On an approach to canonicalizing elliptic Feynman integrals
Abstract
We present generic expressions for the integrands of canonical bases under maximal cut in elliptic Feynman integral families with multiple kinematic scales. Such integrals frequently arise in phenomenologically relevant scattering processes. The derivation of our results starts from the Legendre normal form of elliptic curves, where the geometric properties of the curves are simple and explicit, and further kinematic singularities are presented as marked points. The simplicity of the normal form allows a straightforward construction of canonical bases with an arbitrary number of marked points. They can then be mapped into any univariate elliptic integral families via an appropriate M\"obius transformation, leading to universal expressions for the integrands. As a demonstration, we discuss the application of our method to several concrete examples, including two new integral families whose canonical bases were not available in the literature. In several examples, we derive canonical bases for the full integral families without any cuts, demonstrating the simplicity of the sub-sector dependence of our canonical bases.
Cite
@article{arxiv.2503.23720,
title = {On an approach to canonicalizing elliptic Feynman integrals},
author = {Jiaqi Chen and Li Lin Yang and Yiyang Zhang},
journal= {arXiv preprint arXiv:2503.23720},
year = {2026}
}
Comments
43 pages, 5 figures, 1 table, 6 ancillary files; v3: offer the univariate canonical basis at the integrand level explicitly, add two new examples not available before; v2, v4: typos fixed and text improved