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

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.

Comments: 10 pages, 10 figures, Talk presented at 14th International Symposium on Radiative Corrections (RADCOR2019), 9-13 September 2019, Palais des Papes, Avignon, France