Differential equations for loop integrals in Baikov representation

TL;DR

This paper proves that differential equations for Feynman loop integrals can be derived directly in Baikov representation without dimension-shift identities and shows how to avoid squared propagators in many cases.

Contribution

It introduces a method to derive differential equations in Baikov representation without dimension-shift identities and reduces squared propagators in complex loop diagrams.

Findings

Differential equations can be derived directly in Baikov representation.

Avoidance of squared propagators in two- and three-loop diagrams.

Simplification of the setup process for loop integral differential equations.

Abstract

We present a proof that differential equations for Feynman loop integrals can always be derived in Baikov representation without involving dimension-shift identities. We moreover show that in a large class of two- and three-loop diagrams it is possible to avoid squared propagators in the intermediate steps of setting up the differential equations.