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arXiv · 1911.09610

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

Robert Runkel·Zoltán Szőr·Juan Pablo Vesga·Stefan Weinzierl
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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 $i δ$-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.

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Robert Runkel, Zoltán Szőr, Juan Pablo Vesga, Stefan Weinzierl. 2019-11-21. A new formulation of the loop-tree duality at higher loops. https://arxiv.org/abs/1911.09610

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