From trees to loops and back

We argue that generic one-loop scattering amplitudes in supersymmetricYang-Mills theories can be computed equivalently with MHV diagrams or withFeynman diagrams. We first present a general proof of the covariance ofone-loop non-MHV amplitudes obtained from MHV diagrams. This proof relies onlyon the local character in Minkowski space of MHV vertices and on an applicationof the Feynman Tree Theorem. We then show that the discontinuities of one-loopscattering amplitudes computed with MHV diagrams are precisely the same asthose computed with standard methods. Furthermore, we analyse collinear limitsand soft limits of generic non-MHV amplitudes in supersymmetric Yang-Millstheories with one-loop MHV diagrams. In particular, we find a simple explicitderivation of the universal one-loop splitting functions in supersymmetricYang-Mills theories to all orders in the dimensional regularisation parameter,which is in complete agreement with known results. Finally, we present concreteand illustrative applications of Feynman's Tree Theorem to one-loop MHVdiagrams as well as to one-loop Feynman diagrams.Comment: 52 pages, 17 figures. Some typos in Appendix A correcte