Loop-by-loop differential equations for dual (elliptic) Feynman integrals
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Publication:6101295
DOI10.1007/JHEP03(2023)155arXiv2210.09898OpenAlexW4353088293MaRDI QIDQ6101295
Author name not available (Why is that?)
Publication date: 31 May 2023
Published in: (Search for Journal in Brave)
Abstract: We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then, we test our formalism on a simple, but non-trivial, example: the two-loop three-mass elliptic sunrise family of integrals. We obtain an epsilon-form differential equation within the correct function space in a sequence of relatively simple algebraic steps. In particular, none of these steps relies on the analysis of -series. Then, we discuss interesting properties satisfied by our dual basis as well as its simple relation to the known epsilon-form basis of Feynman integrands. The underlying K3-geometry of the three-loop four-mass sunrise integral is also discussed. Finally, we speculate on how to construct a "good" loop-by-loop basis at three-loop.
Full work available at URL: https://arxiv.org/abs/2210.09898
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