Systematics of one-loop scattering amplitudes in N=4 super-Yang-Mills theories

One-loop scattering amplitudes in N=4 super-Yang-Mills (SYM) theories are analyzed in the paradigm of maximal helicity violating Feynman diagrams. There are very limited number of loop integrals to be evaluated. For a process with n external particles, there are only [n/2]−1 generically independent integrals. Furthermore, the relations between leading Nc amplitudes An;1 and sub-leading amplitudes An;c are found to be identical to those obtained from conventional field theory calculations, which can be interpreted as an indirect support for the paradigm.