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arXiv · 2405.19868

Discontinuities of banana integrals in dispersion relation representation

Xu-Liang Chen·Peng-Fei Yang·Wei Chen
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Abstract

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.

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Xu-Liang Chen, Peng-Fei Yang, Wei Chen. 2024-05-30. Discontinuities of banana integrals in dispersion relation representation. https://doi.org/10.1088/0256-307x%2F41%2F11%2F111101

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