Abstract
We identify two families of ten-point Feynman diagrams that generalize the elliptic double box, and show that they can be expressed in terms of the same class of elliptic multiple polylogarithms to all loop orders. Interestingly, one of these families can also be written as a dlog form. For both families of diagrams, we provide new 2ℓ-fold integral representations that are linearly reducible in all but one variable and that make the above properties manifest. We illustrate the simplicity of this integral representation by directly integrating the three-loop representative of both families of diagrams. These families also satisfy a pair of second-order differential equations, making them ideal examples on which to develop bootstrap techniques involving elliptic symbol letters at high loop orders.
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Acknowledgments
We thank Ömer Gürdoğan for fruitful discussions, as well as Song He, Qu Cao and Yichao Tang, for making us aware of their upcoming work [105] and kindly coordinating. The work of RM, MvH, MW and CZ was supported by the research grant 00025445 from Villum Fonden and the ERC starting grant 757978.
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McLeod, A., Morales, R., von Hippel, M. et al. An infinite family of elliptic ladder integrals. J. High Energ. Phys. 2023, 236 (2023). https://doi.org/10.1007/JHEP05(2023)236
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DOI: https://doi.org/10.1007/JHEP05(2023)236