The $\varepsilon$-form of the differential equations for Feynman integrals in the elliptic case

TL;DR

This paper demonstrates that an $oldsymbol{ ext{ extit{ extepsilon}}}$-form of differential equations for Feynman integrals can be achieved even when they do not evaluate to multiple polylogarithms, using a non-algebraic basis change.

Contribution

It shows how to obtain an $ ext{ extepsilon}$-form for Feynman integrals outside the polylogarithm class through a non-algebraic basis transformation, exemplified by the kite integral.

Findings

$ ext{ extepsilon}$-form can be achieved for elliptic Feynman integrals.

A non-algebraic change of basis is used to obtain the $ ext{ extepsilon}$-form.

The method applies to integrals beyond multiple polylogarithms.

Abstract

Feynman integrals are easily solved if their system of differential equations is in $\varepsilon$-form. In this letter we show by the explicit example of the kite integral family that an $\varepsilon$-form can even be achieved, if the Feynman integrals do not evaluate to multiple polylogarithms. The $\varepsilon$-form is obtained by a (non-algebraic) change of basis for the master integrals.