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Loop-by-loop differential equations for dual (elliptic) Feynman integrals
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DOI：10.1007/JHEP03(2023)155.png)
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摘要
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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 q-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.
Keyword:
Scattering Amplitudes
Differential and Algebraic Geometry
期刊
IF:
5.5
论文数:
4.0W
被引数:
13.7W
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