| THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS |
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Discontinuities of Banana Integrals in Dispersion Relation Representation |
| Xu-Liang Chen1, Peng-Fei Yang1, and Wei Chen1,2* |
1School of Physics, Sun Yat-sen University, Guangzhou 510275, China
2Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, Huizhou 516000, China
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| Cite this article: |
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Xu-Liang Chen, Peng-Fei Yang, and Wei Chen 2024 Chin. Phys. Lett. 41 111101 |
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Abstract We derive the discontinuities of banana integrals using the dispersion relation iteratively, and 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 the 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.
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Received: 01 September 2024
Published: 25 November 2024
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| PACS: |
11.15.Bt
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(General properties of perturbation theory)
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11.55.Fv
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(Dispersion relations)
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12.20.Ds
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(Specific calculations)
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