Discontinuities of banana integrals in dispersion relation representation
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.
Keywords
Cite
@article{arxiv.2405.19868,
title = {Discontinuities of banana integrals in dispersion relation representation},
author = {Xu-Liang Chen and Peng-Fei Yang and Wei Chen},
journal= {arXiv preprint arXiv:2405.19868},
year = {2024}
}
Comments
7 pages, 1 figure. Published in Chinese Physics Letters