Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals

Understand

We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism.

• We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms.
• Then, we test our formalism on a simple, but non-trivial, example: the two-loop three-mass elliptic sunrise family of integrals.
• We obtain an epsilon-form differential equation within the correct function space in a sequence of relatively simple algebraic steps.