$\varepsilon$-forms for non-planar triangles with elliptic curves at two loops

TL;DR

This paper extends methods for elliptic integrals to complex two-loop non-planar triangle Feynman diagrams, deriving canonical differential equations and solutions despite reduced symmetry.

Contribution

It introduces a generalization of elliptic integral techniques to non-planar two-loop triangles with elliptic curves, addressing their unique sub-sector complexities.

Findings

Derived canonical differential equations for non-planar two-loop triangles

Solved these equations with appropriate boundary conditions

Extended elliptic integral methods to more complex Feynman diagrams

Abstract

In this talk, we discuss how to generalize ideas developed for Banana integrals to two two-loop non-planar triangle Feynman integrals involving elliptic curves, which have non-trivial sub-sectors and whose Picard-Fuchs operators share less symmetry than Banana integrals, to obtain the canonical differential equations and to solve them with suitable boundary conditions.