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Two-loop integral reduction from elliptic and hyperelliptic curves. (English) Zbl 1388.81391

Summary: We show that for a class of two-loop diagrams, the on-shell part of the integration-by-parts (IBP) relations correspond to exact meromorphic one-forms on algebraic curves. Since it is easy to find such exact meromorphic one-forms from algebraic geometry, this idea provides a new highly efficient algorithm for integral reduction. We demonstrate the power of this method via several complicated two-loop diagrams with internal massive legs. No explicit elliptic or hyperelliptic integral computation is needed for our method.

MSC:

81T18 Feynman diagrams
14J81 Relationships between surfaces, higher-dimensional varieties, and physics
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