A recursive solution of the Yang-Mills theory S-matrix to arbitrary loop order?
Rutger Boels (DESY Hamburg)

Scattering amplitudes are important in many seemingly distant corners of high energy physics, such as the corner containing the LHC starting up in Geneva as well as the corner with maximally supersymmetric Yang-Mills theory in four dimensions. The challenge in both these corners is to compute scattering amplitudes to high leg and loop order. Even with state-of-the art methods developed in recent years it remains however a challenge to reach beyond the one loop order, especially in QCD. In this talk I will discuss a possible extension of Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relations from the tree to arbitrary loop level. These relations allow one at tree level to compute any scattering amplitude from scattering amplitudes with fewer legs. A key step in the derivation at tree level was the so-called large BCFW-shift behavior of the scattering amplitudes. A derivation of this will be presented in this talk which is independent of the loop order and shows that the *integrand* of scattering amplitudes can be reconstructed from its so-called 'single cuts'. The difference of a shift of the integrand and the integrals will be made manifest at one loop order for the important case of pure Yang-Mills theory. I will explain how and why these result suggests that the perturbation theory of Yang-Mills theory is much simpler than one might expect and might lead to a completely recursive solution to any Yang-Mills theory.