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 N_c amplitudes A_{n;1} and sub-leading amplitudes A_{n;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.