Computing one-loop amplitudes from the holomorphic anomaly of unitarity cuts

Abstract

We propose a systematic way to carry out the method introduced in F. Cachazo, hep-th/0410077 for computing certain unitarity cuts of one-loop $\mathcal{N}=4$ amplitudes of gluons. We observe that the class of cuts for which the method works involves all next-to-MHV $n$-gluon one-loop amplitudes of any helicity configurations. As an application of our systematic procedure, we obtain the complete seven-gluon one-loop leading-color amplitude ${A}_{7;1}({1}^{\ensuremath{-}},{2}^{\ensuremath{-}},{3}^{\ensuremath{-}},{4}^{+},{5}^{+},{6}^{+},{7}^{+})$.