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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/2405.19868 |
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| _version_ | 1866916456511307776 |
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| author | Chen, Xu-Liang Yang, Peng-Fei Chen, Wei |
| author_facet | Chen, Xu-Liang Yang, Peng-Fei Chen, Wei |
| contents | We derive the discontinuities of banana integrals using the dispersion relation iteratively. We find a series of identities between the parameterized discontinuities of banana integrals (p-DOBIs). Similar to elliptic integrals, these identities enable the reduction of various p-DOBIs to be a linear combination of some fundamental ones. We present a practical application of p-DOBIs for deriving Picard-Fuchs operator. Then we establish the expression of generalized dispersion relation, which enables us to obtain the dispersion relation representation of arbitrary banana integrals. Moreover, we propose a hypothesis for generalized dispersion relation and p-DOBIs, which provides a simple way to calculate the discontinuities and transform dispersion relation representation to p-DOBIs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19868 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discontinuities of banana integrals in dispersion relation representation Chen, Xu-Liang Yang, Peng-Fei Chen, Wei High Energy Physics - Phenomenology High Energy Physics - Theory We derive the discontinuities of banana integrals using the dispersion relation iteratively. We find a series of identities between the parameterized discontinuities of banana integrals (p-DOBIs). Similar to elliptic integrals, these identities enable the reduction of various p-DOBIs to be a linear combination of some fundamental ones. We present a practical application of p-DOBIs for deriving Picard-Fuchs operator. Then we establish the expression of generalized dispersion relation, which enables us to obtain the dispersion relation representation of arbitrary banana integrals. Moreover, we propose a hypothesis for generalized dispersion relation and p-DOBIs, which provides a simple way to calculate the discontinuities and transform dispersion relation representation to p-DOBIs. |
| title | Discontinuities of banana integrals in dispersion relation representation |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.19868 |