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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.06551 |
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| _version_ | 1866909286081232896 |
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| author | de Doncker, E Yuasa, F Ishikawa, T Kato, K |
| author_facet | de Doncker, E Yuasa, F Ishikawa, T Kato, K |
| contents | We focus on numerical techniques for expanding 3-loop Feynman integrals with respect to the dimensional regularization parameter $\varepsilon,$ which is related to the space-time dimension as $ν= 4-2\varepsilon,$ and describes underlying UV singularities located at the boundaries of the integration domain. As a function of the squared momentum $s,$ the expansion coefficients exhibit thresholds that generally delineate regions for their computational techniques. For the problem at hand, a sequence of integrations with a linear extrapolation as $\varepsilon\rightarrow 0$ may be performed to determine leading coefficients of the $\varepsilon$-expansion numerically. For the "baseball" Feynman diagram, we have used extrapolation with respect to an additional parameter to improve the accuracy of the $\varepsilon$-expansion coefficients in case of singularities internal to the domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06551 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 3-loop Feynman Integral Extrapolations for the Baseball Diagram de Doncker, E Yuasa, F Ishikawa, T Kato, K High Energy Physics - Phenomenology We focus on numerical techniques for expanding 3-loop Feynman integrals with respect to the dimensional regularization parameter $\varepsilon,$ which is related to the space-time dimension as $ν= 4-2\varepsilon,$ and describes underlying UV singularities located at the boundaries of the integration domain. As a function of the squared momentum $s,$ the expansion coefficients exhibit thresholds that generally delineate regions for their computational techniques. For the problem at hand, a sequence of integrations with a linear extrapolation as $\varepsilon\rightarrow 0$ may be performed to determine leading coefficients of the $\varepsilon$-expansion numerically. For the "baseball" Feynman diagram, we have used extrapolation with respect to an additional parameter to improve the accuracy of the $\varepsilon$-expansion coefficients in case of singularities internal to the domain. |
| title | 3-loop Feynman Integral Extrapolations for the Baseball Diagram |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2408.06551 |