Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes

We identify a large class of one-loop amplitudes for massless particles that can be constructed via unitarity from tree amplitudes, without any ambiguities. One-loop amplitudes for massless supersymmetric gauge theories fall into this class; in addition, many non-supersymmetric amplitudes can be rearranged to take advantage of the result. As applications, we construct the one-loop amplitudes for n-gluon scattering in N = 1 supersymmetric theories with the helicity configuration of the Parke-Taylor tree amplitudes, and for six-gluon scattering in N = 4 super-Yang-Mills theory for all helicity configurations. Research supported in part by the US Department of Energy under grant DE-FG0391ER40662 and in part by the Alfred P. Sloan Foundation under grant BR-3222. Research supported by the Department of Energy under grant DE-AC03-76SF00515. †Address after Sept. 1, 1994: University College of Swansea, UK. Research supported in part by the NSF under grant PHY-9218990 and in part by the Department of Energy under grant DE-FG03-91ER40662. ‡Laboratory of the Direction des Sciences de la Matière of the Commissariat à l’Energie Atomique of France.