Anton Stone, Thomas |
| author_facet | Jones, Stephen Olsson, Anton Stone, Thomas |
| contents | We present a method for rewriting dimensionally regulated Feynman parameter integrals in the Minkowski regime as a sum of real, positive integrands multiplied by complex prefactors. This representation eliminates the need for contour deformation, allowing for direct numerical or analytic evaluation of the integrals. We develop an algorithm to construct such representations for a broad class of integrals and demonstrate its generalisation through selected examples. Our approach is applied to integrals up to three loops, including cases with internal masses and off-shell external legs. The resulting expressions are suitable for evaluation using existing techniques, such as sector decomposition, where we observe performance gains of up to four orders of magnitude in certain cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_24073 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positive Integrands from Feynman Integrals in the Minkowski Regime Jones, Stephen Olsson, Anton Stone, Thomas High Energy Physics - Phenomenology High Energy Physics - Theory We present a method for rewriting dimensionally regulated Feynman parameter integrals in the Minkowski regime as a sum of real, positive integrands multiplied by complex prefactors. This representation eliminates the need for contour deformation, allowing for direct numerical or analytic evaluation of the integrals. We develop an algorithm to construct such representations for a broad class of integrals and demonstrate its generalisation through selected examples. Our approach is applied to integrals up to three loops, including cases with internal masses and off-shell external legs. The resulting expressions are suitable for evaluation using existing techniques, such as sector decomposition, where we observe performance gains of up to four orders of magnitude in certain cases. |
| title | Positive Integrands from Feynman Integrals in the Minkowski Regime |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.24073 |