Towards a Loop–Tree Duality at Two Loops and Beyond

We present an extension of the duality theorem, previously defined by S. Catani et al on the one–loop level, to higher loop orders. The duality theorem provides a relation between loop integrals and tree–level phase–space integrals. Here, the one–loop relation is rederived in a way which is more suitable for its extension to higher loop orders. This is shown in detail by considering the two–loop N–leg master diagram and by a short discussion of the four master diagrams at three loops, in this sketching the general structure of the duality theorem at even higher loop orders.