English

Two-loop Integral Reduction from Elliptic and Hyperelliptic Curves

High Energy Physics - Theory 2016-01-27 v2 High Energy Physics - Phenomenology

Abstract

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.

Keywords

Cite

@article{arxiv.1507.06310,
  title  = {Two-loop Integral Reduction from Elliptic and Hyperelliptic Curves},
  author = {Alessandro Georgoudis and Yang Zhang},
  journal= {arXiv preprint arXiv:1507.06310},
  year   = {2016}
}

Comments

minor changes: more references added

R2 v1 2026-06-22T10:16:45.039Z