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 iδ -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

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... . These objects can be computed efficiently via recurrence relations.