Beyond a single elliptic curve

TL;DR

This paper explores the interaction of two elliptic curves in Feynman integrals, deriving a differential equation that captures their combined effects, advancing understanding of complex elliptic structures in quantum field theory.

Contribution

It introduces a novel analysis of Feynman integrals involving two elliptic curves and derives an associated differential equation in epsilon-form, highlighting their interplay.

Findings

Derived a differential equation in epsilon-form for a Feynman integral with two elliptic curves

Analyzed mixed entries of the differential equation depending on both elliptic curves

Enhanced understanding of elliptic curve interactions in quantum field calculations

Abstract

In this talk we discuss the interplay of two elliptic curves, which occur in different sub-sectors of Feynman integrals. We analyse a particular Feynman integral depending on two elliptic curves and derive an associated differential equation in $\varepsilon$-form. We discuss the mixed entries of the differential equation, which depend on both elliptic curves.