One-Loop Gluonic Amplitudes from Single Unitarity Cuts

We show that one-loop amplitudes in massless gauge theories can be determined from single cuts. By cutting a single propagator and putting it on-shell, the integrand of an n-point one-loop integral is transformed into an (n + 2)-particle tree level amplitude. The single-cut approach described here is complementary to the double or multiple unitarity cut approaches commonly used in the literature. In common with these approaches, if the cut is taken in four dimensions, one finds only the cut-constructible parts of the amplitude, while if the cut is in D = 4 − 2ǫ dimensions, both rational and cut-constructible parts are obtained. We test our method by reproducing the known results for the fully rational all-plus and mostly-plus QCD amplitudes, A (1) 4 (1 +, 2+, 3+, 4+) and A (1) 5 (1 +, 2+, 3+, 4+, 5+). We also rederive expressions for the scalar loop contribution to the four-gluon MHV amplitude, A (1,N=0) 4 (−,−,+,+) which has both cut-constructible and rational contributions, and the fully cut-constructible n-gluon MHV amplitude in N = 4 Supersymetric Yang-Mills, A (1,N=4) 4 (−,−,+, . . . ,+). October 16, 2008