Feynman Integral Reductions by Intersection Theory with Orthogonal Bases and Closed Formulae
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911891210633216 |
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| author | Crisanti, Giulio Smith, Sid |
| author_facet | Crisanti, Giulio Smith, Sid |
| contents | We present a prescription for choosing orthogonal bases of differential $n$-forms belonging to quadratic twisted period integrals, with respect to the intersection number inner product. To evaluate these inner products, we additionally propose a new closed formula for intersection numbers beyond $\mathrm{d} \log$ forms. These findings allow us to systematically construct orthonormal bases between twisted period integrals of this type. In the context of Feynman integrals, this represents all diagrams at one-loop. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18178 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Feynman Integral Reductions by Intersection Theory with Orthogonal Bases and Closed Formulae Crisanti, Giulio Smith, Sid High Energy Physics - Theory High Energy Physics - Phenomenology We present a prescription for choosing orthogonal bases of differential $n$-forms belonging to quadratic twisted period integrals, with respect to the intersection number inner product. To evaluate these inner products, we additionally propose a new closed formula for intersection numbers beyond $\mathrm{d} \log$ forms. These findings allow us to systematically construct orthonormal bases between twisted period integrals of this type. In the context of Feynman integrals, this represents all diagrams at one-loop. |
| title | Feynman Integral Reductions by Intersection Theory with Orthogonal Bases and Closed Formulae |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2405.18178 |