Tree-Loop Duality Relation beyond simple poles

Understand

We develop the Tree-Loop Duality Relation for two- and three-loop integrals with multiple identical propagators (multiple poles).

• This is the extension of the Duality Relation for single poles and multiloop integrals derived in previous publications.
• We prove a generalization of the formula for single poles to multiple poles and we develop a strategy for dealing with higher-order pole integrals by reducing them to single pole integrals using Integration By Parts.