A new formulation of the loop-tree duality at higher loops

TL;DR

This paper introduces a novel formulation of the loop-tree duality theorem applicable to higher loop diagrams, enabling efficient computation of loop integrals as sums over tree-like structures with modified prescriptions.

Contribution

It presents a new approach to express higher loop integrals as weighted sums of trees with dual propagators, facilitating more efficient calculations.

Findings

Valid for both massless and massive cases

Allows calculation of loop integrands as sums of tree graphs

Enables efficient computation via recurrence relations

Abstract

We present a new formulation of the loop-tree duality theorem for higher loop diagrams valid both for massless and massive cases. $l$-loop integrals are expressed as weighted sum of trees obtained from cutting $l$ internal propagators of the loop graph. In addition, the uncut propagators gain a modified $i \delta$-prescription, named dual-propagators. In this new framework one can go beyond graphs and calculate the integrand of loop amplitudes as a weighted sum of tree graphs, which form a tree-like object. These objects can be computed efficiently via recurrence relations.